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					Eötvös Loránd Tudományegyetem
   Természettudományi Kar
     Matematikai Intézet



Matematikus mesterképzési szak
         angol nyelven


     Szakindítási kérelem




   ELTE TTK Matematikai Intézet
             2009
2                     Angol nyelvű matematikus mesterképzés




                            Tartalomjegyzék


    A kérelem indoklása                                         3

    Masters program in mathematics:. English supplement         4
    1. List of courses                                          5
    2. Examples                                                10
    3. Personal conditions                                     12
    4. Personal data                                           23
    5. Language proficiency                                   150
    6. Course descriptions                                    160
    7. Course list: English–Hungarian                         277
    8. Course list: Hungarian–English                         284
3                     Angol nyelvű matematikus mesterképzés: indoklás




                                A kérelem indoklása
       Az Eötvös Loránd Tudományegyetem Természettudományi Karának Matematikai
Intézetében – a korábbi osztatlan ötéves képzés utódaként – 2009 ősze óta folyik akkreditált
mesterképzés matematikus szakon, magyar nyelven. Emellett, a korábbi évekhez hasonlóan, a
régi típusú képzés keretein belül a magyar nyelvű oktatás mellett rendszeresen fogadtunk
külföldi diákokat, akiknek az oktatása angol nyelven folyt.
       Hogy ez a hagyomány ne szakadjon meg, a kifutó program helyett szeretnénk az új
mesterképzés angol nyelvű változatát is akkreditáltatni. A képzésben a magyar nyelvű
oktatásban tanító tanárok igen nagy hányada venne részt. Az angol nyelvű képzés során az
egyes órákat vagy külön óraként, a magyar nyelvű változattal párhuzamosan hirdetnénk meg,
vagy – a magyar hallgatók beleegyezése esetén – csak angolul tartanánk meg őket, illetve
esetenként olvasókurzus formájában vehetnék föl őket a külföldi diákok. A számonkérések
módja és a program egyéb feltételei megegyeznek a magyar nyelvű programéval.
       Jelen becsléseink szerint félévente kb. 10–20 külföldi diák fogadására lenne lehetőség
(és remélhetőleg, esély is), s a teljes kurzuskínálatnak kb. a felét tudjuk meghirdetni minden
félévben, melyek közül az igényekhez igazodva alakulna ki a féléves órarend.


       Beadványunk tartalmazza a magyar akkreditációs anyag értelemszerűen módosított
angol nyelvű változatát, pontosabban a fontosabb részek angol nyelvű fordítását, így a
tantárgyak fölsorolását, a két mintatantervet, az angol nyelven (is) oktatók személyes adatait,
kiegészítve a nyelvtudásukra vonatkozó anyaggal, továbbá a tantárgyak részletes leírását,
valamint – a magyar és az angol program könnyebb összehasonlíthatósága céljából – egy
kétirányú szótárt a tantárgyak angol és magyar megnevezései között. Kérelmünkhöz külön
mellékeljük a magyar nyelvű akkreditációs beadvány anyagát.




                                           Indoklás
Masters program in Mathematics


        English Supplement
                              MSc program in mathematics: overview                         5



                    MSc in mathematics: List of courses

(B) Basic courses (20 credits)
 Subject                                  Hours       Credits Coordinator
 Analysis 4 (BSc)                           4+2        4+2        János Kristóf
 Basic algebra (reading course)             0+2         5         Péter Pál Pálfy
 Basic geometry (reading course)            0+2         5         Gábor Moussong
 Complex functions (BSc)                    3+2        3+2        Gábor Halász
 Differentialgeometry I. (BSc)              2+2        2+3        László Verhóczki
 Geometry III. (BSc)                        3+2        3+2        Balázs Csikós
 Intorduction to topology (BSc)             2+0         2         András Szűcs
 Probability and statistics                 3+2        3+3        Tamás Móri
 Reading course in analysis                 0+2         5         Árpád Tóth
 Set theory (BSc)                           2+0         2         Péter Komjáth


(C) Core courses (at least 30 credits from at least 4 different subject groups)
 Subject                                     Hours       Credits Coordinator
 Algebra and number theory
 Groups and representations                    2+2           2+3      Péter Pál Pálfy
 Number theory II                              2+0            2       András Sárközy
 Rings and algebras                            2+2           2+3      István Ágoston
 Analysis
 Function series                               2+0            2       János Kristóf
 Fourier-integral                              2+1           2+1      Gábor Halász
 Functional analysis II                        1+2           1+2      Zoltán Sebestyén
 Topics in analysis                            2+1           2+2      Tamás Keleti
 Geometry
 Algebraic topology                            2+0            2       András Szűcs
 Combinatorial geometry                        2+1           2+2      György Kiss
 Differential geometry II.                     2+0            2       László Verhóczki
 Differential topology                         2+0            2       András Szűcs
 Topics in differential geometry               2+0            2       Balázs Csikós
 Stochastics
 Discrete parameter martingales                2+0            2       Tamás Móri
 Markov chains in discrete and
                                               2+0            2       Vilmos Prokaj
 continuous time
 Multivariate statistical methods              4+0            4       György Michaletzky

                                           Overview
6                                MSc program in mathematics: overview



    Statistical computing 1                       0+2           3       András Zempléni
    Discrete mathematics
    Algorithms I                                  2+2          2+3      Zoltán Király
    Discrete mathematics                          2+2          2+3      László Lovász
    Mathematical logic                            2+0           2       Péter Komjáth
    Operations research
    Continuous optimization                       3+2          3+3      Tibor Illés
    Discrete optimization                         3+2          3+3      András Frank


(D) Differentiated courses (at least 44 credits from at least 3 different
subject groups)
    Subject                                  Hours       Credits Coordinator
    Algebra
    Commutative algebra                        2+2        3+3       József Pelikán
    Current topics in algebra                  2+0         3        Emil Kiss
    Topics in group theory                     2+2        3+3       Péter Pál Pálfy
    Topics in ring theory                      2+2        3+3       István Ágoston
    Universal algebra and lattice theory       2+2        3+3       Emil Kiss
    Number theory
    Combinatorial number theory                2+0         3        András Sárközy
    Exponential sums in number theory          2+0         3        András Sárközy
    Multiplicative number theory               2+0         3        Mihály Szalay
    Analysis
    Chapters of complex function theory        4+0         6        Gábor Halász
    Complex manifolds                          3+2        4+3       Róbert Szőke
    Descriptive set theory                     3+2        4+3       Miklós Laczkovich
    Discrete dinamcal systems                  2+0         3        Zoltán Buczolich
    Dynamical systems                          2+0         3        Zoltán Buczolich
    Dynamical systems and differential
                                               4+2        6+3       Péter Simon
    equations
    Dynamics in one complex variable           2+0         3        István Sigray
    Ergodic theory                             2+0         3        Zoltán Buczolich
    Geometric measure theory                   3+2        4+3       Tamás Keleti
    Nonlinear functional analysis and its
                                               3+2        4+3       János Karátson
    applications
    Operator semigroups                        2+2        3+3       András Bátkai
    Partial differential equations             4+2        6+3       László Simon

                                              Overview
                            MSc program in mathematics: overview                   7


Representations of Banach*-algebras
                                          2+1        2+2     János Kristóf
and abstract harmonic analysis
Riemann manifolds                         2+0         3      Róbert Szőke
Seminar in complex analysis               0+2         2      Róbert Szőke
Special functions                         2+0         3      Gábor Halász
Topological vector spaces and Banach
                                          2+2        3+3     János Kristóf
algebras
Unbounded operators of Hilbert
                                          2+0         3      Zoltán Sebestyén
spaces
Geometry
Algebraic and differential topology       4+2        6+3     András Szűcs
Convex geometry                           4+2        6+3     Károly Böröczky Jr.
Differential toplogy problem solving      0+2         3      András Szűcs
Discrete geometry                         3+2        4+3     Károly Bezdek
Finite geometries                         2+0         3      György Kiss
Geometric foundations of 3D graphics      2+2        3+3     György Kiss
Geometric modelling                       2+0         3      László Verhóczki
Lie groups and symmetric spaces           4+2        6+3     László Verhóczki
Riemannian geometry                       4+2        6+3     Balázs Csikós
Supplementay chapters of topology I
                                          2+0         3      András Némethi
– toplogy of singularities
Supplementay chapters of topology II
                                          2+0         3      András Stipsicz
– low dimensional topology
Stochastics
Analysis of time series                   2+2        3+3     László Márkus
Cryptography                              2+0         3      István Szabó
Introduction to information theory        2+0         3      István Szabó
Statistical computing 2                   0+2         3      András Zempléni
Statistical hypothesis testing            2+0         3      Villő Ciszár
Stochastic processes with independent
                                          2+0         3      Vilmos Prokaj
increment, limit theorems
Discrete mathematics
Applied discrete mathematics seminar      0+2         2      Zoltán Király
Codes and symmetric structures            2+0         3      Tamás Szőnyi
Complexity theory                         2+2        3+3     Vince Grolmusz
Complexity theory seminar                 0+2         2      Vince Grolmusz
Data mining                               2+2        3+3     András Lukács
Design, analysis and implementation
                                          2+2        3+3     Zoltán Király
of algorithms and data structures I



                                         Overview
8                               MSc program in mathematics: overview



    Design, analysis and implementation
                                              2+0         3      Zoltán Király
    of algorithms and data structures II
    Discrete mathematics II                   4+0         6      Tamás Szőnyi
    Geometric algorithms                      2+0         3      Katalin Vesztergombi
    Graph theory seminar                      0+2         2      László Lovász
    Mathematics of networks and the
                                              2+0         3      András Benczúr
    WWW
    Selected topics in graph theory           2+0         3      László Lovász
    Set theory I                              4+0         6      Péter Komjáth
    Set theory II                             4+0         6      Péter Komjáth
    Operations research
    Applications of operation research        2+0         3      Gergely Mádi-Nagy
    Approximation algorithms                  2+0         3      Tibor Jordán
    Business Economics                        2+0         3      Róbert Fullér
    Combinatorial algorithms I.               2+2        3+3     Tibor Jordán
    Combinatorial algorithms II.              2+0         3      Tibor Jordán
    Combinatorial structures and
                                              0+2         3      Tibor Jordán
    algorithms
    Computational methods in operation
                                              0+2         3      Gergely Mádi-Nagy
    reserach
    Game theory                               2+0         3      Tibor Illés
    Graph theory                              2+0         3      András Frank, Zoltán Király
    Graph theory tutorial                     0+2         3      András Frank, Zoltán Király
    Integer programming I.                    2+0         3      Tamás Király
    Integer programming II.                   2+0         3      Tamás Király
    Inventory management                      2+0         3      Gergely Mádi-Nagy
    Investments analysis                      0+2         3      Róbert Fullér
    LEMON library: Solving optimization
                                              0+2         3      Alpár Jüttner
    problems in C++
    Linear optimization                       2+0         3      Tibor Illés
    Macroeconomics and the theory of
                                              2+0         3      Gergely Mádi-Nagy
    economic equilibrium
    Manufacturing process management          2+0         3      Tamás Király
    Market analysis                           2+0         3      Róbert Fullér
    Matroid theory                            2+0         3      András Frank
    Microeconomy                              2+0         3      Gergely Mádi-Nagy
    Multiple objective optimization           0+2         3      Róbert Fullér
    Nonliear optimization                     3+0         4      Tibor Illés
    Operations research project               0+2         3      Róbert Fullér
    Polyhedral combinatorics                  2+0         3      Tamás Király

                                             Overview
                            MSc program in mathematics: overview            9


Scheduling theory                         2+0         3      Tibor Jordán
Stochastic optimization                   2+0         3      Csaba Fábián
Stochastic optimization practice          0+2         3      Csaba Fábián
Structures in combinatorial
                                          2+0         3      Tibor Jordán
optimization




                                         Overview
10                               MSc program in mathematics: overview



                          MSc in matematics: Examples
The following two sequences of courses illustrate how the credit requirements of the MSc
program can be fulfilled.

           Subject area                          Subject                    Level Hours Credits
     1. term

     Algebra                Groups and representations                       C     2+2     5
     Analysis               Functional analysis                              C     1+2     4
     Analysis               Topics in analysis                               C     2+1     4
     Analysis               Algebraic topology                               C     2+0     2
     Analysis               Differential topology                            C     2+0     2
     Analysis               Chapters of complex function theory              D     4+0     6
     Analysis               Differential topology problem solving            D     0+2     3
                            General subject                                  G     2+0     2

                            Total:                                                  22    28
                            Number of exams: 7

           Subject area                          Subject                    Level Hours Credits
     2. term
     Algebra.               Algebraic and differential topology              D     4+2     9
     Stochastics.           Introduction to information theory               D     2+0     3
     Analysis               Topological vector spaces and Banach algebras    D     2+2     6
     Analysis.              Nonlinear functional analysis                    D     3+2     7
                            Special course                                   O     2+0     2
                            General subject                                  G     2+0     2

                            Total:                                                  21    29
                            Number of exams: 6

           Subject area                          Subject                    Level Hours Credits
     3. term
     Operations research    Continuous optimization                          C     3+2     7
     Discrete mathematics   Discrete mathematics.                            C     2+2     5
     Geometry               Topics in differential geometry                  C     2+0     2
     Analysis               Riemann surfaces                                 D     2+0     3
     Algebra                Topics in ring theory                            D     2+0     3
     Discrete mathematics   Set theory I.                                    D     4+0     6
                            General subject                                  G     2+0     2

                            Total:                                                  21    28
                            Number of exams: 7

           Subject area                          Subject                    Level Hours Credits
     4. term
     Geometry               Geometric measure theory                         D     3+2     7
     Analysis.              Complex manifolds                                D     3+2     7
     Discrete mathematics   Set theory II.                                   D     4+0     6

                            Total:                                                  14    20
                            Number of exams: 3


                                                 Overview
                          MSc program in mathematics: overview                             11




      Subject area                        Subject                    Level Hours Credits
1. term
Analysis             Analysis 4.                                      B     4+2     6
Algebra              Basic algebra (reading course)                   B     0+2     5
Geometry             Differential geometry I.                         B     2+2     5
Stochastics          Probablity and statistics                        B     3+2     6
                     General subject                                  G     2+0     2

                     Total:                                                  19    24
                     Number of exams: 5


      Subject area                        Subject                    Level Hours Credits
2. term
Probablity theory    Multivariate statistical methods                 C     4+0     5
Probablity theory    Statistical computing 1.                         C     0+2     2
Geometry             Discrete geometry                                D     3+2     7
Stochastics          Introduction to information theory               D     2+0     3
Analysis             Topological vector spaces and Banach algebras    D     2+2     6
                     General subject                                  G     2+0     2

                     Total:                                                  19    25
                     Number of exams: 5


      Subject area                        Subject                    Level Hours Credits
3. term
Analysis             Functional analysis                              C     1+2     4
Analysis             Topics in analysis                               C     2+1     4
opkut.               Continuous optimization                          C     3+2     6
Algebra              Groups and representations                       C     2+2     5
számtud.             Discrete mathematics                             C     2+2     5
Stochastics          Cryptography                                     D     2+0     3
                     General subject                                  G     2+0     2

                     Total:                                                  23    29
                     Number of exams: 7


      Subject area                        Subject                    Level Hours Credits
4. term
Analysis             Nonlinear functional analysis                    D     3+2     6
Algebra              Exponential sums in number theory                D     2+0     3
Geometry             Geometric measure theory                         D     3+2     7
Analysis             Complex manifolds                                D     3+2     7

                     Total:                                                  17    23
                     Number of exams: 4




                                         Overview
12                                              MSc program in mathematics: overview



                             MSc in matematics: Personal conditions

Program coordinator, subprogram coordinators,coordinators of final exams
Name of coordinators and type of                Degree/title         Position            Type of Number of     Total credit value
          responsibility                                                                 employ- coordinated   of BSc and MSc
   ( pc: program coordinator,                                                             ment    programs      courses coordi-
spc: subprgram coordinator with                                                                                   nated by the
       given subprogram,                                                                                        lecturer: in this
 fec: coordinator of final exam)                                                                               program / in this
                                                                                                                 institution / in
                                                                                                                    Hungary
András Szűcs                              pc          acad.        full professor           FT        1             16/22/22



Course list – coordinators, lecturers
                 COURSE NAMES                                                    Lecturers
                (BASIC AND CORE                 Lecturers            Deg-       Position Typ Givi Givi Total credit value
                   COURSES)             (For each subject block      ree /                e of ng    ng   of BSc and MSc
                                       the first name stands for     title               empl lectu tutor courses coordi-
                                       the coordinator’s name)                            oy- res ials       nated by the
                                                                                         ment Y/N Y/N      lecturer: in this
                                                                                                          program / in this
                                                                                                            institution / in
                                                                                                               Hungary
                                                         MSc in mathematics
                  1. Analysis IV                                              assoc.
                                       Kristóf János                CSc                      FT   Y       Y    18/18/18
                  (BSc)                                                       prof.
                                       Miklós Laczkovich            acad.     full prof.     FT   Y       N    7/22/22
                                       Zoltán Sebestyén             DSc       full prof.     FT   Y       Y    6/10/10
                                                                              assoc.
                                       János Karátson               PhD                      FT   Y       Y    7/20/20
                                                                              prof.
                                                                              assoc.
                                       Tamás Keleti                 PhD                      FT   Y       Y    7/16/16
                                                                              prof.
                                                                              assoc.
                                       Péter Simon                  PhD                      FT   Y       Y    9/22/22
                                                                              prof.
                                                                              sen. asst.
                                       András Bátkai                PhD                      FT   N       Y    6/11/11
Basic courses




                                                                              prof.
                                                                              sen. asst.
                                       László Fehér                 PhD                      FT   N       Y    –
                                                                              prof.
                                                                              sen. asst.
                                       Árpád Tóth                   PhD                      FT   N       Y    5/5/5
                                                                              prof.
                                       Eszter Sikolya               PhD       asst. prof.    FT   N       Y    –
                                       Ferenc Izsák                 PhD       asst. prof. FT      N       Y    –
                                       István Sigray                PhD       lecturer       FT   N       Y    3/3/3
                  2. Complex           Gábor Halász                 acad.     full prof.     FT   Y       N    13/24/24
                  functions(BSc)                                              assoc.
                                       Róbert Szőke                 CSc                      FT   Y       Y    13/20/20
                                                                              prof.
                                                                              sen. asst.
                                       Árpád Tóth                   PhD                      FT   N       Y    5/5/5
                                                                              prof.
                                       István Sigray                PhD       lecturer       FT   N       Y    3/3/3
                  3. Introduction to   András Szűcs                 acad      full prof.     FT   Y       N    16/22/22


                                                                   Overview
                            MSc program in mathematics: overview                          13


topology (BSc)                                      assoc.
                   Róbert Szőke            CSc                    FT   Y   N   13/20/20
                                                    prof.
                                                    sen. asst.
                   László Fehér            PhD                    FT   Y   N   –
                                                    prof.
                                                    sen. asst.
                   Árpád Tóth              PhD                    FT   Y   N   5/5/5
                                                    prof.
4. Reading course                                   assoc.
                  Árpád Tóth               PhD                    FT   Y   Y   5/5/5
in analysis                                         prof.
                                                    sen. asst.
                   László Fehér            PhD                    FT   Y   Y   –
                                                    prof.
5. Geometry III.                                    assoc.
                   Balázs Csikós           CSc                    FT   Y   Y   9/25/25
(BSc)                                               prof.
                                                    sen. asst.
                   Gábor Moussong          PhD                    FT   Y   Y   5/5/5
                                                    prof.
                   Gyula Lakos             PhD      asst. prof.   FT   N   Y   –
6. Differential                                     assoc.
                   László Verhóczki        PhD                    FT   Y   Y   12/24/24
geometry (BSc)                                      prof.
                                                    assoc.
                   Balázs Csikós           CSc                    FT   Y   Y   9/25/25
                                                    prof.
                                                    sen. asst.
                   Gábor Moussong          PhD                    FT   Y   Y   5/5/5
                                                    prof.
7. Set theory
(intorductory)     Péter Komjáth           DSc      full prof.    FT   Y   N   12/20/20
(BSc)
8. Probability and                                  assoc.
                   Tamás Móri              CSc                    FT   Y   Y   8/25/25
statistics                                          prof.
                   György Michaletzky      DSc      full prof.    FT   Y   N   4/24/24
                                                    assoc.
                   András Zempléni         CSc                    FT   Y   Y   6/24/24
                                                    prof.
                                                    assoc.
                   Miklós Arató            CSc                    FT   Y   Y   0/26/26
                                                    prof.
9. Basic algebra   Péter Pál Pálfy         acad.    full prof.    O    Y   Y   11/22/22
(reading course)                                    assoc.
                   István Ágoston          CSc                    FT   Y   Y   11/11/11
                                                    prof.
                   Emil Kiss               DSc      full prof.    FT   Y   Y   9/23/23
                                           dr.      sen. asst.
                   József Pelikán                                 FT   Y   Y
                                           univ     prof.
                                                    assoc.
                   Csaba Szabó             DSc                    FT   Y   Y
                                                    prof.
10. Basic                                           Sen. Asst.
                   Gábor Moussong          PhD                    FT   Y   Y   5/5/5
geometry                                            prof.
                   Károly Bezdek           DSc      full prof.    FT   Y   Y   7/12/12
                                                    assoc.
                   Károly Böröczky Jr.     DSc                    O    Y   Y   11/11/11
                                                    prof.
                                                    assoc.
                   Balázs Csikós           CSc                    FT   Y   Y   9/25/25
                                                    prof.
                                             dr.    sen. asst.
                   Gábor Kertész                                  FT   Y   Y   –
                                            univ    prof.
                                                    assoc.
                   György Kiss             PhD                    FT   Y   Y   13/18/18
                                                    prof.




                                         Overview
14                                          MSc program in mathematics: overview



               COURSE NAMES                                              Lecturers
              (BASIC AND CORE               Lecturers          Deg-     Position Typ Givi Givi Total credit value
                 COURSES)           (For each subject block    ree /              e of ng    ng   of BSc and MSc
                                   the first name stands for   title             empl lectu tutor courses coordi-
                                   the coordinator’s name)                        oy- res ials       nated by the
                                                                                 ment Y/N Y/N      lecturer: in this
                                                                                                  program / in this
                                                                                                    institution / in
                                                                                                       Hungary
                                                     MSc in mathematics
                1. Groups and      Péter Pál Pálfy             acad.   full prof.    O    Y    Y        11/22/22
                representations
                                   Piroska Csörgő              CSc     assoc.        FT   N    Y           –
                                                                       prof.
                                   Péter Hermann               CSc     assoc.        FT   Y    Y           –
                                                                       prof.
                                   József Pelikán              dr.     sen. asst.    FT   Y    Y         6/6/6
                                                               univ.   prof.
                                   Csaba Szabó                 DSc     assoc.        FT   Y    Y           –
                                                                       prof.
                2. Rings and       István Ágoston              CSc     assoc.        FT   Y    Y        11/11/11
                algebras                                               prof.
                                   Emil Kiss                   DSc     full prof.    FT   Y    Y        9/23/23
                                   József Pelikán              dr.     sen. asst.    FT   Y    Y         6/6/6
                                                               univ.   prof.
                3. Number theory   András Sárközy              acad.   full prof.    FT   Y    Y        6/16/16
                II (BSC)
                                   Róbert Freud                CSc     assoc.        FT   Y    Y         0/8/8
                                                                       prof.
                                   Gyula Károlyi               CSc     assoc.        FT   N    Y         0/4/4
                                                                       prof.
                                   Katalin Pappné Kovács       CSc     assoc.        FT   N    Y           –
Core corses




                                                                       prof.
                                   Mihály Szalay               CSc     assoc.        FT   Y    Y         3/7/7
                                                                       prof.
                4. Fourier integral Gábor Halász               acad.   full prof.    FT   Y             13/24/24
                                    Róbert Szőke               CSc     assoc.        FT   Y    Y        13/20/20
                                                                       prof.
                                   István Sigray               PhD     lecturer      FT   Y              3/3/3
                                   Árpád Tóth                  PhD     assoc.        FT   Y              5/5/5
                                                                       prof.
                5. Topics in       Tamás Keleti                PhD     assoc.        FT   Y             7/16/16
                analysis                                               prof.
                                   Miklós Laczkovich           acad.   full prof.    FT   Y             7/22/22
                                   Zoltán Buczolich            CSc     assoc.        FT   Y    Y        9/19/19
                                                                       prof.
                6. Topics in       Balázs Csikós               CSc     assoc.        FT   Y             9/25/25
                differential                                           prof.
                geometry           Gyula Lakos                 PhD     asst. prof.   FT   N                –
                                   Gábor Moussong              PhD     sen. asst.    FT   Y              5/5/5
                                                                       prof.
                                   László Verhóczki            PhD     assoc.        FT   Y             12/24/24
                                                                       prof.
                7. Differential    László Verhóczki            PhD     assoc.        FT   Y             12/24/24
                Geometry II.                                           prof.



                                                           Overview
                              MSc program in mathematics: overview                          15


                     Balázs Csikós           CSc      assoc.        FT   Y       9/25/25
                                                      prof.
                     Gyula Lakos             PhD      asst. prof.   FT   N          –
                     Gábor Moussong          PhD      sen. asst.    FT   Y        5/5/5
                                                      prof.
8. Combinatorial     György Kiss             PhD      assoc.        FT   Y   Y   13/18/18
geometry                                              prof.
                     Károly Böröczky Jr.     DSc      assoc.        O    Y   Y   11/11/11
                                                      prof.
                     Gábor Kertész           dr.      sen. asst.    FT   Y   Y      –
                                             univ     prof.
9. Algebraic         András Szűcs            acad.    full prof.    FT   Y       16/22/22
topology             Balázs Csikós           CSc      assoc.        FT   Y        9/25/25
                                                      prof.
                     László Fehér            PhD      sen. asst.    FT   Y          –
                                                      prof.
                     Gábor Moussong          PhD      sen. asst.    FT   Y        5/5/5
                                                      prof.
                     András Némethi          DSc      sci.          O    Y        3/3/3
                                                      advisor
                     András Stipsicz         DSc      sen. res.     O    Y        3/3/3
                                                      fellow
                     Róbert Szőke            CSc      assoc.        FT   Y   Y   13/20/20
                                                      prof.
                     Árpád Tóth              PhD      assoc.        FT   Y        5/5/5
                                                      prof.
10. Differential     András Szűcs            acad     full prof.    FT   Y       16/22/22
topology             Balázs Csikós           CSc      assoc.        FT   Y        9/25/25
                                                      prof.
                     László Fehér            PhD      sen. asst.    FT   Y          –
                                                      prof.
                     Gábor Moussong          PhD      sen. asst.    FT   Y        5/5/5
                                                      prof.
                     András Némethi          DSc      sci.          O    Y        3/3/3
                                                      advisor
                     András Stipsicz         DSc      tud.          O    Y        3/3/3
                                                      fmtárs
                     Árpád Tóth              PhD      assoc.        FT   Y        5/5/5
                                                      prof.
11. Mathematical     Péter Komjáth           DSc      full prof.    FT   Y   N   12/20/20
logic
12. Markov           Vilmos Prokaj           PhD      assoc.        FT   Y   N   5/23/23
chains in discrete                                    prof.
and continuous       György Michaletzky      DSc      full prof.    FT   Y   N   4/24/24
time                 Villő Csiszár                    asst. prof.   FT   Y   N    3/3/3

13. Discrete         Tamás Móri              CSc      assoc.        FT   Y   N   8/25/25
parameter                                             prof.
martingales          Vilmos Prokaj           PhD      assoc.        FT   Y   N   5/23/23
                                                      prof.
                     György Michaletzky      DSc      full prof.    FT   Y   N   4/24/24
14. Statistical      András Zempléni         CSc      assoc.        FT   N   Y   6/24/24
computing 1.                                          prof.
                     Tamás Pröhle                     asst. prof.   FT   N   Y      –
15. Multivariate     György Michaletzky      DSc      full prof.    FT   Y   N   4/24/24



                                           Overview
16                                   MSc program in mathematics: overview


       statistical         Miklós Arató                 CSc       assoc.        FT   Y    N        0/26/26
       methods                                                    prof.
                           Tamás Pröhle                           asst. prof.   FT   Y    N           –
       16. Function        János Kristóf                CSc       assoc.        FT   Y    Y        18/18/18
       series                                                     prof.
       17. Functional      Zoltán Sebestyén             DSc       full prof.    FT   Y    Y        6/10/10
       analysis II
       18. Discrete        András Frank                 DSc       full prof.    FT   Y    Y        21/21/21
       optimization
       19. Continuous      Tibor Illés                  PhD       assoc.        FT   Y    Y        16/18/20
       optimization                                               prof.
       20. Algorithms I.   Zoltán Király                PhD       assoc.        FT   Y    Y        16/21/21
                                                                  prof.
                           Vince Grolmusz               DSc       full prof.    FT   Y    Y        8/16/16
                           Tibor Jordán                 DSc       assoc.        FT   Y    Y        21/23/23
                                                                  prof.
                           András Benczúr               PhD       sen. asst.    O    Y    Y         3/3/3
                                                                  prof.
       21. Discrete        László Lovász                acad.     full prof.    FT   Y    Y        10/10/10
       mathematics         Zoltán Király                PhD       assoc.        FT   Y    Y        16/21/21
                                                                  prof.


     COURSE NAMES                                                   Lecturers
     DIFFERENTIATED                 Lecturers            Deg-      Position Typ Givi Givi Total credit value
        COURSES             (For each subject block      ree /               e of ng    ng   of BSc and MSc
                           the first name stands for     title              empl lectu tutor courses coordi-
                           the coordinator’s name)                           oy- res ials       nated by the
                                                                            ment       Y/N    lecturer: in this
                                                                                             program / in this
                                                                                               institution / in
                                                                                                  Hungary
                                             MSc in mathematics
1. Topics in group         Péter Pál Pálfy              acad.     full prof.    O    Y    Y        11/22/22
theory                     Piroska Csörgő               CSc       assoc.        FT   N    Y           –
                                                                  prof.
                           Péter Hermann                CSc       assoc.        FT   Y    Y           –
                                                                  prof.
                           József Pelikán               dr.       sen. asst.    FT   Y    Y         6/6/6
                                                        univ.     prof.
                           Csaba Szabó                  DSc       assoc.        FT   Y    Y           –
                                                                  prof.
2. Topics in ring theory   István Ágoston               CSc       assoc.        FT   Y    Y        11/11/11
                                                                  prof.
                           Emil Kiss                    DSc       full prof.    FT   Y    Y        9/23/23
                           József Pelikán               dr.       sen. asst.    FT   Y    Y         6/6/6
                                                        univ.     prof.
3. Commutative algebra     József Pelikán               dr.       sen. asst.    FT   Y    Y         6/6/6
                                                        univ.     prof.
                           István Ágoston               CSc       assoc.        FT   Y    Y        11/11/11
                                                                  prof.
                           Gyula Károlyi                CSc       assoc.        FT   N    Y         0/4/4
                                                                  prof.
4. Universal algebra and   Emil Kiss                    DSc       full prof.    FT   Y    Y        9/23/23
lattice theory             Péter Pál Pálfy              acad.     full prof.    O    Y    Y        11/22/22
                           Csaba Szabó                  DSc       assoc.        FT   Y    Y           –
                                                                  prof.

                                                       Overview
                                    MSc program in mathematics: overview                         17


5. Current topics in       Emil Kiss               DSc      full prof.   FT   Y   Y   9/23/23
algebra                    István Ágoston          CSc      assoc.       FT   Y   Y   11/11/11
                                                            prof.
                           Piroska Csörgő          CSc      assoc.       FT   N   Y      –
                                                            prof.
                           Péter Hermann           CSc      assoc.       FT   Y   Y      –
                                                            prof.
                           Péter Pál Pálfy         acad.    full prof.   O    Y   Y   11/22/22
                           József Pelikán          dr.      sen. asst.   FT   Y   Y    6/6/6
                                                   univ.    prof.
                           Csaba Szabó             DSc      assoc.       FT   Y   Y      –
                                                            prof.
6. Combinatorial number András Sárközy             acad.    full prof.   FT   Y   Y   6/16/16
theory                  Róbert Freud               CSc      assoc.       FT   Y   Y    0/8/8
                                                            prof.
                           Gyula Károlyi           CSc      assoc.       FT   N   Y    0/4/4
                                                            prof.
7. Exponential sums in     András Sárközy          acad.    full prof.   FT   Y   Y   6/16/16
number theory              Gyula Károlyi           CSc      assoc.       FT   N   Y    0/4/4
                                                            prof.
8. Multiplicative number Mihály Szalay             CSc      assoc.       FT   Y   Y    3/7/7
theory                                                      prof.
                         Gyula Károlyi             CSc      assoc.       FT   N   Y    0/4/4
                                                            prof.
9. Topological vector      János Kristóf           CSc      assoc.       FT   Y   Y   18/18/18
spaces and Banach                                           prof.
algebras
10. Representations of     János Kristóf           CSc      assoc.       FT   Y   Y   18/18/18
Banach-*-algebras and                                       prof.
abstract harmonic
analysis
11. Nonlinear functional   János Karátson          PhD      assoc.       FT   Y   Y   7/20/20
analysis and its                                            prof.
applications
12. Operator semigroups    András Bátkai           PhD      sen. asst.   FT   Y   Y   6/11/11
                                                            prof.
13. Unbounded              Zoltán Sebestyén        DSc      full prof.   FT   Y   Y   6/10/10
operators of Hilbert
spaces
14. Descriptive set        Miklós Laczkovich       acad.    full prof.   FT   Y   Y   7/22/22
theory
15. Geometric              György Kiss             PhD      assoc.       FT   Y   Y   13/18/18
foundations of 3D                                           prof.
graphics
16. Geometric modelling    László Verhóczki        PhD      assoc.       FT   Y   Y   12/24/24
                                                            prof.
17. Geometric measure      Tamás Keleti            PhD      assoc.       FT   Y   Y   7/16/16
theory                                                      prof.
                           Zoltán Buczolich        CSc      assoc.       FT   Y   Y   9/19/19
                                                            prof.
18. Complex manifolds      Róbert Szőke            CSc      assoc.       FT   Y   Y   13/20/20
                                                            prof.
                           Árpád Tóth              PhD      assoc.       FT   Y   Y    5/5/5
                                                            prof.
19. Chapters of complex    Gábor Halász            acad.    full prof.   FT   Y   Y   13/24/24
function theory            Róbert Szőke            CSc      assoc.       FT   Y   Y   13/20/20
                                                            prof.


                                                 Overview
18                                MSc program in mathematics: overview


                         Árpád Tóth              PhD      assoc.        FT   Y   Y    5/5/5
                                                          prof.
20. Riemann surfaces     Róbert Szőke            CSc      assoc.        FT   Y   Y   13/20/20
                                                          prof.
                         Gábor Halász            acad.    full prof.    FT   Y   Y   13/24/24
                         Árpád Tóth              PhD      assoc.        FT   Y   Y    5/5/5
                                                          prof.
                         István Sigray           PhD      lecturer      FT   Y   Y    3/3/3
21. Special functions    Gábor Halász            acad.    full prof.    FT   Y   Y   13/24/24
                         István Sigray           PhD      lecturer      FT   Y   Y    3/3/3
22. Seminar in complex   Róbert Szőke            CSc      assoc.        FT   Y   Y   13/20/20
analysis                                                  prof.
23. Riemannian           Balázs Csikós           CSc      assoc.        FT   Y   Y   9/25/25
geometry                                                  prof.
                         László Verhóczki        PhD      assoc.        FT   Y   Y   12/24/24
                                                          prof.
                         Gábor Moussong          PhD      sen. asst.    FT   Y   Y    5/5/5
                                                          prof.
                         Róbert Szőke            CSc      assoc.        FT   Y   Y   13/20/20
                                                          prof.
                         Gyula Lakos             PhD      asst. prof.   FT   N   Y      –
24. Lie groups and       László Verhóczki        PhD      assoc.        FT   Y   Y   12/24/24
symmetric spaces                                          prof.
                         Balázs Csikós           CSc      assoc.        FT   Y   Y   9/25/25
                                                          prof.
                         Gábor Moussong          PhD      sen. asst.    FT   Y   Y    5/5/5
                                                          prof.
                         Róbert Szőke            CSc      assoc.        FT   Y   Y   13/20/20
                                                          prof.
                         Gyula Lakos             PhD      asst. prof.   FT   N   Y      –
25. Convex geometry      Károly Böröczky Jr      DSc      assoc.        O    Y   Y   11/11/11
                                                          prof.
                         Károly Bezdek           DSc      full prof.    FT   Y   Y   7/12/12
                         Gábor Kertész           dr.      sen. asst.    FT   Y   Y      –
                                                 univ     prof.
26. Discrete geometry    Károly Bezdek           DSc      full prof.    FT   Y   Y   7/12/12
                         Károly Böröczky Jr      DSc      assoc.        O    Y   Y   11/11/11
                                                          prof.
                         Gábor Kertész           dr.      sen. asst.    FT   Y   Y      –
                                                 univ     prof.
27. Finite geometries    György Kiss             PhD      assoc.        FT   Y   Y   13/18/18
                                                          prof.
                         Tamás Szőnyi            DSc      full prof.    FT   Y   Y    9/9/9
                         Péter Sziklai           CSc      assoc.        FT   Y   Y    0/9/9
                                                          prof.
28. Differential topology András Szűcs           acad     full prof.    FT   Y   N   16/22/22
problem solving           Balázs Csikós          CSc      assoc.        FT   Y   Y   9/25/25
                                                          prof.
                         László Fehér            PhD      sen. asst.    FT   Y   Y      –
                                                          prof.
                         Gyula Lakos             PhD      asst. prof.   FT   N   Y      –
                         Gábor Lippner                    res.          O    N   Y      –
                                                          fellow
                         Gábor Moussong          PhD      sen. asst.    FT   Y   Y    5/5/5
                                                          prof.
                         Endre Szabó             PhD      res.          O    N   Y      –
                                                          fellow


                                               Overview
                                   MSc program in mathematics: overview                             19


                          Árpád Tóth                 PhD       assoc.       FT   Y   Y    5/5/5
                                                               prof.
29. Algebraic and         András Szűcs               acad      full prof.   FT   Y   N   16/22/22
differential topology     Balázs Csikós              CSc       assoc.       FT   Y   Y   9/25/25
                                                               prof.
                          László Fehér               PhD       sen. asst.   FT   Y   Y      –
                                                               prof.
                          Gábor Moussong             PhD       sen. asst.   FT   Y   Y    5/5/5
                                                               prof.
                          András Némethi             DSc       sci.         O    Y   Y    3/3/3
                                                               advisor
                          András Stipsicz            DSc       sen. res.    O    Y   Y    3/3/3
                                                               fellow
                          Árpád Tóth                 PhD       assoc.       FT   Y   Y    5/5/5
                                                               prof.
30. Supplementary         András Némethi (András DSc           sci.         O    Y   Y    3/3/3
chapters of topology I. – Szűcs)                               advisor
Topology of               Balázs Csikós          CSc           assoc.       FT   Y   Y   9/25/25
singularities.                                                 prof.
                          László Fehér           PhD           sen. asst.   FT   Y   Y      –
                                                               prof.
                          Gábor Moussong             PhD       sen. asst.   FT   Y   Y    5/5/5
                                                               prof.
                          András Stipsicz            DSc       sen. res.    O    Y   Y    3/3/3
                                                               fellow
                          Árpád Tóth                 PhD       assoc.       FT   Y   Y    5/5/5
                                                               prof.
31. Supplementary         András Stipsicz (András    DSc       sen. res.    O    Y   Y    3/3/3
Chapters of Topology II   Szűcs)                               fellow
Low dimensional           Balázs Csikós              CSc       assoc.       FT   Y   Y   9/25/25
manifolds                                                      prof.
                          László Fehér               PhD       sen. asst.   FT   Y   Y      –
                                                               prof.
                          Gábor Moussong             PhD       sen. asst.   FT   Y   Y    5/5/5
                                                               prof.
                          András Némethi             DSc       sci.         O    Y   Y    3/3/3
                                                               advisor
                          Árpád Tóth                 PhD       assoc.       FT   Y   Y    5/5/5
                                                               prof.
32. Set theory I          Péter Komjáth              DSc       full prof.   FT   Y   N   12/20/20
33. Set theory II         Péter Komjáth              DSc       full prof.   FT   Y   N   12/20/20
34. Complexity theory     Vince Grolmusz             DSc       full prof.   FT   Y   Y   8/16/16
                          Zoltán Király                        assoc.       FT   Y   Y   16/21/21
                                                     PhD       prof.
                          László Lovász              acad.     full prof.   FT   Y   Y   10/10/10
35. Applied discrete      Zoltán Király                        assoc.       FT   Y   Y   16/21/21
mathematics seminar                                  PhD       prof.
36. Geometric             Katalin Vesztergombi       CSc       assoc.       FT   Y   Y    3/3/3
algorithms                                                     prof.
37. Selected topics in    László Lovász              acad.     full prof.   FT   Y   Y   10/10/10
graph theory              Zoltán Király              PhD       assoc.       FT   Y   Y   16/21/21
                                                               prof.
38. Graph theory          László Lovász              acad.     full prof.   FT   Y   Y   10/10/10
seminar
39. Intorduction to       István Szabó               CSc.      assoc        O    Y   N    6/9/9
information theory                                             prof.




                                                    Overview
20                                    MSc program in mathematics: overview


40. Stochastic processes    Vilmos Prokaj            PhD      assoc.        FT   Y   N   5/23/23
with independent                                              prof..
increment, limit
theorems
41. Analysis of time        László Márkus            CSc      assoc.        FT   Y   Y   6/22/22
series                                                        prof.
42. Cryptography            István Szabó             CSc      assoc.        O    Y   N    3/6/6
                                                              prof.
43. Statistical             Villő Csiszár                     asst. prof.   FT   Y   N    3/3/3
hypotheses testing
44. Statistical computing   András Zempléni          CSc      assoc.        FT   Y   Y   6/24/24
2                                                             prof.
45. Discrete                Tamás Szőnyi             DSc      full prof.    FT   Y   Y    9/9/9
mathematics II              Zoltán Király            PhD      assoc.        FT   Y   Y   16/21/21
                                                              prof.
                            László Lovász            acad.    full prof.    FT   Y   Y   10/10/10
46. Dynamical systems       Péter Simon              PhD      assoc.        FT   Y   Y   9/22/22
and differential                                              prof.
equations
47. Partial differential    László Simon             DSc      full prof.    FT   Y   Y   9/25/25
equations
48. Dynamical systems       Zoltán Buczolich         CSc      assoc.        FT   Y   Y   9/19/19
                                                              prof.
49. Discrete dynamical      Zoltán Buczolich         CSc      assoc.        FT   Y   Y   9/19/19
systems                                                       prof.
50. Ergodic theory          Zoltán Buczolich         CSc      assoc.        FT   Y   Y   9/19/19
                                                              prof.
51. Dynamics in one         István Sigray            PhD      Lecturer      FT   Y        3/3/3
complex variable
52. Approximation           Tibor Jordán             DSc      assoc.        FT   Y   Y   21/23/23
algorithms                                                    prof.
53. Applications of         Gergely Mádi-Nagy        PhD      sen. asst.    FT   Y   Y   15/12/21
operation reserach                                            prof.
54. Investment analysis     Róbert Fullér            CSc      assoc.        FT   Y   Y   15/21/24
                                                              prof.
55. Integer Programming Tamás Király                 PhD      sen. asst.    FT   Y   Y   12/18/18
I.                                                            prof.
56. Integer Programming Tamás Király                 PhD      sen. asst.    FT   Y   Y   12/18/18
II.                                                           prof.
57. Graph theory        András Frank                 DSc      full prof.    FT   Y   Y   21/21/21
                        Zoltán Király                PhD      assoc.        FT   Y   Y   16/21/21
                                                              prof.
58. Graph theory tutorial András Frank               DSc      full prof.    FT   Y   Y   21/21/21
                          Zoltán Király              PhD      assoc.        FT   Y   Y   16/21/21
                                                              prof.
59.Game theory              Tibor Illés              PhD      assoc.        FT   Y   Y   16/18/20
                                                              prof.
60. Inventory               Gergely Mádi-Nagy        PhD      assoc.        FT   Y   Y   15/21/21
management                                                    prof.
61. Combinatorial           Tibor Jordán             DSc      assoc.        FT   Y   Y   21/23/23
algorithms I.                                                 prof.
62. Combinatorial           Tibor Jordán             DSc      assoc.        FT   Y   Y   21/23/23
algorithms II                                                 prof.
63. Structures in com-      Tibor Jordán             DSc      full prof.    FT   Y   Y   21/23/23
binatorial optimization




                                                   Overview
                                     MSc program in mathematics: overview                          21


64. Combinatorial          Tibor Jordán             DSc      assoc.        FT   Y   Y   21/23/23
structures and                                               prof.
algorithms
65. LEMON library:         Alpár Jüttner                     asst. prof.   O    N   Y    3/3/3
solving optimization
problems in C++
66. Linear optimization    Tibor Illés              PhD      assoc.        FT   Y   Y   16/18/20
                                                             prof.
67. Matroid theory         András Frank             DSc      full prof.    FT   Y   Y   21/21/21
68. Macroeconomy and       Gergely Mádi-Nagy        PhD      sen. asst.    O    Y   Y   15/21/21
the theory of economic                                       prof.
equilibrium
68. Microeconomy           Gergely Mádi-Nagy        PhD      sen. asst.    O    Y   Y   15/21/21
                                                             prof.
69. Nonlinear              Tibor Illés              PhD      assoc.        FT   Y   Y   16/18/20
optimization                                                 prof.
70. Computational          Gergely Mádi-Nagy        PhD      sen. asst.    FT   Y   Y   15/21/21
methods in operations                                        prof.
research
71. Operations research    Róbert Fullér            CSc      assoc.        FT   Y   Y   15/21/24
project                                                      prof.
72. Market analysis        Róbert Fullér            CSc      assoc.        FT   Y   Y   15/21/24
                                                             prof.
73. Polyhedral             Tamás Király             PhD      sen. asst.    FT   Y   Y   12/18/18
combinatorics                                                prof.
74. Stochastic             Csaba Fábián             PhD      sen. asst.    O    Y   Y   6/19/25
optimization                                                 prof.
75. Stochastic             Csaba Fábián             PhD      sen. asst.    O    Y   Y   6/19/25
optimization practice                                        prof.
76. Manufacturing          Tamás Király             PhD      sen. asst.    FT   Y   Y   12/18/18
process management                                           prof.
77. Multiple objective     Fullér Róbert            CSc      assoc.        FT   Y   Y   15/21/24
optimization                                                 prof.
78. Scheduling theory      Tibor Jordán             CSc      assoc.        FT   Y   Y   21/23/23
                                                             prof.
79. Business economics     Róbert Fullér            CSc      assoc.        FT   Y   Y   15/21/24
                                                             prof.
80. Optional subject                                N/A
81. Data mining            András Lukács            CSc      sen. res.     O    Y   Y    6/6/6
                                                             fellow.
82. Mathematics of    András Benczúr                PhD      sen. asst.    O    Y   Y    3/3/3
networks and the WWW                                         prof.
83. Complexity theory Vince Grolmusz                DSc      full prof.    FT   Y   Y   8/16/16
seminar               Zoltán Király                 PhD      assoc.        FT   Y   Y   16/21/21
                                                             prof.
                           László Lovász            acad.    full prof.    FT   Y   Y   10/10/10
84. Design, analysis and   Zoltán Király            PhD      assoc.        FT   Y   Y   16/21/21
implementation of                                            prof.
algorithms and data        András Benczúr           PhD      sen. asst.    O    Y   Y    3/3/3
structures I                                                 prof.
                           Tibor Jordán             DSc      assoc.        FT   Y   Y   21/23/23
                                                             prof.
85. Design, analysis and   Zoltán Király            PhD      assoc.        FT   Y   Y   16/21/21
implementation of                                            prof.
algorithms and data
structures II
86. Codes and              Tamás Szőnyi             DSc      full prof.    FT   Y   Y    9/9/9

                                                  Overview
22                              MSc program in mathematics: overview


symmetric structures   Péter Sziklai           CSc      assoc.    FT   Y   Y   0/9/9
                                                        prof.




                                             Overview
                               MSc program in mathematics: personal data                      23



                   MSc in Mathematics: Personal data
Name: István Ágoston

Date of birth: 1959
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, associate professor
Scientific degree (discipline): CSc (mathematics)
Major Hungarian scholarships: Széchenyi professor's scholarship (2000–2003)

Teaching activity (with list of courses taught so far):
Eötvös University (1984– ):
     algebra (for students in mathematics; lecture, practice)
     algebra and number theory (for students in teaching mathematics; lecture, practice)
     linear algebra (for students in informatics; lecture, practice)
     analysis (for students in teaching mathematics; lecture, practice)
     ring theory, homological algebra, Lie algebras, representation theory (for students in
     mathematics; lecture)
Carleton University, Ottawa (1986–1991, 1996, 2002, 2004)
     linear algebra (general audience; lecture, practice)
     calculus, analysis, complex functions, combinatorics, abstract algebra, numerical
     analysis, linear programming, matheatical logic, formal languages and automata theory
     (general audience and honours students in mathematics; practice)
University of Ottawa(2002)
     group theory (students in mathematics; lecture, practice)
BSM (1997, 1998)
    basic algebra (students in mathematics; lecture, practice)
    group representations (students in mathematics; lecture, practice)

Other professional activity:
     25 years of teaching experience, 3 diploma thesis supervisions, 1 Ph.D. thesis
     supervision
     20 papers with over 100 citations
     over 25 lectures at international conferences and seminars

Up to 5 selected publications from the past 5 years:
1.   Ágoston, I., Dlab, V., Lukács, E.: Quasi-hereditary extension algebras, Algebras and
     Representation theory 6 (2003), 97–117.
2.   Ágoston, I., Dlab, V., Lukács, E.: Standardly stratified extension algebras, Comm. Alg.
     33 (2005), 1357–1368.
3.   Ágoston, I., Dlab, V., Lukács, E.:: Approximations of algebras by standardly stratified
     algebras, Journal of Algebra 319 (2008), 4177–4198.

The five most important publications:
1.   Ágoston, I., Dlab, V., Lukács, E.: Homological duality and quasi-heredity, Canadian
     Journal of Mathematics 48 (1996), 897–917.
                                             Personal data
24                           MSc program in mathematics: personal data


2.   Ágoston, I., Lukács, E., Ringel, C.M.: Realizations of Frobenius functions, Journal of
     Algebra 210 (1998), 419–439.
3.   Ágoston, I., Happel, D., Lukács E., Unger, L.: Finitistic dimension of standardly
     stratified algebras, Comm. Alg., 28(6) (2000) 2745–2752.
4.   Ágoston, I., Happel, D., Lukács E., Unger, L.: Standardly stratified algebras and tilting,
     J. of Algebra, 226 (2000) 144–160.
5.   Ágoston, I., Dlab, V., Lukács, E.: Quasi-hereditary extension algebras, Algebras and
     Representation theory 6 (2003), 97–117.

Activity in the scientific community, international relations
     Periodica Mathematica Hungarica (managing editor, 1994–1997)
     organizer of international conferences in algebra (1992, 1996, 1999, 2001);
     leader of German–Hungarian cooperation projects (1998–1999, 2001–2003)
     member of the granting committee of the Hungarian NSRF (OTKA), 2000–2002
     local coordinator of a CEEPUS project (2003–2005)
     leader of a Canadian–Hungarian cooperation project (2004–2006)
     OTKA project leader (2007–2011)
     long term visits in Canada (altogether 26 months), Germany (2,5 months)
     coauthors from Canada, Germany and Japan




                                           Personal data
                               MSc program in mathematics: personal data                        25


Name: Miklós Arató

Date of birth: 1962
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, associate professor
Scientific degree (discipline): CSc (mathematics)
Major Hungarian scholarships:

Teaching activity (with list of courses taught so far):
Eötvös University (1985– ):
probability theory (for students in applied mathematics, informatics; lecture, practice)
probability theory (for students in mathematics; practice)
statistics (for students in informatics; lecture, practice)
statistics (for students in mathematics, applied mathematics; practice)
multivariate statistics (for students in mathematics, applied mathematics; lecture, practice)
premium calculation (for students in mathematics, applied mathematics; lecture, practice)
financial processes (for students in mathematics, applied mathematics; lecture, practice)
risk processes (for students in mathematics, applied mathematics; lecture, practice)


Other professional activity:
23 years of teaching experience, 22 diploma thesis supervisions, 1 Ph.D. thesis supervisions;
over 15 lectures at international conferences;
19 publications;

Up to 5 selected publications from the past 5 years:
1. N.M. Arató, D. Bozsó, P. Elek and A. Zempléni: Forecasting and Simulating Mortality
    Tables, Mathematical and Computer Modelling (2008)
2. T. Faluközy, I. I. Vitéz and N. M. Arató: Stochastic models for claims reserving in
    insurance business, RECENT ADVANCES IN STOCHASTIC MODELING AND
    DATA ANALYSIS (2007)
3. Miklós Arató: Will there be annuities from voluntary pension funds?, Economic Review
    (2006)
4. Miklós Arató: Who shall we bow out of the pension funds?, Economic Review (2006)
5. N. M. Arató, I. L. Dryden and C. C. Taylor: Hierarchical Bayesian modelling of spatial
    age-dependent mortality, Computational Statistics & Data Analysis (2006)

The five most important publications:
1. N.M. Arató: On a limit theorem for generalized Gaussian random fields corresponding to
stochastic partial differential equations, Probability Theory and Applic. (1989)
2. N.M. Arató: Equivalence of Gaussian measures corresponding to generalized Gaussian
random fields, Appl. Math. Lett. (1989)
3. N.M. Arató: The estimate of potential in stochastic Schrödinger's equation, Computers
Math. Applic. (1995)
4. N.M. Arató: Mean estimation of Brownian and Ornstein-Uhlenbeck Sheets, Probability
Theory and Applic. (1997)

                                             Personal data
26                           MSc program in mathematics: personal data


5. N.M. Arató: On the estimation of the mean value of Levy's Brownian motion, Probability
Theory and Applic. (1998)

Activity in the scientific community, international relations
     president of the Hungarian Actuarial Society, 2003-2007;
     member of the Board of the Hungarian Actuarial Society, 1995-;
     member of the International Bernoully Society, 1990–;




                                           Personal data
                               MSc program in mathematics: personal data                      27


Name: András Bátkai

Date of birth: 1972
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, assistant professor
Scientific degree (discipline): PhD (mathematics)
Major Hungarian scholarships: Bolyai scholarship (2004–2007)

Teaching activity (with list of courses taught so far):
Eötvös University (2000– ):
analysis (for students in mathematics; lecture, practice)
calculus (for students in biology; practice)
special corses for PhD students

Other professional activity:
Over 10 years of teaching experience, 5 diploma thesis supervisions;
over 20 lectures at international conferences;
Three organized conferences
17 research articles and one monograph;

Up to 5 selected publications from the past 5 years:
1. A.B., Schnaubelt, R., Asymptotic behaviour of parabolic problems with delays in the
   highest order derivatives, Semigroup Forum 69(2004), 369-399.
2. A.B., K.J. Engel, "Abstract wave equations with generalized Wentzell boundary
   conditions", J. Diff. Eqs. 207 (2004), 1-20.
3. Spectral problems for operator matrices (with P. Binding, A. Dijksma, R. Hryniv and H.
   Langer), Math. Nachr. 278 (2005), 1408-1429.
4. Polynomial stability of operator semigroups (with K.J. Engel, J. Prüss and R. Schnaubelt),
   Math. Nachr. 279 (2006), 1425-1440.
5. Cosine families generated by second order differential operators on W1,1(0,1) with
   generalized Wentzell boundary conditions (with K.J. Engel and M. Haase), Applicable
   Analysis 84 (2005), 867-876.

The five most important publications:
1. Semigroups for delay equations (with S. Piazzera), monograph, A. K. Peters: Wellesley
   MA, Research Notes in Mathematics vol. 10, ISBN: 1-56881-243-4, 2005.
2. Bátkai, A., Piazzera, S., „Semigroups and linear partial differential equations with delay‖,
   J. Math. Anal. Appl. 64(2001), 1-20.
3. Bátkai, A., Fasanga, E., Shvidkoy, R., „Hyperbolicity of delay equations via Fourier
   multipliers‖, Acta Sci. Math (Szeged) 69(2003), 131-145.
4. Bátkai, A., „Hyperbolicity of linear partial differential equations with delay‖, Integral Eq.
   Oper. Th. 44(2002), 383-396.
5. Bátkai, A., Piazzera, S., „A semigroup method for delay equations with relatively bounded
   operators in the delay term‖, Semigroup Forum 64(2002), 71-89.

Activity in the scientific community, international relations
   Marie Curie Postdoctoral Fellowships in Vienna and Rome;

                                             Personal data
28                          MSc program in mathematics: personal data


     „Farkas Gyula‖ and „Alexits György‖ prize;
     coauthors from Germany, Italy, USA, France;
     Alexander von Humboldt fellowship;




                                          Personal data
                               MSc program in mathematics: personal data                   29


Name: András A. Benczúr

Date of birth: 1969
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, assistant professor (part time) and
        Computer and Automation Institute, Hungarian Academy of Sciences (full time)
Scientific degree (discipline): PhD (applied mathematics)
Major Hungarian scholarships:

Teaching activity (with list of courses taught so far):
Eötvös University (1997– ):
Theory of algorithms, in English and in Hungarian;
Advanced algorithms for Data Mining, Data Streams and the World Wide Web, graduate
courses.
Central European University:
Statistics, in English

Other professional activity:
Over 10 years of teaching experience, over 15 lectures at international conferences
Project coordinator in a number of R&D project concerning text mining, personalization and
similarity search technologies, network data mining, approximate counting of very large data
streams, efficient algorithms for massive data

Up to 5 selected publications from the past 5 years:
1. To Randomize or Not To Randomize: Space Optimal Summaries for Hyperlink Analysis.
   In Proc. of 15th WWW Conference, 2006. (Joint with T. Sarlós, K. Csalogány, D.
   Fogaras and B. Rácz.)
2 SpamRank: Fully automatic link spam detection, Proc. Airweb 2005. (Joint with Károly
   Csalogány, Tamás Sarlós and Máté Uher), to appear in Information Retrieval.
3. Primal-dual approach for directed vertex connectivity augmentation and generalizations
   Proc 16th ACM-SIAM Symp. on Discrete Algorithms, pp. 500-509, 2005. (Joint with
   László A.Végh). Transactions on Algorithms, to appear.
4. A. A. Benczúr, K. Csalogány, T. Sarlós: Similarity Search to Fight Web Spam. In Proc.
   Airweb 2006 in conjunction with SIGIR 2006.

The five most important publications:
1. To Randomize or Not To Randomize: Space Optimal Summaries for Hyperlink Analysis.
   In Proc. of 15th WWW Conference, 2006. (Joint with T. Sarlós, K. Csalogány, D.
   Fogaras and B. Rácz.)
2 SpamRank: Fully automatic link spam detection, Proc. Airweb 2005. (Joint with Károly
   Csalogány, Tamás Sarlós and Máté Uher), to appear in Information Retrieval.
3. Primal-dual approach for directed vertex connectivity augmentation and generalizations
   Proc 16th ACM-SIAM Symp. on Discrete Algorithms, pp. 500-509, 2005. (Joint with
   László A.Végh). Transactions on Algorithms, to appear.
4. A. A. Benczúr, K. Csalogány, T. Sarlós: Similarity Search to Fight Web Spam. In Proc.
   Airweb 2006 in conjunction with SIGIR 2006.

                                             Personal data
30                           MSc program in mathematics: personal data


5. Approximating s-t minimum cuts in O(n2) time, J. Alg 37(1): 2-36, 2000. (Joint with
   David R. Karger)

Activity in the scientific community, international relations




                                           Personal data
                               MSc program in mathematics: personal data                    31


Name: Károly Bezdek

Date of birth: 1955
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, professor
Scientific degree (discipline): Doctor of Science (mathematics)
Major Hungarian scholarships: Széchenyi scholarship (1998–2001)

Teaching activity (with list of courses taught so far):
Eötvös University (1978– ):
Geometry (all levels), various topics in convex and discrete geometry (for students in
mathematics; lecture, practice)
University of Calgary (2004–)
Transformation Geometry, Differential Geometry, Geometry, Discrete Geometry, Convex
Polytopes, Convexity, Analytic Convexity – Higher Dimensions

Other professional activity:
30 years of teaching experience, 10 diploma thesis supervisions, 4 Ph.D. thesis supervisions;
over 20 lectures at international conferences;
97 publications;

Up to 5 selected publications from the past 5 years:
1. Bezdek, K., Lángi, Zs., Naszódi, M., and Papez, P.: Ball-Polyhedra, Discrete Comput.
   Geom. 38(2) (2007), 201-230.
2. Bezdek, K., and Litvak, A.: On the vertex index of convex bodies, Advances in
   Mathematics 215(2) (2007), 626-641.
3. Bezdek, K., Naszódi, M., and Oliveros-Braniff, D.: Antipodality in hyperbolic space,
   Journal of Geometry, 85 (2006), 22-31.
4. Bezdek, K.: On the monotonicity of the volume of hyperbolic convex polyhedra, Beiträge
   zur Algebra und Geometrie. Contributions to Algebra and Geometry 46(2) (2005), 609-
   614.
5. Bezdek, K., and Daróczy-Kiss, E.: Finding the best face on a Voronoi polyhedron – the
   strong dodecahedral conjecture revisited, Monatshefte für Mathematik, 145 (2005), 191-
   206.

The five most important publications:
1. Bezdek, K.: Circle-packings into convex domains of the Euclidean and hyperbolic plane
   and the sphere, Geometriae Dedicata, 21 (1986), 249-255.
2. Bezdek, K., and Connelly, R.: Covering curves by translates of a convex set, Amer. Math.
   Monthly 96/9 (1989), 789-806.
3. Bezdek, K.: The problem of illumination of the boundary of a convex body by affine
   subspaces, Mathematika 38 (1991), 362-375.
4. Bezdek, K.: Improving Rogers’ upper bound for the density of unit ball packings via
   estimating the surface area of Voronoi cells from below in Euclidean d−space for
   all d ≥ 8, Discrete Comput. Geom. 28 (2002), 75-106.
5. Bezdek, K., and Connelly, R.: Pushing disks apart - the Kneser-Poulsen conjecture
   in the plane, J. reine angew. Math. 553 (2002), 221-236.


                                             Personal data
32                           MSc program in mathematics: personal data


Activity in the scientific community, international relations
      Editor in chief of the journal Contribution to Discrete Mathematics, 2006– ;
      Organizer of several international conferences;
      Coauthors from USA, Canada, England, Germany, Mexico;
      Invited speaker at international conferences and workshops more than 100 times;
      Visiting professor at
     – Cornell University, New York, USA;
     – University of Texas at Austin, Texas, USA;
     – University of Calgary, Calgary, Kanada .




                                           Personal data
                               MSc program in mathematics: personal data                    33


Name: Károly Böröczky, Jr.

Date of birth: 1964
Highest degree (discipline): diploma in mathematics
Present employer, position: Rényi Institute, Eötvös University, associate professor
Scientific degree (discipline): Doctor of Science (mathematics)
Major Hungarian scholarships: Széchenyi scholarship (1998–2001), Bolyai Scholarship
(2001-2004, 2005-2008)

Teaching activity (with list of courses taught so far):
Eötvös University (1994– ):
Geometry (for students in mathematics; lecture, practice)
BSM (1994– ):
Complex functions, Algebraic Topology, Topics in Analysis (lecture, practice)

Other professional activity:
1 diploma thesis supervisions, 1 Ph.D. thesis supervision;
over 20 lectures at international conferences;
60 publications;

Up to 5 selected publications from the past 5 years:
1. K. Böröczky, Jr.: Finite packing and covering, Cambridge University Press, 2004.
2. K. Böröczky, Jr.: The stability of the Rogers-Shepard inequality, Adv. Math.,
       190 (2005), 47-76.
3. K. Böröczky, Jr.: Finite packing and covering by congruent convex domains. Disc. Comp.
Geom., 30 (2003), 185-193.
4. K. Böröczky, Jr., M. Reitzner: Approximation of Smooth Convex Bodies by Random
Circumscribed Polytopes. Annals of Applied Prob., 14 (2004), 239-273.
5. K. Böröczky, Jr.: Finite coverings in the hyperbolic plane.
Discrete and Computational Geometry, 33 (2005), 165-180.

The five most important publications:
1. K. Böröczky, Jr.: Finite packing and covering, Cambridge University Press, 2004.
2. K. Böröczky, Jr.: The stability of the Rogers-Shepard inequality, Adv. Math.,
   190 (2005), 47-76.
3. K. Böröczky, Jr.: Approximation of general smooth convex bodies. Adv. Math.,
   153 (2000), 325-341.
4. K. Böröczky, Jr.: Finite coverings in the hyperbolic plane. Discrete and Computational
   Geometry, 33 (2005), 165-180.
5. K. Böröczky, Jr.: About four-ball packings, Mathematika, 40 (1993), 226-232.

Activity in the scientific community, international relations
organizer of seven international conferences;
visiting professor at universities in Germany, England, USA;
coordinator of various Hungarian and EU grants


                                             Personal data
34                             MSc program in mathematics: personal data


Name: Zoltán Buczolich

Date of birth: 1961
Highest degree (discipline): diploma in Mathematics
Present employer, position: Eötvös University, associate professor
Scientific degree (discipline): D. Sc. (mathematics), + habilitation at the Eötvös University
Major Hungarian scholarships: Széchenyi Professor scholarship (1997–2001),
                                 Öveges Professor scholarship (2006-2007)

Teaching activity (with list of courses taught so far):
Eötvös University (1985– ):
analysis (8 different couses for students in mathematics education + B. Sc. Medium level
mathematics; lecture, practice)
Discrete Dynamical systems (for students in mathematics, applied mathematics, graduate
school; lecture)
Chapters in Dynamical Systems (for students in mathematics, applied mathematics, graduate
school; lecture)
Ergodic Theory (for students in mathematics, applied mathematics, graduate school; lecture)
Complex Funcions (for students in Mathematics, practice)
Budepest Semesters in mathematics (1990–96 ):
Complex Functions (lecture, practice)
University of California Davis, (1989-1990): Calculus, Differential Equations, Harmonic
Analysis.
University of Wisconsin, Milwaukee (1994): Calculus and Introduction to Fractal Geometry.
Michigan State University, (2001-2002): Calculus, Analysis, Honors Analysis.
University of North Texas, (2003): Business Calculus.


Other professional activity:
23 years of continuous teaching experience, 13 diploma thesis supervisions, 2 student
research paper supervisions, over 50 lectures at international conferences; over 30 lectures at
departmental seminars of foreign universities, 72 publications;

Up to 5 selected publications from the past 5 years:
1. Z. Buczolich and C. E. Weil, Infinite Peano Derivatives, extensions, and the Baire one
property, Atti Semin. Mat. Fis. Univ. Modena Reggio Emilia (2004), no. 1, 117--149 (2005).
2. I. Assani, Z. Buczolich and D. Mauldin, An L^1 Counting problem in Ergodic Theory, J.
Anal. Math. {\bf 95} (2005), 221--241.
3. Z. Buczolich and U. B. Darji, Pseudoarcs, Pseudocircles, Lakes of Wada and Generic Maps
on S^2, Topology Appl. 150 (2005), no. 1-3, 223--254.
4. Z. Buczolich, Solution to the gradient problem of C. E. Weil, Rev. Mat. Iberoamericana,
21 (2005) No. 3., 889-910.
5. Z. Buczolich, Universally L^1 good sequences with gaps tending to infinity, Acta Math.
Hungar., 117 (1-2) (2007), 91-40.



                                             Personal data
                             MSc program in mathematics: personal data                        35


The five most important publications:
[1] Z. Buczolich, A general Riemann complete integral in the plane, Acta Math. Hungar. 57
(1991), no. 3-4, 315–323.
[2] Z. Buczolich, Density points and bi-Lipschitz functions in Rm, Proc. Amer. Math. Soc.
116 (1992), no. 1, 53–59.
[3] Z. Buczolich, Arithmetic averages of rotations of measurable functions, Ergodic Theory
Dynam. Systems 16 (1996), no. 6, 1185–1196.
[4] Z. Buczolich, Solution to the gradient problem of C. E. Weil, Rev. Mat. Iberoamericana,
21 (2005) No. 3., 889-910.
[5] I. Assani, Z. Buczolich and D. Mauldin, An L1 Counting problem in Ergodic Theory, J.
Anal. Math. 95 (2005), 221–241.



Activity in the scientific community, international relations
   Real Analysis Exchange (editor), 2004– ;
   organizer of three international conferences and a Summer School;
   secretary of the Scientific commitee of the Bolyai Mathematical Society (1990-93);
   member of the Mathematical commitee of the Hungarian Academy of Sciences (1994-96);
   member of the granting committee of the Hungarian NSRF (OTKA), 1996–2000;
   coauthors from USA, Poland, France, Belgium;
   visiting professor at universities in USA;
   member of the Hungarian and the American Mathematical Society.




                                           Personal data
36                             MSc program in mathematics: personal data


Name: Balázs Csikós

Date of birth: 1959
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, associate professor
Scientific degree (discipline): CSc (mathematics)
Major Hungarian scholarships: Széchenyi scholarship (2000–2003)

Teaching activity (with list of courses taught so far):
Eötvös University (1988– ):
Lie Groups, Algebraic Curves (for PhD students in mathematics; lectures)
Geometry, Algebraic Topology, Differential Geometry, Theory of Bundles and Connections,
General Differential Geometric Structures (for students in mathematics; lectures and
practices)
Geometric Foundations of 3D graphics (for students in applied mathematics; computer lab
practice)
BSM (1990– ):
Topics in Geometry, Algebraic Topology, Differential Topology, Differential Geometry.
(lectures)
CEU (2002– ):
Differential Geometry, Lie Groups (for PhD students, lectures)

Other professional activity:
20 years of teaching experience, 12 diploma thesis supervisions, 2 Ph.D. thesis supervisions;
over 26 lectures at international conferences;
28 publications;

Up to 5 selected publications from the past 5 years:
1. Bezdek, K., Connelly, R., and Csikós, B.: On the perimeter of the intersection of congruent
    disks. Beiträge zur Algebra und Geometrie, 47(1) (2006), 53-62.
2. Bezdek, K., Bisztriczky, T., Csikós, B., and Heppes, A.: On the transversal Helly numbers
    of disjoint and overlapping disks, Archiv der Math., 87(1) (2006), 86-96.
3. Csikós, B., and Moussong, G.: On the Kneser-Poulsen Conjecture in Elliptic Space.
    Manuscripta Math., 121(4) (2006), 481-489.
4. Csikós, B., Lángi, Zs., and Naszódi, M.: A generalization of the discrete isoperimetric
    inequality for piecewise smooth curves of constant geodesic curvature, Periodica Math.
    Hung., 53(1-2) (2006), 121-132.
5. Csikós, B., Németh, B., and Verhóczki, L.: Volumes of principal orbits of isotropy
    subgroups in compact symmetric spaces, Houston Journal of Math., 33(3) (2007), 719-
    734.

The five most important publications:
1. Csikós, B.: On the volume of the union of balls, Discrete Comput. Geom., 20 (1998), 449-
   461.
2. Csikós, B.: On the volume of flowers in space forms, Geometriae Dedicata, 86 (2001), 59-
   79.


                                             Personal data
                             MSc program in mathematics: personal data                          37


3. Csikós, B.: A Schläfli-type formula for polytopes with curved faces and its application to
    the Kneser-Poulsen conjecture, Monatshefte für Mathematik, 147(4) (2006), 273-292.
4. Csikós, B.: On the Rigidity of Regular Bicycle (n,k)-gons. Contributions to Discrete
    Mathematics, 2(1) (2007). 94-107.
5. Csikós, B. and Verhóczki, L.: Classification of Frobenius Lie algebras of dimension ≤ 6.
    Publ. Math. Debrecen, 70(3-4) (2007), 427-451.

Activity in the scientific community, international relations
   deputy director of the Institute of Mathematics (2006–) and head of the Department of
   Geometry (2008–) at Eötvös University;
   organizer of 2 international conferences;
   member of the granting committee of the Hungarian NSRF (OTKA), 1999–2006;
   member of the Bolyai Mathematical Society;
   coauthors from Canada, South Africa, USA;
   visiting professor at universities in Hungary (CEU), Belgium, Canada;




                                           Personal data
38                             MSc program in mathematics: personal data


Name: Villő Csiszár

Date of birth: 1975
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, associate professor
Scientific degree (discipline): -
Major Hungarian scholarships: -

Teaching activity (with list of courses taught so far):
Probability theory (for students in informatics and mathematics; lecture, practice)
Statistics (for students in informatics and mathematics; lecture, practice)
Information theory (for students in mathematics; lecture)
Markov chains (for students in mathematics; lecture)
Large deviations (for students in mathematics; lecture)

Other professional activity:
8 years of teaching experience, 2 diploma thesis supervisions.

Up to 5 selected publications from the past 5 years:
1. Csiszár, V., Móri, T. F.: The convexity method of proving moment-type inequalities.
Statist. Probab. Lett.,66 (2004).
2. Csiszár, V., Móri, T. F., Székely, G. J.: Chebyshev-type inequalities for scale mixtures.
Statist. Probab. Lett.,71 (2005).
3. Csiszár, V., Móri, T. F.: Sharp integral inequalities for products of convex functions.
JIPAM J. Inequal. Pure Appl. Math. 8/4 (2007), Art. 94 (electronic).
4. Csiszár, V., Rejtő, L., Tusnády, G.: Statistical inference on random structures. In: Győri, E.,
Katona, G. O. H., Lovász, L. (eds.): Horizon of Combinatorics. Bolyai Society Mathematical
Studies 17, Springer, Berlin (2008).
5. Csiszár, V.: Conditional independence relations and log-linear models for random
matchings. Acta Math. Hungar. Online First (2008).

The five most important publications:
1. Makra, Horváth, Zempléni, Csiszár, Rózsa, Motika: Some characteristics of air quality
parameters in Southern Hungary. EURASAP Newsletter 42 (2001).
2. Csiszár, V., Móri, T. F.: The convexity method of proving moment-type inequalities.
Statist. Probab. Lett.,66 (2004).
3. Csiszár, V., Móri, T. F., Székely, G. J.: Chebyshev-type inequalities for scale mixtures.
Statist. Probab. Lett.,71 (2005).
4. Csiszár, V., Rejtő, L., Tusnády, G.: Statistical inference on random structures. In: Győri, E.,
Katona, G. O. H., Lovász, L. (eds.): Horizon of Combinatorics. Bolyai Society Mathematical
Studies 17, Springer, Berlin (2008).
5. Csiszár, V.: Conditional independence relations and log-linear models for random
matchings. Acta Math. Hungar. Online First (2008).

Activity in the scientific community, international relations:
Member of the Bolyai Mathematical Society


                                             Personal data
                               MSc program in mathematics: personal data                  39


Name: Piroska Csörgő

Date of birth: 1950
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, associate professor
Scientific degree (discipline): CSc (mathematics)
Major Hungarian scholarships: Széchenyi István scholarship (2003–2006)

Teaching activity (with list of courses taught so far):
Eötvös University (1974– ):
     algebra and number theory (for students in mathematics; lecture and practice)
     linear algebra (for students in informatics; practice)
     introduction to mathematics (for students in informatics, practice)
     analysis (for students in mathematics; practice)

Other professional activity:
34 years of teaching experience, over 10 diploma thesis supervisisons, over 20 lectures at
international conferences, 31 publications

Up to 5 selected publications from the past 5 years:
1.   P. Csörgő, Abelian inner mappings and nilpotency class greater than two, European
     Journal of Combinatorics 28 (2007), 858–867.
2.   P. Csörgő, On connected transversals to abelian subgroups and looptheoretical
     consequences, Archiv der Mathematik 47 (2005), 242–265.
3.   P. Csörgő, A. Drápal, Left conjugacy closed loops of nilpotency class two, Resultate der
     Mathematik 47 (2005), 242–265.
4.   M. Asaad, P. Csörgő, Characterization of finite groups with some S-quasinormal
     subgroups, Monatshefte für Mathematik, 146 (2005), 263–266.
5.   P. Csörgő, M. Herzog, On supersolvable groups and the nilpotator, Communications in
     Algebra Vol. 32, No2. (2004), 609-620.

The five most important publications:
1.   P. Csörgő, Abelian inner mappings and nilpotency class greater than two, European
     Journal of Combinatorics 28 (2007), 858–867.
2.   P. Csörgő, On connected transversals to abelian subgroups and looptheoretical
     consequences, Archiv der Mathematik 47 (2005), 242–265.
3.   P. Csörgő, M. Niemenmaa, On connected transversals to nonabelian subgroups,
     European Journal of Combinatorics 23 (2002), 179–185.
4.   P. Csörgő, M. Niemenmaa, Solvability conditions for loops and groups, Journal of
     Algebra 232 (2000), 336–342.
5.   M. Asaad, P. Csörgő, The influence of minimal subgroups on the structure of finite
     groups, Archiv der Mathematik 72 (1999), 401–404.

Activity in the scientific community, international relations
     opponent of theses and membership in committees for PhD, CSc and DSc degrees
     refereeing to many international journals
     editor at Journal of Mathematical Sciences: Advances and Applications (2008– )

                                             Personal data
40                        MSc program in mathematics: personal data


     visiting professor at universities in Chicago and in Prague
     coauthors from USA, Finland, Germany, Czech Republic, Israel and Egypt




                                        Personal data
                               MSc program in mathematics: personal data                41


Name: Csaba Fábián

Date of birth: 1958
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, assistant professor
Scientific degree (discipline): PhD (mathematics)
Major Hungarian scholarships:

Teaching activity (with list of courses taught so far):
Eötvös University (1992– ):
Operations research (for students in informatics; lecture, practice);
Stochastic programming, Simulation, OR methods in risk management (for students in
mathematics; lecture);
OR software (for students in informatics; practice);
Linear programming methods and solvers (for students in mathematics; practice).
Organizer of Seminar in continuous optimization (for researchers and students in
mathematics).

Other professional activity:
16 years of teaching experience,
over 10 diploma thesis supervisions, 3 Ph.D. thesis supervisions;
over 10 lectures at international conferences;

12 publications;
4 optimization packages with applications in transportation, chemistry, and military.
12 citations to above works.

Up to 5 selected publications from the past 5 years:
1. C.I. Fábián ―Decomposing CVaR minimization in two-stage stochastic models‖.
   Stochastic Programming E-Print Series 20-2005.
2. C.I. Fábián and Z. Szőke ―Solving two-stage stochastic programming problems with level
   decomposition‖. Computational Management Science 4 (2007), 313-353.
3. C.I. Fábián ―Handling CVaR objectives and constraints in two-stage stochastic models‖.
   European Journal of Operational Research 191 (2008) (special issue on Continuous
   Optimization in Industry, T. Illés, M. Lopez, J. Vörös, T. Terlaky, G-W. Weber, eds.),
   888-911.
4. C.I. Fábián and A. Veszprémi ―Algorithms for handling CVaR-constraints in dynamic
   stochastic programming models with applications to finance‖. The Journal of Risk 10
   (2008), 111-131.
5. C.I. Fábián, G. Mitra, and D. Roman ―Processing Second-order Stochastic Dominance
   models using cutting-plane representations‖. CARISMA Technical Report 75 (2008),
   Brunel University, West London.

The five most important publications:
1. C.I. Fábián ―Bundle-type methods for inexact data‖. Central European Journal of
   Operations Research 8 (2000) (special issue, T. Csendes and T. Rapcsák, eds.), 35-55.


                                             Personal data
42                         MSc program in mathematics: personal data


2. C.I. Fábián, A. Prékopa, and O. Ruf-Fiedler ―On a dual method for a specially structured
   linear programming problem‖. Optimization Methods and Software 17 (2002), 445-492.
3. C.I. Fábián and Z. Szőke ―Solving two-stage stochastic programming problems with level
   decomposition‖. Computational Management Science 4 (2007), 313-353.
4. C.I. Fábián ―Handling CVaR objectives and constraints in two-stage stochastic models‖.
   European Journal of Operational Research 191 (2008) (special issue on Continuous
   Optimization in Industry, T. Illés, M. Lopez, J. Vörös, T. Terlaky, G-W. Weber, eds.),
   888-911.
5. C.I. Fábián and A. Veszprémi ―Algorithms for handling CVaR-constraints in dynamic
   stochastic programming models with applications to finance‖. The Journal of Risk 10
   (2008), 111-131.




                                         Personal data
                               MSc program in mathematics: personal data                      43


Name: István Faragó

Date of birth: 1950
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, associate professor
Scientific degree (discipline): CSc (mathematics)
Major Hungarian scholarships: Széchenyi scholarship (2001–2004)

Teaching activity (with list of courses taught so far):
Eötvös University (1977– ):
Applied analysis (for students in mathematics; lecture)
analysis (for students in meteorology; lecture, practice)
Differential equation (for students in earth sciences; lecture)

Other professional activity:
30 years of teaching experience, 15 diploma thesis supervisions, 5 Ph.D. thesis supervisions;
over 40 lectures at international conferences;
110 publications;.

Up to 5 selected publications from the past 5 years:
1. I. Faragó, C. Palencia, Sharpening the estimate of the stability bound in the maximum-
norm of the Crank--Nicolson scheme for the one-dimensional heat equation, Appl. Numer.
Math. 42 (2002) 133-140.
2. J. Bartholy, I. Faragó, A. Havasi, Splitting method and its application in air pollution
modelling, Idöjárás, 105 (2001) 39-58.
3. M. Botchev, I. Faragó, A. Havasi, Testing weighted splitting schemes on a one-column
transport-chemistry model, in: S. Margenov, J. Wasniewski, P. Yalamov eds; Large-Scale
Scientific Computing, Lect. Notes Comp. Sci., 2907, Springer Verlag, 2004, 295-302.
4 A. Dorosenko, I. Faragó, Á. Havasi, V. Prussov, , On the numerical solution       of the
three-dimensional advection-diffusion equation, Problems in Programming, 7 (2006) 641-
647.
5. P. Csomós, I. Faragó, Error analysis of the numerical solution obtained by applying
operator splitting , Mathematical and Computer Modelling , 2007.



The five most important publications:

1. I. Faragó, J. Karátson. Numerical solution of nonlinear elliptic problems via
     preconditioning operators. Theory and applications. Nova Science Publisher, New York,
     402 p. 2002.
2. . I. Faragó, R. Horváth, Discrete maximum principle and adequate discretizations of
     linear parabolic problems, SIAM Scientific Computing, 28 (2006) 2313-2336.
3.      I. Faragó, B. Gnandt, Á. Havasi, Additive and iterative splitting methods and their
     numerical investigation, Computers and Mathematics with Applications, 55 (2008) 2266-
     2279.
4. I. Faragó, P. Thomsen, Z. Zlatev, On the additive splitting procedures and their computer
     realization, Applied Mathematical Modelling, 32 (2008) 1552-1569.

                                             Personal data
44                           MSc program in mathematics: personal data


5. I. Faragó, Á. Havasi, Consistency analysis of operator splitting methods for C0-
   semigroups, Semigroup Forum, 74 (2007) 125-139



Activity in the scientific community, international relations

International Journal of Comp. Science in Eng. (editorial board), Open Mathematical Journal
    (editorial board),
organizer of eight international conferences and workshops; guest editor of six journal special
    issues,
coauthors from Denmark, Finland, Germany, Spain, Bulgaria and Ukraina
visiting professor at universities in Germany, Spain, Denmark, Canada, USA, Finland




                                           Personal data
                               MSc program in mathematics: personal data                      45


Name: László Fehér

Date of birth: 1963
Highest degree (discipline): PhD.
Present employer, position: Eötvös University, assistant professor
Major Hungarian scholarships: Bolyai scholarship (2007–2009)

Teaching activity (with list of courses taught so far):
Eötvös University (1987– 92, 2001-):
analysis (practice and lecture), Topology (practice and lecture)
Algebraic topology, Differential Geometry (practice and lecture)
Differential topology, Complex functions (practice), Equivariant cohomology, Spin
Geometry.
Univ. Of Notre Dame USA (1993-97) Calculus all level (practice)
Introductory Math (lecture) 1998
Budapest Semester in Math. (2000-2002)
Topology Algebraic topology, (practice and lecture)


Other professional activity:
20 years of teaching experience, 4 diploma thesis supervisions, 1 Ph.D. thesis supervision;
over 20 lectures at international conferences;
14 publications;

Up to 5 selected publications from the past 5 years:
1. The degree of the discriminant of irreducible representations, elfogadva: Journal of
Algebraic Geometry math.AG/0502500 (with Richárd Rimányi and András Némethi)
2. Schur and Schubert polynomials as Thom polynomials - Cohomology of moduli spaces
(with Richárd Rimányi) Cent. European J. Math. 4 (2003) 418—434
3. On the structure of Thom polynomials of singularities, Bull. London Math. J. 39 (2007),
541-549 (with Richárd Rimányi)
4. Positivity of quiver coefficients (with A. S. Buch, Richárd Rimányi) Adv. Math. . 197
(2005) 306-320
5. On second order Thom-Boardman singularities: Fundamenta Mathematica 191 (2006),
249-264 (with Balázs Kőműves)


The five most important publications:
1. The degree of the discriminant of irreducible representations, elfogadva: Journal of
Algebraic Geometry math.AG/0502500 (with Richárd Rimányi and András Némethi)
2. Schur and Schubert polynomials as Thom polynomials - Cohomology of moduli spaces
(with Richárd Rimányi) Cent. European J. Math. 4 (2003) 418--434
3. On the structure of Thom polynomials of singularities, Bull. London Math. J. 39 (2007),
541-549 (with Richárd Rimányi)


                                             Personal data
46                           MSc program in mathematics: personal data


4. Positivity of quiver coefficients (with A. S. Buch, Richárd Rimányi) Adv. Math. . 197
(2005) 306-320
5. On second order Thom-Boardman singularities: Fundamenta Mathematica 191 (2006),
249-264 (with Balázs Kőműves)


Activity in the scientific community, international relations




                                           Personal data
                               MSc program in mathematics: personal data                      47


Name: Alice Fialowski

Date of birth: 1951
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, associate professor
Scientific degree (discipline): CSc (mathematics)
Major Hungarian scholarships: Széchenyi Professors’ Scholarship (1998–2001) , Széchenyi
scholarship (2002– 2006)

Teaching activity (with list of courses taught so far):
Eötvös University (1974-79, 1994– ), BUTE (1984–94), Univ. of Pennsylvania, Philadelphia
(1987–1989), Univ. of California, Davis (1990–1995),
complex analysis, functiopnal analysis, calculus and probability theory, introductory calculus,
real analysis, algebra, intorductory analysis, Lie groups and Lie algebras, multivariate
analysis, linear algebra, applied linear algebra, elements of analysis, infinite dimensional Lie
algebras, cohomolgy of Lie algebras

Other professional activity:
Over 27years of teaching experience, 51 research papers, several diploma and Ph.D. students,
a large number of ivited lectures in 18 countries

Up to 5 selected publications from the past 5 years:
Fialowski, A., Schlichenmaier, M., „Krichever-Novikov algebras as global deformations of
the Virasoro algebra‖, Comm. Contemp. Math. 5, No. 6 (2003), 921-945.
Fialowski, A., de Montigny, M., ,,On Deformations and Contractions of Lie Algebras‖, J.
Physics A: Math. Gen., 38 (2005), 649-663.
Fialowski, A., Penkava, M., „ Strongly homotopy Lie algebras of one even and two odd
dimensions‖, Math. QA/0308016, Jour. of Algebra vol. 283(2005), 125-148.
Fialowski, A., Millionschikov, D.: ,,Cohomology of graded Lie algebras of maximal class‖,
Journal of Algebra, 296 (2006), 157-176.
Fialowski, A., Wagemann, F., ,,Cohomology and deformations of the infinite diemsnional
filiform Lie algebra m_0‖, Journal of Algebra 318 (2007), 1002-1026.


The five most important publications:
Fialowski, A., „Deformations of Lie algebras‖, Mat. Sbornyik USSR, 127 (169), (1985), 476-
482; English translation: Math USSR-Sb., 55 (1986), no.2., 467-473.
Fialowski, A., „Ont he cohomology of infinite dimensional nilpotent Lie algebras‖, Adv. In
Math., 97 (1993), 267-277-
Fialowski, A., Fuchs, D.B., „Construction of Miniversal Deformations of Lie Algebras‖, Jour.
of Func. Anal. (1999), 161(1), 76-110.
Fialowski, A., Penkava, M., „Deformation Theory of Infinity Algebras‖, Jour. of Algebra, 255
(2002), 59-88.



                                             Personal data
48                           MSc program in mathematics: personal data


Fialowski, A., Schlichenmaier, M., „Global Deformations of the Witt Algebra of Krichever-
Novikov Type‖, Comm. in Contemporary Math., 5 (2003), 921-945.


Activity in the scientific community, international relations
Member of the Bolyai Mathematical Society, of the AMS, EMS
Member of the committee for international relations of the AMS (1993–1996)
Member of several conferences amd workshops (e.g. Lie algebras and Lie groups, 1995,
  Oberwolfach Conference 1996, 2006, 2010, Seminar Sophus Lie 2007)
Humboldt Fellowship (1986–1988)
NSF-OTKA grant with Michael Penkava (Univ. of Wisconsin.)
NATO grant Marc de Montigny, Univ. Albert, Canada.
Member of the editorial board for Journal of Lie theory, Journal of Generalized Lie theory
  and Appl., Springer book series Algebra and Applications




                                           Personal data
                               MSc program in mathematics: personal data                      49


Name: András Frank

Date of birth: 1949
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, full professor
Scientific degree (discipline): DSc (mathematics)
Major Hungarian scholarships: Széchenyi scholarship (1997–2000)

Teaching activity (with list of courses taught so far):
Eötvös University (22 years):
Operations research, graph theory, matroid theory, ployhedral combinatorics, combinatorial
algorithms, Structures in combinatorial optimization

Other professional activity:
Guest researcher at University of Bonn (1984–1986, 1989–1993)
Over 70 publications, over 900 citations in about 500 publications
7 Ph.D. supervisions
invited addresses at the British Conference of Combinatorics (1993), at the Symposium on
Mathematical Programming in Ann Arbour (1994), at the International Mathematical
Congress (1998), over 60 other conference lectures
Grünwald Prize (1979), Science Award (Eötvös University, 1996), Bolyai Farkas Prize
(2001), Szele Tibor Prize (2002)

Up to 5 selected publications from the past 5 years:
1. A. Frank, T. Király, and M. Kriesell, On decomposing a hypergraph into k-connected
   sub-hypergraphs, in: Submodularity, (guest editor S. Fujishige) Discrete Applied
   Mathematics, Vol. 131, Issue 2. (September 2003). pp. 373-383.
2. A. Frank, T. Király, and Z. Király, On the orientation of graphs and hypergraphs, in:
   Submodularity, (guest editor S. Fujishige) Discrete Applied Mathematics, Vol. 131, Issue
   2. (September 2003). pp. 385-400.
3. A Frank, Restricted t-matchings in bipartite graphs, in: Submodularity, (guest editor S.
   Fujishige) Discrete Applied Mathematics, Vol. 131, Issue 2. (September 2003). pp. 337-
   346.
4. A. Frank and T. Király, Combined connectivity augmentation and orientation problems,
   in: Submodularity, (guest editor S. Fujishige) Discrete Applied Mathematics, Vol. 131,
   Issue 2. (September 2003). pp. 401-419.


The five most important publications:
1. A. Frank, An algorithm for submodular functions on graphs, Annals of Discrete
   Mathematics, 16 (1982) 97-120.
2. A. Frank, Edge-disjoint paths in planar graphs, J. of Combinatorial Theory, Ser. B. No. 2
   (1985), 164-178.
3. A. Frank, Augmenting graphs to meet edge-connectivity requirements, SIAM J. on
   Discrete Mathematics, (1992 February), Vol.5, No 1., pp.22-53. A preliminary version


                                             Personal data
50                           MSc program in mathematics: personal data


4. A. Frank and T. Jordán, Minimal edge-coverings of pairs of sets, J. Combinatorial
   Theory, Ser. B. Vol. 65, No. 1 (1995, September) pp. 73-110.
5. A. Frank and Z. Király, Graph orientations with edge-connection and parity constraints,
   Combinatorica, Vol. 22, No. 1. (2002), pp. 47-70.


Activity in the scientific community, international relations
     member of organizing and program committees for seven international conferences
     member ships: Bolyai Matematical Society, AMS, SIAM, Operations Research
     Committee of the Hungarian Academy of Sciences, Applied Mathematics Committee of
     the European Mathematical Society, granting committee of the Hungarian NSRF (OTKA)
     (1997–2000), Széchenyi Scholarship Committee (1998), several other award committees
     member of the editorial board of SIAM Journal on Discrete Mathematics
     leader of several OTKA projects (1995–1998, 1999–2001, 2002–2005), OTKA project for
     Hungarian–Dutch cooperation (2001–2004), AMFK (1995), DONET (Discrete
     Optimization Network, 1993-1998), Hungarian–Israeli cooperation project ADONET
     (2003– ), European cooperaton, France Telekom (2002–2005), Egervárz Research Group
     (2001– )
     guest editor of one volume for Mathematical Programming, series B




                                           Personal data
                               MSc program in mathematics: personal data                    51


Name: Róbert Freud

Date of birth: 1947
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, Mathematical Institute, Department of Algebra
and Number Theory, associate professor
Scientific degree (discipline): CSc (mathematics)
Major Hungarian scholarships: Széchenyi professor's scholarship (1997–2000)


Teaching activity (with list of courses taught so far):
Eötvös University , Department of Algebra and Number Theory since1968
     nearly all algebra and number theory courses for students in pure mathematics and
     teacher training.
Teaching also combinatorics and analysis at several universities in the USA as visiting
     faculty.

Other professional activity:
The performance in mathematics and its instruction and popularization are marked by the
following prizes:
      National Contest for Secondary School Students (1964),
      Who Is Good in Science (1964),
      Schweitzer Memorial Competition (1967),
      National Conference for Students in Scientific Research (1969, 1970),
      Rényi Kató Prize (for scientific results as a university student, 1970),
      Grünwald Géza Prize (for scientific results as a young researcher 1976),
      Oustanding Instructor of Eötvös University Faculty of Science (1989, 2003),
      Pro Universitate Medal (1996),
      Beke Manó Prize (for popularization of mathematics 1997).

Up to 5 selected publications from the past 5 years:
1.   Linear Algebra, university textbook, 518 pages, ELTE Eötvös Kiadó (1996-2007, six
     editions)
2.   Number Theory, university textbook (with Edit Gyarmati), Nemzeti Tankönyvkiadó
     2000, 740 pages, improved edition 2006, 810 pages.

The five most important publications:
1.   Linear Algebra, university textbook, 518 pages, ELTE Eötvös Kiadó (1996-2007, six
     editions)
2.   Number Theory, university textbook (with Edit Gyarmati), Nemzeti Tankönyvkiadó
     2000, 740 pages, improved edition 2006, 810 pages.
3.   On sets characterizing additive arithmetical functions I-II, Acta Arithmetica 35 (1979),
     333-343, és 37 (1980), 35-41;
4.   On disjoint sets of differences (with Paul Erdős), J. Number Theory 18 (1984), 99-109;
5.   On sums of a Sidon-sequence (with Paul Erdős), J. Number Theory 38 (1991), 196-205.



                                             Personal data
52                           MSc program in mathematics: personal data


Activity in the scientific community, international relations
     organization of international conferences (ICME-6, colloquia in number theory),
     committee member of Schweitzer Memorial Competition,
     chair of committee of National Contest for Secondary School Students,
     popularization of mathematics (lectures, papers, translation of books, postgradual
     training of teachers),
     member of educational committees of Eötvös University Faculty of Science and of
     teacher training in mathematics.




                                           Personal data
                               MSc program in mathematics: personal data                    53


Name: Katalin Fried

Date of birth: 1958
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, associate college professor
Scientific degree (discipline): PhD (mathematics)
Major Hungarian scholarships:

Teaching activity (with list of courses taught so far):
Eötvös University (1982– )
algebra, number theory, numerical methods, informatics, elementary mathematics, analysis
tutorial

Other professional activity:
over 25 years of teaching experience
a large number of lectures in conferences on didactics
several books for elementary schools students

Up to 5 selected publications from the past 5 years:
n elem permutációi rekurzió nélkül, Tanárképzés–Tanártovábbképzés, 2002.
Matematikai csemegék, Matematikai Módszertani Lapok, Budapest, 3–4. (2002), 9–11.
További váratlan kérdések a bűvös négyzetről, Kőszegi matematikatanári konferencia-kötet,
2004
Matematika 5–8. tankönyv (társszerzőkkel), Nemzeti Tankönyvkiadó, 2004-2007.

The five most important publications:
Rare Bases For Finite Intervals of Integers, Acta Math. Sci. Szeged, Vol. 52 (1988), 303–305.
Rare Bases of Order h, Annales Univ. Sci. Budapest., 37 (1994) 243–245.
A note on a multiplicative problem, Annales Univ. Sci. Budapest., 40 (1997), 187–190.
A proof of Escher's (only?) theorem, Annales Univ. Sci. Budapest., 43. (2000), 159–163.

Activity in the scientific community, international relations
Member of the Bolyai Mathematical Society
Technical editor of the Annales Budapest. Sect. Mathematica




                                             Personal data
54                             MSc program in mathematics: personal data


Name: Róbert Fullér

Date of birth: 1958
Highest degree (discipline): diploma in program-designer mathematics
Present employer, position: Eötvös University, associate professor
Scientific degree (discipline): CSc (mathematics)
Major Hungarian scholarships: Széchenyi Professor Scholarship (1998–2001), Széchenyi
István Scholarship (2003-2006)

Teaching activity (with list of courses taught so far):
Eötvös Loránd University (1993– ):
Investments Analysis (for students in mathematics; lecture)
Decision Analysis (for students in mathematics; lecture, practice)
Operations Research Models (for students in mathematics; practice)
Multiple Objective Optimization (for students in mathematics; lecture)
Financial Mangement (for students in mathematics; lecture, practice)

Other professional activity:
15 years of teaching experience

Up to 5 selected publications from the past 5 years:
1. Christer Carlsson, Mario Fedrizzi and Robert Fullér, Fuzzy Logic in Management,
   Kluwer Academic Publishers, Boston, 2003.
2. Christer Carlsson, Robert Fullér and Péter Majlender, On possibilistic correlation, Fuzzy
    Sets and Systems, 155(2005) 425-445.
3. Christer Carlsson, Robert Fullér, Markku Heikillä and Péter Majlender, A fuzzy approach
    to R&D project portfolio selection, International Journal of Approximate Reasoning,
    44(2007) 93-105.
4. Robert Fullér and Péter Majlender, On interactive fuzzy numbers, Fuzzy Sets and Systems,
    143(2004) 355-369.
5. Robert Fullér and Péter Majlender, On weighted possibilistic mean and variance of fuzzy
    numbers, Fuzzy Sets and Systems, 136(2003) 363-374.

The five most important publications:
1. Robert Fullér, Introduction to Neuro-Fuzzy Systems, Springer, 2000.
2. Christer Carlsson and Robert Fullér, Fuzzy Reasoning in Decision Making and
    Optimization, Springer, 2002.
3. Robert Fullér and Péter Majlender, On obtaining minimal variablity OWA operator
    weights, Fuzzy Sets and Systems, 136(2003) 203-215.
4. Robert Fullér and Péter Majlender, An analytic approach for obtaining maximal entropy
    OWA operator weights, Fuzzy Sets and Systems, 124(2001) 53-57.
5. Christer Carlsson and Robert Fullér, On possibilistic mean value and variance of fuzzy
    numbers, Fuzzy Sets and Systems, 122(2001) 315-326.

Activity in the scientific community, international relations
Referee for:
Fuzzy Sets and Systems, Information Sciences, IEEE Transactions on Fuzzy Systems, Soft

                                             Personal data
                           MSc program in mathematics: personal data                     55


Computing, European Journal of Operational Research, IEEE Transactions on Neural
Networks, Il Nuovo Cimento B, The Journal of the Franklin Institute, IEEE Transactions on
Systems, Man, and Cybernetics, Soochow Journal of Mathematics, Acta Mathematica
Hungarica, Omega - The International Journal of Management Science, Applied Artificial
Intelligence, Computers & Industrial Engineering, IEEE Transactions on Instrumentation and
Measurement, International Journal of Neural Systems, International Journal of Uncertainty,
Fuzziness and Knowledge-Based Systems, International Journal of Mathematics and
Mathematical Sciences, Acta Cybernetica, Journal of Modelling in Management, International
Journal of Approximate Reasoning, Computers and Mathematics with Applications, Fuzzy
Optimization and Decision Making, International Journal of Systems Science, Environmental
Modelling & Software, Knowledge and Information Systems, European Journal of Industrial
Engineering. Reviewer for Mathematical Reviews.




                                         Personal data
56                             MSc program in mathematics: personal data


Name: Vince Grolmusz

Date of birth: 1961
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, full professor
Scientific degree (discipline): PhD, CSc, DSc (mathematics)
Major Hungarian scholarships: Széchenyi scholarship (2002–2005)

Teaching activity (with list of courses taught so far):
Eötvös University (1990– ): Combinatorics, computer science
BSM (1988–98 ) Introduction to Computing

Other professional activity:
18 years of teaching experience, 10 diploma thesis supervisions, 3 Ph.D. thesis supervisions;
over 30 lectures at international conferences; 26 publications in journals; 8 US patents;

Up to 5 selected publications from the past 5 years:
Grolmusz, V.: Computing Elementary Symmetric Polynomials with a Sub-Polynomial
Number of Multiplications, SIAM Journal on Computing, Vol. 32, No. 6 (2003), pp 1475-
1487.
Grolmusz, V.: A Note on Set Systems with no Union of Cardinality 0 Modulo m, Discrete
Mathematics and Theoretical Computer Science (DMTCS) Vol 6, No. 1 (2003), pp 41-44.
Grolmusz, V., Tardos, G.: A Note on Non-Deterministic Communication Complexity with
Few Witnesses, Theory of Computing Systems, Vol 36, No. 4 (2003), pp 387-391.
Grolmusz, V.: A Note on Explicit Ramsey Graphs and Modular Sieves, Combinatorics,
Probability and Computing Vol. 12, (2003) pp. 565-569 (an invited paper).
Grolmusz, V.: Constructing Set-Systems with Prescribed Intersection Sizes, Journal of
Algorithms, Vol. 44 (2002), pp. 321-337.



The five most important publications:
Grolmusz, V.: Computing Elementary Symmetric Polynomials with a Sub-Polynomial
Number of Multiplications, SIAM Journal on Computing, Vol. 32, No. 6 (2003), pp 1475-
1487.
Grolmusz, V.: Constructing Set-Systems with Prescribed Intersection Sizes, Journal of
Algorithms, Vol. 44 (2002), pp. 321-337.
Grolmusz, V., Sudakov, B.: k-wise Set-Intersections and k-wise Hamming-Distances, J.
Combin. Theory Ser. A 99 (2002), no. 1, 180--190.
Grolmusz, V.: Separating the Communication Complexities of MOD m and MOD p Circuits,
Journal of Computer and Systems Sciences, Vol. 51, (1995), No. 2




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                             MSc program in mathematics: personal data                      57


Grolmusz, V., Tardos, G.: Lower Bounds for (MOD p, MOD m) Circuits, SIAM Journal on
Computing, Vol. 29, (2000), No. 4, pp. 1209-1222
Grolmusz, V.: Superpolynomial Size Set-Systems with Restricted Intersections mod 6 and
Explicit Ramsey Graphs, Combinatorica, Vol. 20, (2000), No. 1, pp. 73-88.


Activity in the scientific community, international relations
   Visiting prof at the University of Chicago, 1999; Coordinator of EU FP5, FP6 and large
   Hungarian research projects.




                                           Personal data
58                             MSc program in mathematics: personal data


Name: Katalin Gyarmati

Date of birth:
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, associate professor
Scientific degree (discipline): PhD (mathematics)

Teaching activity (with list of courses taught so far):
Eötvös University (1999– ):
     number theory (for students in mathematics; practice)
     linear algebra (for students in informatics; practice)
     computational number theory (for students in mathematics, lecture)
     exponential sums and its applications in number theory (for students in mathematics,
     lecture)

Other professional activity:
       9 years of teaching experience, over 16 lectures at international conferences;
       24 publications.

Up to 5 selected publications from the past 5 years:
1.    K. Gyarmati, A. Sárközy, Equations in finite fields with restricted solution sets, I.
      (Character sums.) , Acta Math. Hungar. 118 (2008), 129-148.
2.    K. Gyarmati, A. Sárközy, Equations in finite fields with restricted solution sets, II.
      (Algebraic equations.), Acta Math. Hungar. 119 (2008), 259-280.
3.    K. Gyarmati, S. Konyagin, I. Z. Ruzsa, Double and triple sums modulo a prime, CRM
      Proceedings & lecture Notes, Volume 43, AMS 2008, 271-278.
4.    K. Gyarmati, On the number of divisors which are values of a polynomial, The
      Ramanujan Journal, to appear.
5.    K. Gyarmati, M. Matolcsi, I. Z. Ruzsa, A superadditivity and submultiplicativity
      properties for cardinalities of sumsets, Combinatorica, to appear.

The five most important publications:
1.    K. Gyarmati, On a problem of Diophantus, Acta Arith. 97.1 (2001), 53-65.
2.    K. Gyarmati, On the correlation of binary sequences, Studia Sci. Math. Hungar. 42
      (2005), 59-75.
3.    K. Gyarmati, A. Sárközy, A. Pethõ, On linear recursion and pseudorandomness, Acta
      Arith. 118 (2005), 359-374.
4.    K. Gyarmati, A. Sárközy, Equations in finite fields with restricted solution sets, I.
      (Character sums.) , Acta Math. Hungar. 118 (2008), 129-148.
5.    K. Gyarmati, M. Matolcsi, I. Z. Ruzsa, A superadditivity and submultiplicativity
      properties for cardinalities of sumsets, Combinatorica, to appear

Activity in the scientific community, international relations
     Középiskolai Matematikai Lapok (editor in chief, 1996–1999)
     member of OTKA (2003-)
     coauthors from France, Canada, Germany and Hungary.


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                               MSc program in mathematics: personal data                   59


Name: Gábor Halász

Date of birth: 1941
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, Department of Analysis, professor
Scientific degree (discipline): fellow of HAS (mathematics)
Major Hungarian scholarships:

Teaching activity (with list of courses taught so far):
For over 20 years:
Introduction to Complex Functions, Fourier Integral, Geometric Function Theory, Riemann
Surfaces, Chapters from Complex Function Theory, Special Functions, Approximation
Theory.
Special courses: Analysis in Probability, Tauberian Theorems, Arithmetic Functions.

Other professional activity:
1964-1991: Alfréd Rényi Institute of Mathematics of HAS (1976-1991: head of the Function
Theory Department)

Up to 5 selected publications from the past 5 years:



The five most important publications:
Über die Mittelwerte multiplikativer zahlentheretischer Funktionen, Acta Math. Hung.
19(1968), 365-403.
On the distribution of roots of Riemann zeta and allied functions I, J. Number Theory
1(1969), 121-137 (Turán Pállal közösen).
Tauberian theorems for univalent functions, Studia Sci. Math. Hung. 4(1969), 421-440.
Estimates for the concentration function of combinatorial number theory and probability, Per.
Math. Hung. 8(1977), 197-211.
On Roth's method in the theory of irregularities of point distributions, Recent Progress in
    Analytic Number Theory, vol. 2, Academic Press (1981), 79-94.

Activity in the scientific community, international relations
János Bolyai Mathematical Society (committee member), Doctoral Committee of Section
   Mathematics of HAS (member), member of the editorial boards of Acta Math. Hung.,
   Studia Sci. Math. Hung., Analysis, Acta Arithmetica.




                                             Personal data
60                             MSc program in mathematics: personal data


Name: Norbert Hegyvári

Date of birth: 1956
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, professor of college
Scientific degree (discipline): CSc (mathematics)
Major Hungarian scholarships: Széchenyi scholarship (2000–2003)

Teaching activity (with list of courses taught so far):
Eötvös University (1985– ):
algebra (for students in mathematics; lecture, practice)
analysis (for students mathematics; lecture, practice)
 probability theory (for students mathematics; lecture, practice) at ELTE Teacher Training
College,
analysis (for students mathematics; lecture, practice), at Dept. of Analysis



Other professional activity:
20 years of teaching experience, ~30 diploma thesis supervisions,;
~15 lectures at international conferences;
39 publications;
2 books;

Up to 5 selected publications from the past 5 years:
[1] Hegyvári, N, F. Hennecart and A. Plagne, A proof of two Erdős' conjectures on restricted
addition and further results ( Journal fuer die reine und angewandte Mathematik (Crelle) 560
2003, 199–220 )
[2] On Combinatorial Cubes, The Ramanujan Journal 8 (2004), no.3, 303-307
[3] Arithmetical and group topologies, Acta Math. Hungar. 106 (3) (2005), 187-195
[4] On intersecting properties of partitions of integers Combin. Probab. Comput. (14) 03,
(2005), 319-323
[5] Answer to the Burr-Erdős question on restricted addition
and further results, Combinatorics, Probability and Computing,
Volume 16, Issue 05, Sep 2007, pp 747-756
(with F. Hennecart and A. Plagne)



The five most important publications:
[1] Hegyvári, N, F. Hennecart and A. Plagne, A proof of two Erdős' conjectures on restricted
addition and further results (Journal fuer die reine und angewandte Mathematik (Crelle) 560,
2003, 199–220)
[2] Hegyvári, N, F. Hennecart, On Monochromatic sums of squares and primes, Journal of
Number Theory, Volume 124, Issue 2,
June 2007, Pages 314-324

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                             MSc program in mathematics: personal data                       61


[3] Hegyvári, Norbert, On the representation of integers as sums of distinct terms from a fixed
set Acta Arith. 92.2 2000. 99–104.
[4] Hegyvári, On the dimension of the Hilbert cubes. J. Number Theory 77
(1999), no. 2, 326--330.
[5] N.Hegyvári, A Sárközy, On Hilbert cubes in certain sets. Ramanujan J. 3 (1999), no.3,
303--314.

Activity in the scientific community, international relations
organizer of two international conferences;;
coauthors from England, France, China
visiting (for a month) at universities in Germany, England, France, USA;




                                           Personal data
62                             MSc program in mathematics: personal data


Name: Peter Hermann

Date of birth: 1953
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, associate professor
Scientific degree (discipline): CSc (mathematics)

Teaching activity (with list of courses taught so far):
Eötvös University (1977– ):
     algebra and number theory (for students in mathematics; lecture, practice)
BSM (1993– )
    Basic and advanced algebra (lecture, practice)
CEU (2004– )
   Basic Algebra I (for Ph.D. students in mathematics)

Other professional activity:
     30 years of teaching experience, more than 10 diploma thesis supervisions, 1 Ph.D.
     (CSc) thesis supervision;
     lectures at international conferences;
     15 publications

Up to 5 selected publications from the past 5 years:


The five most important publications:
1.   On the product of all elements in a finite group (with J. Dénes), Annals of Discrete
     Math. 15 (1982), 107-111. (MR 86c:20024; 20D60(05B15))
2.   Separability properties of finite groups hereditary for certain products (with K. Corrádi
     and L. Héthelyi), Arch. Math. 44 (1985), 210-215. (MR 86d:20025; 20D40 (20D20))
3.   On the product of all nonzero elements of a finite ring, Glasgow Math. J. 30 (1988),
     325-330. (MR 89m:16027; 16A44)
4.   On -quasinormal subgroups in finite groups, Arch. Math. 53 (1989), 228-234.(MR
     90i:20028; 20D40(20D20))
5.   On finite p-groups with isomorphic maximal subgroups, J. Austral. Math. Soc. (Series
     A) 48 (1990), 199-213. (MR 91a:20024; 20D15)

Activity in the scientific community, international relations
     KöMaL (Mathematical and Physical Journal for Secondary Schools; member of the
     Editorial Board in Mathematics), 1988–;




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                               MSc program in mathematics: personal data                       63


Name: Tibor Illés

Date of birth: 1963
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös Loránd University, associate professor
Scientific degree (discipline): phd (mathematics)
Major Hungarian scholarships:

Teaching activity (with list of courses taught so far):
Eötvös University (1992– ):
operations research (for students in (applied) mathematics; lecture, practice)
linear programming (for students in (applied)mathematics; lecture)
nonlinear programming (for students in (applied) mathematics; lecture)
game theory (for students in (applied) mathematics; lecture)
continuous optimization (for students in (applied) mathematics; lecture)
discrete programming (for students in (applied) mathematics; lecture)

Other professional activity:
Research projects: 11 projects in applied mathematics ( 4 times as participant, 7 times as
project head), 5 OTKA projects in basic research (3 times as participant, 2 times as project
head)
Publications: 33 journal articles, 9 chapters in edited volumes, 24 working papers, 21 research
reports,


Up to 5 selected publications from the past 5 years:
1. Akkeles, A. A., Balogh L. and Illés T., New variants of the criss-cross method for
linearly constrained, convex quadratic programming, European Journal of
Operational Research, Vol. 157, No. 1:74-86, 2004.
2. Illés T. and Terlaky T., Pivot Versus Interior Point Methods: Pros and Cons,
European Journal of Operational Research, 140:6-26, 2002.
3. Boratas-Sensoy, Z., Illés T. and Kas P., Entropy and Young Programs: Relations and
Self-concordance, Central European Journal of Operations Research, 10:261-276, 2002.
4. Illés T., Peng, J., Roos, C. and Terlaky T., A Strongly Polynomial Rounding
Procedure Yielding A Maximally Complementary Solution for P*(κ) Linear
Complementarity Problems, SIAM Journal on Optimization, 11:320-340, 2000.
5. Illés T. and Pisinger, D., Upper Bounds on the Covering Number of Galois-planes
with Small Order, Journal on Heuristics, 7:59-76, 2000.


The five most important publications:
1. Illés T., Peng, J., Roos, C. and Terlaky T., A Strongly Polynomial Rounding
   Procedure Yielding A Maximally Complementary Solution for P*(κ) Linear
   Complementarity Problems, SIAM Journal on Optimization, 11:320-340, 2000.




                                             Personal data
64                           MSc program in mathematics: personal data


2. Illés T. and Kassay G., Theorems of the Alternative and Optimality Conditions for
   Convexlike and General Convexlike Programming, Journal of Optimization Theory and
   Applications, 101:243-257, 1999.
3. Illés T. and Kassay G., Farkas Type Theorems for Generalized Convexities, Pure
   Mathematics and Applications 5:225-229, 1994.
4. Illés T., Mayer J. and Terlaky T., Pseudoconvex Optimization for a Special Problem of
   Paint Industry, European Journal of Operations Research 79:537-548, 1994.
5. Illés T., Szőnyi T. and Wettl F., Blocking Sets and Maximal Strong Representative
   Systems in Finite Projective Planes, Proceedings of the Conference "Blocking Sets",
   Giessen, 97-107, 1991.

Activity in the scientific community, international relations
Member of János Bolyai Mathematical Society, Hungarian Operations Research Society,
Mathematical Programming Society, EUROPT WG, EURO Working Group on Continuous
Optimization




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                               MSc program in mathematics: personal data                      65


Name: Ferenc Izsák

Date of birth: 1976
Highest degree (discipline): diploma in pure mathematics
Present employer, position: Eötvös University, teaching assistant
Scientific degree (discipline): PhD (applied mathematics)
Major Hungarian scholarships: -

Teaching activity (with list of courses taught so far):
Eötvös University (2001– ):
analysis (for students in applied mathematics, physics; practice)
introductory mathematics (for students in biology, environmental study, chemistry; lecture,
practice)
partial differential equations (for students in applied and pure mathematics, meteorology;
practice)
finite element methods (for students in the mathematics doctoral school; lecture)
mathematical modeling (for students in applied mathematics; lecture)

Other professional activity:
7 years of teaching experience,
21 publications;

Up to 5 selected publications from the past 5 years:
1. Izsák, F., Lagzi, I.: Simulation of Liesegang pattern formation using a discrete stochastic
   model, Chemical Physics Letters, 371(3-4) (2003), 321-326.
2. Izsák, F.: An existence theorem for a type of functional differential equations with
   infinite delay, Acta Math. Hung., 108(1-2) (2005), 135-151.
3 van der Vegt, J.J.W., Izsák, F., Bokhove, O.: Error analysis of a continuous-
   discontinuous Galerkin finite element method for generalized 2D vorticity dynamics,
   SIAM Journal on Numerical Analysis, 45(4) (2007), 1349-1369.
4. Izsák, F., Harutyunyan, D., van der Vegt, J.J.W.: Implicit a posteriori error estimates for
   the Maxwell equations, Mathematics of Computation, 77(263) (2008), 1355=1386.
5. Harutyunyan, D., Izsák, F., van der Vegt, J.J.W.: Adaptive finite element techniques for
   the Maxwell equations using implicit a posteriori error estimates, Computer Methods in
   Applied Mathematics and Engineering, 197(17-18) (2008), 1620-1638.

The five most important publications
1. Izsák, F., Lagzi, I.: Simulation of Liesegang pattern formation using a discrete stochastic
      model, Chemical Physics Letters, 371(3-4) (2003), 321-326.
2. Izsák, F.: An existence theorem for a type of functional differential equations with
      infinite delay, Acta Math. Hung., 108(1-2) (2005), 135-151.
3. van der Vegt, J.J.W., Izsák, F., Bokhove, O.: Error analysis of a continuous-
      discontinuous Galerkin finite element method for generalized 2D vorticity dynamics,
      SIAM Journal on Numerical Analysis, 45(4) (2007), 1349-1369.
4. Izsák, F., Harutyunyan, D., van der Vegt, J.J.W.: Implicit a posteriori error estimates    for
      the Maxwell equations, Mathematics of Computation, 77(263) (2008), 1355-1386.


                                             Personal data
66                           MSc program in mathematics: personal data


5. Harutyunyan, D., Izsák, F., van der Vegt, J.J.W.: Adaptive finite element techniques for
     the Maxwell equations using implicit a posteriori error estimates, Computer Methods in
     Applied Mathematics and Engineering, 197(17-18) (2008), 1620-1638.

Activity in the scientific community, international relations
     coordinator with the Erasmus – programme (University of Twente)
     active research collaboration with the University of Twente;
     coauthors from the Netherlands, Russian Federation, Armenia;




                                           Personal data
                               MSc program in mathematics: personal data                       67


Name: Tibor Jordán

Date of birth: 1967
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, associate professor
Scientific degree (discipline): DSc (mathematics)
Major Hungarian scholarships: Széchenyi scholarship (2000–2003)

Teaching activity (with list of courses taught so far):
Eötvös University (1991–1994, 2000– ):
computer science, discrete mathematics, graph theory, theory of computing, scheduling
theory, combinatorial algorithms, combinatorial structures, approximation algorithms
Technical University of Budapest (1994–1996):
algebra, analysis, discrete mathematics
University of Odense (1996–1998):
connectedness of graphs
University of Aarhus (1999)
combinatorial optimization, discrete mathematics

Other professional activity:
over 50 reasearch articles, over 200 citations, over 50 conference lectures
coauthor of one book
project leader of one OTKA and one FKFP project
Rényi Kató Prize (1991), ), Grünwald Géza Prize (1996).
managing editor of Combinatorica
long term visits at several universities (Bonn, Amsterdam, Odense, Grenoble, Kyoto, Aarhus)

Up to 5 selected publications from the past 5 years:
A. Berg, T. Jordán, A proof of Connelly's conjecture on 3-connected circuits of the rigidity
   matroid, J. Combinatorial Theory, Ser. B., Vol. 88, 77-97, 2003.
B. Jackson, T. Jordán, Non-separable detachments of graphs, J. Combinatorial Theory, Ser.
    B., Vol. 87, 17-37, 2003.
T. Jordán, Z. Szigeti, Detachments preserving local edge-connectivity of graphs, SIAM J.
    Discrete Mathematics, Vol. 17, No. 1, 72-87 (2003).
B. Jackson, T. Jordán, Connected rigidity matroids and unique realizations of graphs, J.
    Combinatorial Theory, Ser. B., in press
B. Jackson, T. Jordán, Independence free graphs and vertex-connectivity augmentation, J.
    Combinatorial Theory, Ser. B., in press


The five most important publications, besides the ones given above:
T. Jordán, On the optimal vertex-connectivity augmentation, J. Combinatorial Theory, Ser. B.,
    Vol. 63, 8-20, 1995.



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68                           MSc program in mathematics: personal data


A. Frank, T. Jordán, Minimal edge-coverings of pairs of sets, J. Combinatorial Theory, Ser.
    B., Vol. 65, 73-110, 1995.
J. Bang-Jensen, H.N. Gabow, T. Jordán and Z. Szigeti, Edge-connectivity augmentation with
    partition constraints, SIAM J. Discrete Mathematics Vol. 12, No. 2, 160-207 (1999).

Activity in the scientific community, international relations
     Member of the Bolyai János Mathematical Society
     Long term visitor at University of Aarhus (Denmark), Odense University (Denmark),
     Queen Mary College, London (Great Britain), Hiroshima University (Japan).




                                           Personal data
                               MSc program in mathematics: personal data                    69


Name: Alpár Jüttner

Date of birth: 1975
Highest degree (discipline): MSc in mathematics
Present employer, position: Eötvös University, associate professor
Scientific degree (discipline): PhD (mathematics)
Major Hungarian scholarships:

Teaching activity (with list of courses taught so far):
Eötvös University (1998– ):
operations research (for students in mathematics and in informatics; practice)
complexity theory (for students in matematics; practice)

Other professional activity:
5 years of teaching experience, 3 MSc thesis supervisions,
over 10 international conference appearances;
24 publications;
2 international patents;

Up to 5 selected publications from the past 5 years:
[1] Csaba Antal, János Harmatos, Alpár Jüttner, Gábor Tóth, and Lars Westberg. Cluster-
    based resource provisioning method for optical backbone. Journal of Optical Networking,
    5(11):829-840, October 2006.
[2] Alpár Jüttner. On budgeted optimization problems. SIAM Journal on Discrete
    Matemathics, 20(4):880-892, 2006.
[3] Alpár Jüttner. Optimization with additional variables and constraints. Operations Research
    Letters, 33(3):305-311, May 2005.
[4] Alpár Jüttner and Ádám Magi. Tree based broadcast in ad hoc networks. Mobile Networks
    and Applications (MONET) - Special Issue on ―WLAN Optimization at the MAC and
    Network Levels‖, 10(5):753-762, oct 2005.
[5] Alpár Jüttner, András Orbán, and Zoltán Fiala. Two new algorithms for UMTS access
    network topology design. European Journal of Operational Research, 164(2):456-474,
    July 2005.

The five most important publications:

[1] Alpár Jüttner. On budgeted optimization problems. SIAM Journal on Discrete
    Matemathics, 20(4):880-892, 2006.
[2] Alpár Jüttner. Optimization with additional variables and constraints. Operations Research
    Letters, 33(3):305-311, May 2005.
[3] Alpár Jüttner, András Orbán, and Zoltán Fiala. Two new algorithms for UMTS access
    network topology design. European Journal of Operational Research, 164(2):456-474,
    July 2005.
[4] Alpár Jüttner, István Szabó, and Áron Szentesi. On bandwidth efficiency of the hose
    resource management model in virtual private networks. In Infocom. IEEE, April 2003.
[5] Alpár Jüttner, Balázs Szviatovszki, Ildikó Mécs, and Zsolt Rajkó. Lagrange relaxation
    based method for the QoS routing problem. In Infocom. IEEE, April 2001.


                                             Personal data
70                           MSc program in mathematics: personal data


Activity in the scientific community, international relations
      2005-2008: COST293 Management Comittee member
     2007-2009: Maire Curie Research Fellowship at University of Bedfordshire, Luton, UK




                                           Personal data
                               MSc program in mathematics: personal data                         71


Name: János Karátson

Date of birth: 1966
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, associate professor
Scientific degree (discipline): PhD (mathematics)
Major Hungarian scholarships: Magyary scholarship (1999-2002), Bolyai scholarship (2002–
2005 and 2007-2010)


Teaching activity (with list of courses taught so far): at Eötvös University (since 1990):
functional analysis (for students in applied mathematics, basic level and specialization
in numerics; lecture, practice),
partial differential equations (for students in meteorology; lecture, practice),
ordinary differential equations (for students in physics; lecture, practice),
analysis, ordinary differential equations (for students in applied mathematics; practice)

MSc and PhD thesis supervisions: for students in (applied) mathematics

In English: translation of scientific texts (for Hungarian students), Mathematics (for foreign
students)

Other professional activity:
52 papers and 1 monograph;
regular lectures in international conferences;
international collaborations (Netherlands, Bulgaria, USA, Sweden, Finland);

Up to 5 selected publications from the past 5 years:
[1] Axelsson, O., Karátson J., On the superlinear convergence of the conjugate gradient
method for nonsymmetric normal operators, Numer. Math. 99 (2004), 197-223.
[2] Karátson J., Lóczi L., Sobolev gradient preconditioning for the electrostatic potential
equation, Comput. Math. Appl. 50 (2005), pp. 1093-1104.
[3] Karátson J., Korotov, S., Discrete maximum principles for finite element solutions of
nonlinear elliptic problems with mixed boundary conditions, Numer. Math 99 (2005), No. 4,
669-698.
[4] J. Karátson, J. W. Neuberger, Newton's method in the context of gradients, Electron. J.
Diff. Eqns. Vol. 2007(2007), No. 124, pp. 1-13.
[5] Axelsson, O., Karátson J., Mesh independent superlinear PCG rates via compact-
equivalent operators, SIAM J. Numer. Anal., 45 (2007), No.4, pp. 1495-1516.


The five most important publications:
[1] Faragó I., Karátson J., Numerical solution of nonlinear elliptic problems via
preconditioning operators: theory and application. Advances in Computation, Volume 11,
NOVA Science Publishers, New York, 2002.


                                             Personal data
72                           MSc program in mathematics: personal data


 [2] Karátson J., Faragó I., Variable preconditioning via quasi-Newton methods for nonlinear
problems in Hilbert space, SIAM J. Numer. Anal. 41 (2003), No. 4, 1242-1262.
[3]-[5]: same as above

Activity in the scientific community, international relations:
Collaboration with Prof. O. Axelsson (Nijmegen - Uppsala), I. Lirkov (Sofia), S. Korotov
   (Helsinki), J. Neuberger (North Texas).
Regular refereeing for international papers.
Membership in editorial board of Numer. Lin. Algebra.
Organization in two international conferences.
Visiting professorship in Helsinki.
Reviewing for AMS Mathematical Reviews and Zentralblatt.




                                           Personal data
                               MSc program in mathematics: personal data                      73


Name: Gyula Károlyi

Date of birth: 1964
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, associate professor
Scientific degree (discipline): CSc (mathematics)
Major Hungarian scholarships: Széchenyi professor's scholarship (2000–2003)
     Bolyai Fellowship (2003–2006, 2007–2010)

Teaching activity (with list of courses taught so far):
Eötvös University (1985– ):
     algebra, number theory (for students in mathematics; lecture, practice)
     linear algebra (for students in informatics; practice)
     algebraic numbre theory, combinatorial geometry and number theory (for students in
     mathemtics and problem soling seminar)
ETH Zürich (2001–2002)
    graph theory (for students in mathematics, informatics, engineering; lecture and
    practice)
University of Memphis
     business calculus (for general audience; lecture)
     combinatorial number theory (for students in mathematics; lecture)

Other professional activity:
     23 years of teaching experience, 4 diploma thesis supervisions
     coordinator and suervisor of undergraduate research at Eötvös University (1996–2006)
     over 80 letctures at international conferences and seminars in renowned institutions
     around the world
     35 publications in refereed international journals and volumes

Up to 5 selected publications from the past 5 years:
1.   Károlyi, Gy., The Erdős–Heilbronn problem in abelian groups, Israle Journal of
     Mathematics 139 (2004), 349–359.
2.   Károlyi, Gy., A compatness argument in the additive theory and the polynomial method,
     DiscreteMathematics 302 (2005), 124–144.
3.   Károlyi, Gy., An inverse theorem for the restricted set addition in abelian groups,
     Journal of Algebra 290 (2005), 557–593.
4.   Károlyi, Gy., Cauchy–Davenport theorem in group extensions, L’Enseignement
     Mathématique 51 (2005), 239–254.
5.   Károlyi, Gy., A note on the Hopf–Stiefel function, European Journal of Combinatorics
     27 (2006), 1135–1137.

The five most important publications:
1.   Károlyi, Gy., Geometric discrepancy theorems in higher dimensions, Studia Scientiarum
     Mathematicrum Hungarica 30 (1995), 59–94.
2.   Károlyi, Gy., Irregularities of point distributions relative to homothetic convex bodies I.,
     Monatshefte für Mathematik 120 (1995), 247–279.

                                             Personal data
74                           MSc program in mathematics: personal data


3.   Dasgipta, S., Károlyi, Gy., Serra, O., Szegedy, B.: Transersals of additive latin squares,
     Israel Journal of Mathematics 126 (2001), 17–28.
4.   Károlyi, Gy., An inverse th theorem for the restricted set addition in abelian groups,
     Journal of Algebra 290 (2005), 557–593.
5.   Károlyi, Gy., Cauchy–Davenport theorem in group extensions, L’Enseignement
     Mathématique 51 (2005), 239–254.

Activity in the scientific community, international relations
     Athematical and Physical Journal for Secondary Schools (editor), 1988– ;
     organizer of an international conference, a workshop and a national undergraduate
     research conference;
     member of the János Bolyai Mathematical Society and the Hungarian Humboldt
     Assocation;
     chair of the Hungarian Mathematical Contest (1998–2002);
     member of the granting committee of the Hungarian NSRF (OTKA), 2008–2010;
     coauthors from Canada, the Czech Republic, Germany, Spain, Japan, Switzerland and
     the US;
     visiting professor at universities in Switzerland and in the US;
     visiting reserach fellow in France, in the Netherlands and in the US;




                                           Personal data
                               MSc program in mathematics: personal data                       75


Name: Tamás Keleti

Date of birth: 1970
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, associate professor
Scientific degree (discipline): PhD (mathematics)
Major Hungarian scholarships: Széchenyi Professor Scholarship (2000–2003)

Teaching activity (with list of courses taught so far):
Eötvös University (1992– ):
analysis (for students in mathematics; lecture, practice)
real functions (for students fourth and fifth year students in mathematics; lecture)
problem solving seminar in real analysis (for students in mathematics)
special courses (for students in mathematics): intuitive topology, discrete dynamical systems,
mathematics of fractals

BSM (1999– )
Real functions and measures (lecture, practice)

Other professional activity:
16 years of teaching experience, 6 diploma thesis supervisions, 1 Ph.D. thesis supervisions;
lectures at international conferences;
26 publications;

Up to 5 selected publications from the past 5 years:
1. Udayan B. Darji and TK: Covering the real line with translates of a compact set, Proc.
      Amer. Math. Soc. 131 (2003), 2593-2596.
2. Márton Elekes and TK: Borel sets which are null or non-sigma-finite for every translation
      invariant measure, Adv. Math. 201 (2006), 102-115.
3. Gyula Károlyi, TK, Géza Kós and Imre Ruzsa: Periodic decomposition of integer valued
      functions, Acta Math. Hungar., to appear.
4. TK: Periodic decomposition of measurable integer valued functions, J. Math. Anal. Appl.
      337 (2008), 1394-1403.
5. Bálint Farkas, Viktor Harangi, TK and Szilárd György Révész: Invariant decomposition of
      functions with respect to commuting invertible transformations , Proc. Amer. Math Soc.
      136 (2008), 1325-1336.

The five most important publications:
1. TK: Difference functions of periodic measurable functions, Fund. Math. 157 (1998), no. 1,
     15--32.
2. TK and David Preiss: The balls do not generate all Borel sets using complements and
     countable disjoint unions, Math. Proc. Cambridge Philos. Soc. 128 (2000), no. 3, 539-
     547.
3. Udayan B. Darji and TK: Covering the real line with translates of a compact set, Proc.
     Amer. Math. Soc. 131 (2003), 2593-2596.
4. Márton Elekes and TK: Borel sets which are null or non-sigma-finite for every translation
     invariant measure, Adv. Math. 201 (2006), 102-115.

                                             Personal data
76                           MSc program in mathematics: personal data


5. Bálint Farkas, Viktor Harangi, TK and Szilárd György Révész: Invariant decomposition of
      functions with respect to commuting invertible transformations , Proc. Amer. Math Soc.
      136 (2008), 1325-1336.

Activity in the scientific community, international relations
organizer and often leader the team of the Eötvös University at the International Mathematics
Competition, 1998- ;
coauthors from England, USA, Czech Republic and Greece;
Royal Society/NATO Postdoc scholarship at the University College London, 1997/98;
visiting research instructor at the Michigan State University, 1998/99




                                           Personal data
                               MSc program in mathematics: personal data                     77


Name: Tamás Király

Date of birth: 1975.03.19
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös Loránd University, assistant professor
Scientific degree (discipline): phd (mathematics)
Major Hungarian scholarships: Öveges scholarship, OM Postdoctoral fellowship

Teaching activity (with list of courses taught so far):
Eötvös University (1999– ):
Integer Programming I-II (for students in (applied)mathematics; lecture)
Matroid Theory (for students in (applied)mathematics; lecture)
Applied Module (Combinatorial Optimization) (for students in applied mathematics; practice)
Operations Research (for students in applied mathematics and informatics; practice)

Other professional activity:
Research fellow in the MTA-ELTE Egerváry Research Group on Combinatorial Optimization
Research projects: Öveges project ―Structural properties of Networks‖; joint research with
France Telecom; participation in several OTKA projects
Publications: 9 journal articles, 10 research reports


Up to 5 selected publications from the past 5 years:
1. A. Frank, T. Király, M. Kriesell, On decomposing a hypergraph into k connected sub-
hypergraphs, Discrete Applied Mathematics 131 (2003), 373-383.
2. A. Frank, T. Király, Z. Király, On the orientation of graphs and hypergraphs, Discrete
Applied Mathematics 131 (2003), 385-400.
3. A. Frank, T. Király, Combined connectivity augmentation and orientation problems,
Discrete Applied Mathematics 131 (2003), 401-419.
4. T. Király, Covering symmetric supermodular functions by uniform hypergraphs, Journal of
Combinatorial Theory Series B 91 (2004), 185-200.
5. T. Király, J. Pap, Total dual integrality of Rothblum's description of the stable marriage
polyhedron, Mathematics of Operations Research 33(2) (2008), 283-290.

The five most important publications:
1. A. Frank, T. Király, M. Kriesell, On decomposing a hypergraph into k connected sub-
hypergraphs, Discrete Applied Mathematics 131 (2003), 373-383.
2. A. Frank, T. Király, Z. Király, On the orientation of graphs and hypergraphs, Discrete
Applied Mathematics 131 (2003), 385-400.
3. A. Frank, T. Király, Combined connectivity augmentation and orientation problems,
Discrete Applied Mathematics 131 (2003), 401-419.
4. T. Király, Covering symmetric supermodular functions by uniform hypergraphs, Journal of
Combinatorial Theory Series B 91 (2004), 185-200.
5. T. Király, J. Pap, Total dual integrality of Rothblum's description of the stable marriage
polyhedron, Mathematics of Operations Research 33(2) (2008), 283-290.

Activity in the scientific community, international relations

                                             Personal data
78                       MSc program in mathematics: personal data


Participation in ADONET Marie Curie Research Training Network




                                       Personal data
                               MSc program in mathematics: personal data                       79


Name: Zoltán Király

Date of birth: 1963
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, associate professor
Scientific degree (discipline): PhD (mathematics)
Major Hungarian scholarships: Bolyai scholarship (1999–2002)

Teaching activity (with list of courses taught so far):
Eötvös University (1987– ):
Discrete mathematics (for students in mathematics and in informatics; lecture, practice)
Parallel algorithms (for students in mathematics and in informatics; lecture)
Data structures (for students in mathematics and in informatics; lecture)
Algorithms (for students in mathematics and in informatics; lecture)
Complexity theory (for students in mathematics and in informatics; lecture)
Graph theory (for students in mathematics; lecture, practice)
Combinatorial optimization (for students in informatics; lecture)
Introduction to computer science (for students in informatics; lecture, practice)
Interactive proofs (for students in mathematics; lecture)
Complexity seminar (for students in mathematics and in informatics; seminar)
Applied discrete mathematics seminar (for students in mathematics and in informatics;
seminar)

CEU PhD school (2007 ):
Complexity theory (lecture)



Other professional activity:
21 years of teaching experience, 9 diploma thesis supervisions, 2 Ph.D. thesis supervisions;
over 20 lectures at international conferences;
16 publications in refereed journals;
1 international patent.

Up to 5 selected publications from the past 5 years:

A. Frank, T. Király, Z. Király: ,,On the orientation of graphs and hypergraphs'', Discrete
Applied Mathematics 131 (2003), pp. 385-400.

M. Kano, G. Y. Katona, Z. Király: ,,Packing paths of length at least two'', Discrete
Mathematics, 283, (2004), pp. 129-135.

V. Grolmusz, Z. Király: ,,Generalized Secure Routerless
Routing'', Lecture Notes in Computer Science 3421,
Networking - ICN 2005, part II, eds: P. Lorenz, P. Dini, (2005), pp. 454-462.

Z. Király, Z. Szigeti: ,,Simultaneous well-balanced orientations
 of graphs'', JCT B 96, Issue 5, (2006), pp. 684-692.

                                             Personal data
80                            MSc program in mathematics: personal data




A. Frank, Z. Király, B. Kotnyek: ,,An Algorithm for Node-Capacitated Ring Routing'',
Operations Research Letters, 35, Issue 3, (2007), pp. 385-391.


The five most important publications:
A. Gyárfás, Z. Király, J. Lehel: ,,On-line 3-chromatic graphs. I. Triangle--free graphs'',
SIAM J. Discr. Math. 12, (1999), pp. 385-411.

A. Frank, Z. Király: ,,Graph Orientations with Edge-connection and Parity Contstraints'',
Combinatorica 22, (2002), pp. 47-70.

A. Frank, T. Király, Z. Király: ,,On the orientation of graphs and hypergraphs'', Discrete
Applied Mathematics 131 (2003), pp. 385-400.

M. Kano, G. Y. Katona, Z. Király: ,,Packing paths of length at least two'', Discrete
Mathematics, 283, (2004), pp. 129-135.

Z. Király, Z. Szigeti: ,,Simultaneous well-balanced orientations
 of graphs'', JCT B 96, Issue 5, (2006), pp. 684-692.



Activity in the scientific community, international relations
     Member of BJMT, ICA, EATCS;
     visiting researcher at Rutgers, Princeton, Yale.




                                            Personal data
                               MSc program in mathematics: personal data                       81


Name: Emil Kiss

Date of birth: 1956
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, full professor, Head of the Department of
Algebra and Number Theory
Scientific degree (discipline): DSc (mathematics), dr habil
Major Hungarian scholarships: Széchenyi scholarship (1998–2001)

Teaching activity (with list of courses taught so far):
Eötvös University (from 1978, full time since 1989):
     Classical, linear, abstract, universal algebra and number theory at various levels (for
     students in mathematics and in teacher training; lecture, practice).
La Trobe University, Australia (1986, three semesters):
     algebra, complex analysis, foundations of mathematics (for students in mathematics and
     applied mathematics).
University of Illinois at Chicago (1990, two semesters):
     linear algebra, differential equations, universal algebra (for students in mathematics and
     applied mathematics).
BSM
      two courses (abstract algebra; group theory)

Other professional activity:
      30 years of teaching experience, 2 diploma thesis supervisions;
      over 10 invited plenary lectures at international conferences;
      main advisor and organizer of the Students Scientific Association (1991-1997).
      Committee member for the National High School Mathematical Competition.
      Chairman of the BSc Committee of Education at ELTE.
      39 publications with over 200 citations;

Up to 5 selected publications from the past 5 years:
1)    K. A. Kearnes and E. W. Kiss, Residual smallness and weak centrality, Journal of
      Algebra and Computation, 13(2003), 35-59.
2)    K. A. Kearnes and E. W. Kiss, The triangular principle is equivalent to the triangular
      scheme, Algebra Universalis, 54(2005), 373-383.
3)    E. W. Kiss, M. A. Valeriote, On tractability and congruence distributivity. Logical
      Methods in Computer Science, 3(2:6, 2007), 20 pages.
4)    Emil Kiss, Introduction to algebra, TypoTeX, 2007 (textbook, in Hungarian), 1000
      pages.

The five most important publications:
1)    A. Day and E.W. Kiss, Frames and rings in congruence modular varieties, Journal of
      Algebra, 109 (1987), no. 2, 479-507.
2)    E. W. Kiss, M. A. Valeriote, Abelian algebras and the Hamiltonian property, Journal of
      Pure and Applied Algebra 87:1 (1993), 37-49.


                                             Personal data
82                           MSc program in mathematics: personal data


3)   K. A. Kearnes, E. W. Kiss, M. A. Valeriote, Minimal sets and varieties, Trans. Amer.
     Math. Soc. 350:1 (1998) 1-41.
4)   K. A. Kearnes, E. W. Kiss, Finite algebras of finite complexity, Discrete Math. 207:1-3
     (1999) 89-135.
5)   K. A. Kearnes, E. W. Kiss, M. A. Valeriote, A geometric consequence of residual
     smallness, Ann. Pure Appl. Logic 99:1-3 (1999) 137-169.

Activity in the scientific community, international relations
     reviewer for Mathematical Reviews since 1979
     editor of Algebra Universalis (Birkhauser) since 1998.
     board of the Bolyai research fellowship: member since 2007.
     organizer of the Budapest Erdős Workshop on Tame Congruence Theory;
     coauthors from USA, Canada, Germany, Poland, Russia, Hungary;
     visiting professor at universities in Germany, Australia, Canada, USA.




                                           Personal data
                               MSc program in mathematics: personal data                       83


Name: György Kiss

Date of birth: 1961
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, associate professor
Scientific degree (discipline): Ph.D. (mathematics)

Teaching activity (with list of courses taught so far):
Eötvös University (1987–):
Geometry (for students in mathematics and applied mathematics; lecture, practice)
Finite Geometries (for students in mathematics; lecture)
Discrete and Combinatorial Geometry (for students in mathamatics; lecture)
Applied Geometry (for students in geography; lecture)
University of Szeged (1997– , part time):
Projective Geometry (lecture, practice)
Finite Geometries and Coding Theory (lecture)
Topology (lecture)

Other professional activity:
24 years of teaching experience, more than 20 diploma thesis supervisions,
1 Ph.D. supervision; more than 20 lectures at international conferences;
32 publications;

Up to 5 selected publications from the past 5 years:
1. Kiss, Gy., Marcugini, S., and Pambianco, F.: On blocking sets of inversive planes, J.
Comb. Designs 13 (2005), 268-275.
2. Bezdek, K., Böröczky, K., and Kiss, Gy.: Ont he successive illumination parameters of
conves bodies, Periodica Math. Hung. 53 (2006), 71-82.
3. Blokhuis, A., Kiss, Gy., Kovács, I., Malnič, A., Marušič, D. and Ruff, J.: Semiovals
contained in the union of three concurrent lines, J. Comb. Designs 15 (2007), 491-501.
4. Kiss, Gy.: Small semiovals in PG(2,q), J. Geom. 88 (2008), 110-115.
5. Kiss, Gy.: A survey on semiovals, Contrib. Discrete Math. 3 (2008), 81-95.


The five most important publications:
1. Hirschfeld, J. W. P. and Kiss, Gy.: Tangent sets in finite planes, Discrete Math. 155
    (1996), 107-119.
2. Artzy, R. and Kiss, Gy.: Shape-regular polygons in finite planes, J. Geom. 57 (1996), 20-
    26.
3. Kiss, Gy.: Illumination problems and codes, Periodica Math. Hung. 39 (1999), 65-71.
4. Kiss, Gy.: One-factorization of complete multigraphs and quadrics in PG(2,q), J. Comb.
    Designs 10 (2002), 139-143.
5. Jagos, I., Kiss, Gy., and Pór, A.: On the intersection of Baer subgeometries of PG(n,q2),
    Acta Sci. Math. (Szeged) 69 (2003), 419-429.



                                             Personal data
84                          MSc program in mathematics: personal data


Activity in the scientific community, international relations
     member of the Bolyai Mathematical Society and the American Mathematical Society;
     exterior member of the Centre of Computational and Discrete Geometry (University of
     Calgary;
     coauthors from England, France, Israel, Italy, The Netherlands, Slovenia and South
     Africa;
     visiting professor at universities in Canada, England, Italy and Slovenia;




                                          Personal data
                               MSc program in mathematics: personal data                     85


Name: Péter Komjáth

Date of birth: 1953
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, full professor
Scientific degree (discipline): DSc (mathematics)
Major Hungarian scholarships: Széchenyi scholarship (1997–2000)

Teaching activity (with list of courses taught so far):
Eötvös University (1974– ):
Algebra, number theory, combinatorics, set theory, logic (for students in mathematics; lecture,
practice)
BSM (1985– ):
Set theory, logic, graph algorithms, automata theory (lecture)

Other professional activity:
34 years of teaching experience, 15 diploma thesis supervisions,
over 20 lectures at international conferences;
107 publications;
1 book

Up to 5 selected publications from the past 5 years:
1. P. Komjáth, S. Shelah: Finite subgraphs of uncountably chromatic graphs, Journal of
Graph Theory, 49(2005), 28-38.
2. M. Foreman, P. Komjáth: The club guessing ideal (commentary on a theorem of Gitik and
Shelah), Journal of Math. Logic, 5(2005), 99-147.
3. P. Komjáth, V. Totik: Problems and Theorems in Set Theory, Springer, 2006.



The five most important publications:
1. J. E. Baumgartner, P. Komjath: Boolean algebras in which every chain and antichain is
    countable, Fundamenta Mathematicae, CXI(1981), 125-131.
2. P. Komjáth: A decomposition theorem for Rn, Proc. Amer. Math. Soc. 120(1994), 921-927.
3. P. Komjáth, A consistency result concerning set mappings, Acta Math. Hung. 64, (1994)
    93-99.
4. G. Cherlin, P. Komjáth, There is no universal countable pentagon free graph, Journal of
    Graph Theory 18 (1994), 337-341.
5. Z. Furedi, P. Komjáth: On the existence of countable universal graphs, Journal of Graph
    Theory, 25 (1997), 53-58.

Activity in the scientific community, international relations
   organizer of ten international conferences;
   member and president of various commitees of the Bolyai Mathematical Society;



                                             Personal data
86                             MSc program in mathematics: personal data


Name: Géza Kós

Date of birth: 1967
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, associate professor
Scientific degree (discipline): PhD (mathematics)
Major Hungarian scholarships: Bolyai scholarship (2005–2008)


Teaching activity (with list of courses taught so far):
Eötvös University (1991– ):
real analysis (for students in matehmatics; lectures and practice)
real analysis (for students in physics; practice)
complex analyisis (for students in matehmatics; practice)
geometry (for students in matehmatics; practice)

Other professional activity:
17 years of teaching experience;
4 lectures at international conferences;
20 publications;
2 international patents;

Up to 5 selected publications from the past 5 years:
1.    Floater M. S., Kós G., Reimers M: Mean value coordinates in 3D, Computer-Aided
      Geometric Design 22 (2005), 623–631
2.    Floater M. S., Hormann K., Kós G.:A general construction of barycentric coordinates
      over convex polygons, Advances in Computational Mathematics 244 (2006) 311-331.
3.    Kós G.: Two Turán type inequalities, Acta Mathematica Hungarica Online first, 2008
4.    Károlyi Gy., Keleti T., Kós G., Ruzsa I.:Periodic decomposition of integer valued
      functions, Acta Mathematica Hungarica Online First, 2007.

The five most important publications:
1.    Borwein P., Erdélyi T., Kós G.: Littlewood-type problems on [0,1], Proc. London Math.
      Soc. 3 (79), 1999, 22–46
2.    Kós G., Martin R. R., Várady T.: Methods to recover constant radius rolling ball blends
      in reverse engineering, Computer Aided Geometric Design 17, No. 2 (2000), 127--160
3.    Kós G.: On the constant factor in Vinogradov's Mean Value Theorem, Acta Arithmetica,
      97. No. 2 (2001), 99--101
4.    Kós, G.: An algorithm to triangulate surfaces in 3D using unorganised point clouds,
      Computing Suppl 14, May 2001, 219--232
5.    loater M. S., Kós G., Reimers M: Mean value coordinates in 3D, Computer-Aided
      Geometric Design 22 (2005), 623--631

Activity in the scientific community, international relations
     member of the Problem Selection Committee of the International Mathematical Olympiad,
     2006-


                                             Personal data
                      MSc program in mathematics: personal data                  87


member      of    the    Problem     Selection  Committee     of the  International
MathematicalCompetition for University Students (IMC), 1998-;
chairman of the jury of the Vojtech Jarnik International Mathematical Competition,
2002-2006;
KöMaL, 1986– ;
Kürschák Competition committee, 1990-;
secretary of the Schweitzer competition committee 1992.




                                    Personal data
88                             MSc program in mathematics: personal data


Name: Antal Kováts

Date of birth: 1949
Highest degree (discipline): secondary school teacher of mathematics
Present employer, position: Generali-Providencia Zrt., chief actuary, and Eötvös Loránd
University, associate professor
Scientific degree (discipline): CSc, mathematics
Major Hungarian scholarships: –

Teaching activity (with list of courses taught so far):
Probability theory, Statistics, Stochastic processes, Life contingencies – 35 years of teaching
experience

Other professional activity:
17 years activity as an actuary, chief actuary from 1994

Up to 5 selected publications from the past 5 years:



The five most important publications:
On the generalized Bernstein polynomials. Annales Univ. Sci. Budapest, Sectio Math., 19
   (1976), 93-98.
On the deviation of distributions of sums of independent integer valued random variables. In:
   F. Konecny, J. Mogyoródi, W. Wertz (Eds.) Probability and Statistical Decision Theory
   (Proceedings of 4th Pannonian Symposium on Math. Stat., Bad Tatzmannsdorf, Austria,
   1983). Akadémiai Kiadó, Budapest, 1985, Vol. A, 219-229.
Asymptotic expansions for approximations by generalized Poisson distribution. Annales Univ.
   Sci. Budapest, Sectio Comp., 7 (1987), 99-102. (in Russian)
Aging properties of certain dependent geometric sums. J. Appl. Probab. 29 (1992) 655–666.
   (with T. F. Móri)
Aging solutions of certain renewal type equations. In: J. Galambos, I. Kátai (Eds.) Probability
   Theory and Applications, Essays to the Memory of József Mogyoródi. Kluwer, Dordrecht,
   1992, 125–141. (with T. F. Móri)

Activity in the scientific community, international relations:
Hungarian Actuarial Society (HAS), president 2000–2003,
HAS, board member 2003–




                                             Personal data
                               MSc program in mathematics: personal data                       89


Name: János Kristóf

Date of birth: 1953
Highest degree (discipline): diploma in physics
Present employer, position: Eötvös Loránd University, Department of Applied Analysis and
Computational Mathematics, associate professor
Scientific degree (discipline): CSc (mathematics)
Major Hungarian scholarships:

Teaching activity (with list of courses taught so far):
Eötvös Loránd University (1978– ):
Analysis (for students in physiscs; practice): 15 years
Analysis (for students in physiscs; lecture): 12 years
Topological vector spaces (for students in mathematics; lecture): 5 years
Banach algebras (for students in mathematics; lecture): 14 years
Geometric functional analysis (for students in mathematics; lecture): 14 years
C*-algebras (for students in mathematics; lecture): 10 years
Harmonic analysis (for students in mathematics; lecture): 14 years


Other professional activity:
30 years of teaching experience, 6 diploma thesis supervisions, 3 Ph.D. thesis supervisions;
17 publications;

Up to 5 selected publications from the past 5 years:
1. A characterization of von Neumann-algebras, Acta Sci. Math., 2006. (submitted)
2. A noncommutative spectral theorem for GW*-algebras, Studia Sci. Math., 2006.
    (submitted)
3. On the ultraspectrality of GW*-algebras, Acta Sci. Math., 2007-2008 (in preparation)
4. Non-unital GW*-algebras, Studia Sci. Math., 2008 (in preparation)
5. Elements of mathematical analysis, Vols I-IV, 2003-2008, Hungarian online material at
    address http://www.cs.elte.hu/~krja

The five most important publications:
1. Ortholattis linéarisables, Acta Sci. Math., 49 (1985)
2. C*-norms defined by positive linear forms, Acta Sci. Math., 50 (1986)
3. On the projection lattice of GW*-algebras, Studia Sci. Math., 22 (1987)
4. Commutative GW*-algebras, Acta Sci. Math., 52 (1988)
5. Spectrality in C*-algebras, Acta Sci. Math, 62 (1996)

Activity in the scientific community, international relations




                                             Personal data
90                             MSc program in mathematics: personal data


Name: Miklos Laczkovich

Date of birth: 1948
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, professor
Scientific degree (discipline): MHAS

Teaching activity (with list of courses taught so far):
Eötvös University (1971– ):
analysis (for students in mathematics; lecture, practice)
analysis (for students in mathematics education; lecture, practice)
University College London (2001-):
Mathematics in economics (for students in mathematics; lecture)
BSM (1985-86):
Conjecture and proof (lecture, practice)

Other professional activity:
38 years of teaching experience, 20 diploma thesis supervisions, 4 Ph.D. thesis supervisions;
over 30 lectures at international conferences; about 120 publications.

Up to 5 selected publications from the past 5 years:
1. M. Laczkovich, The removal of pi from some undecidable statements involving elementary
     functions, Proc. Amer. Math. Soc. 131 (2003), no. 7, 2235-2240.
2. M. Laczkovich, Configurations with rational angles and Diophantine trigonometric
    equations. In: B. Aronov, S. Basu, J. Pach and M. Sharir (Editors): Discrete and
    Computational Geometry. The Goodman-Pollack Festschrift. Springer 2003, pp. 571-
    595.
3. M. Laczkovich, Linear functional equations and Shapiro's conjecture, L'Enseignement
    Math\'ematique 50 (2004), 103-122.
4. M. Laczkovich and L. Szekelyhidi, Spectral synthesis on discrete Abelian groups, Proc.
     Cambridge Phil. Soc. 143 (2007), 103-120.
5. S. Gao, S. Jackson, M. Laczkovich and R. D. Mauldin, On the unique representation of
      families of sets, Trans. Amer. Math. Soc. 360 (2008), 939-958.

The five most important publications:
1. M. Laczkovich and D. Preiss, alpha-Variation and transformation into C^n functions,
    Indiana Univ. Math. J. 34 (1985), 405-424.
2. M. Laczkovich, Equidecomposability and discrepancy; a solution of Tarski's circle-
    squaring problem, J. reine und angew. Math. (Crelle's J.) 404 (1990), 77-117.
3. M. Laczkovich, Uniformly spread discrete sets in R^d , J. London Math. Soc. 46 (1992),
     39-57.
4. M. Laczkovich, The difference property. In: Paul Erdos and his Mathematics (editors: G.
     Halasz, L. Lovasz, M. Simonovits and V. T. Sos), Springer, 2002. Vol. I, 363-410.


                                             Personal data
                             MSc program in mathematics: personal data                 91


5. M. Laczkovich, Paradoxes in measure theory. In: Handbook of Measure Theory (editor: E.
     Pap), Elsevier, 2002. Vol. I, 83-123.

Activity in the scientific community, international relations
Formal member of the granting committee of the Szechenyi Professor Scholarship;
formal member of the plenum of the Hungarian Accreditation Committee; formal member of
    the
DSc committee of the HAS, formal member
of the granting committee of the Hungarian NSRF (OTKA).
Head of the Mathematics PhD School of the Eotvos University,
head of the Department of Analysis of the Eotvos University.
Visiting professor at universities in Italy, the UK and the USA.




                                           Personal data
92                           MSc program in mathematics: personal data


Name: Gyula Lakos

Date of birth: 1973
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, assistant
Scientific degree (discipline): PhD (mathematics)
Major Hungarian scholarships: –

Teaching activity (with list of courses taught so far):
Eötvös University (2004– ):
geometry (practice), differential geometry (practice)
differential forms (lecture), general structures in differential geometry (lecture)
Northwestern University(2003–2004):
Linear Algebra, Multivariable Calculus, Differential Equations (lecture, practice)
Massachusetts Institute of Technology(1998–2003):
Multivariable Calculus (recitation), Advanced Mathematical Methods for Engineers (lecture),
Summer Program in Undergraduate Research (coordinating mentor)

Other professional activity: 10 years of teaching experience, 7 preprints, several lecture notes

Up to 5 selected publications from the past 5 years:
1. Lakos, Gy.: Notes on Lebesgue integration, lecture notes, arXiv:math.FA/0506185
2. Lakos, Gy.: On the naturality of the Mathai-Quillen formula, to appear in Studia Math. Sci.
    Hung.
3. Lakos, Gy.: Self-stabilization in certain infinite-dimensional matrix algebras, preprint,
    arXiv:math.KT/0506059
4. Lakos, Gy.: Spectral calculations on locally convex vector spaces, preprint,
    arXiv:math.FA/0611171
5. Lakos, Gy.: Factorization of Laurent series over commutative rings, preprint,
    arXiv:0709.4107

The five most important publications:
1. Lakos, Gy.: Notes on Lebesgue integration, lecture notes, arXiv:math.FA/0506185
2. Lakos, Gy.: On the naturality of the Mathai-Quillen formula, to appear in Studia Math. Sci.
    Hung.
3. Lakos, Gy.: Self-stabilization in certain infinite-dimensional matrix algebras, preprint,
    arXiv:math.KT/0506059
4. Lakos, Gy.: Spectral calculations on locally convex vector spaces, preprint,
    arXiv:math.FA/0611171
5. Lakos, Gy.: Factorization of Laurent series over commutative rings, preprint,
    arXiv:0709.4107

Activity in the scientific community, international relations
     member of the János Bolyai Mathematical Society, (1992–)



                                           Personal data
                               MSc program in mathematics: personal data                            93


Name: László Lovász

Date of birth: 1948
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, professor, director
Scientific degree (discipline): DrSc (mathematics),
      Member of the Hungarian Academy of Science: 1979
Major Hungarian scholarships:

Teaching activity (with list of courses taught so far):
Eötvös University (1971–75, 1982–):
geometry (for students in mathematics; practice), finite mathematics (for students in
mathematics; lecture), combinatorial optimization (for students in mathematics; lecture),
complexity of algorithms (for students in mathematics and informatics; lecture), random
methods and algorithms (for students in mathematics; lecture), topological methods in
combinatorics (for students in mathematics; lecture), algebraic and probabilistic methods in
combinatorics (for students in mathematics; lecture)
József Attila University (1975-1982)
geometry (for students in mathematics; lecture and practice), differential geometry (for
students in mathematics; lecture), discrete optimization (for students in mathematics; lecture
and practice)
Yale University (1993-1999)
introduction to mathematics (lecture), mathematical tools for computer science (lecture)
algorithms (lecture), algebraic methods in combinatorics (lecture), complexity of algorithms
(lecture)
BSM (1987– )discrete mathematics (lecture), geometric graph theory (lecture)

Other professional activity:
36 years of teaching experience, 10 Ph.D. thesis supervisions; over 50 lectures at international
conferences; 250 research publications; 2 US patents; 20 expository articles

Up to 5 selected publications from the past 5 years:
L. Lovász, B. Szegedy: Limits of dense graph sequences, J. Comb. TheoryB 96 (2006), 933–957.
L. Lovász, K. Vesztergombi, U. Wagner, E. Welzl: Convex quadrilaterals and k-sets, in: Towards a
      Theory of Geometric Graphs, (J. Pach, Ed.), AMS Contemporary Mathematics 342 (2004),
      139–148.
L. Lovász: Graph minor theory, Bull. Amer. Math. Soc. 43 (2006), 75–86.
L. Lovász, M. Freedman, A. Schrijver: Reflection positivity, rank connectivity, and homomorphisms
      of graphs, J. Amer. Math. Soc.20 (2007), 37–51.
L. Lovász, S. Vempala: Simulated Annealing in Convex Bodies and an O*(n4) Volume Algorithm, J.
      Comput. System Sci. 72 (2006), 392-417.


The five most important publications:
L. Lovász: Normal hypergraphs and the perfect graph conjecture, Discrete Math. 2 (1972), 253-267;
      reprinted Annals of Discrete Math. 21 (1984) 29-42.

                                             Personal data
94                            MSc program in mathematics: personal data


L. Lovász: Kneser’s conjecture, chromatic number, and homotopy, J. Comb. TheoryA 25 (1978), 319-
      324.
L. Lovász: On the Shannon capacity of graphs, IEEE Trans. Inform. Theory25 (1979), 1-7.
A.K. Lenstra, H.W. Lenstra, L. Lovász: Factoring polynomials with rational coefficients, Math.
      Annalen261 (1982), 515-534.
L. Lovász: Approximating clique is almost NP-complete (with U. Feige, S. Goldwasser, S. Safra and
      M. Szegedy), Proc. 32nd IEEE FOCS (1991), 2-12.


Activity in the scientific community, international relations
President of the International Mathematical Union, 2007-; Executive Committee of the
   International Mathematical Union,
1987-1994. Abel Prize Committee, 2004-2006; Chair, International Bolyai Prize Committee,
   2000-2006; Chair, Nevanlinna Prize Committee, 1988-1990; Presiduum of the Hungarian
   Academy of Sciences, 1990-1993, 2008-;Member, Program Committee of ICM 2002;
   Editor-in-Chief, Combinatorica, 1981-.
Member of editorial board for 12 other journals: J. Combinatorial Theory (B), Discrete Math.,
   Discrete Applied Math., Geometric and Functional Analysis, J. Graph Theory, Europ. J.
   Combinatorics, Discrete and Computational Geometry, Random Structures and
   Algorithms, Electronic Journal of Combinatorics, Acta Mathematica Hungarica, Acta
   Cybernetica, Természet Világa




                                            Personal data
                               MSc program in mathematics: personal data                   95


Name: András Lukács

Date of birth: 1968
Highest degree (discipline): diploma in mathematics
Present employer, position: Computer and Automation Institute, reserach fellow,
        Eötvös Loránd University, reserach fellow
Scientific degree (discipline): CSc (mathematics)
Major Hungarian scholarships: OTKA postdoctoral fellowship (2000–2003)-

Teaching activity (with list of courses taught so far):
Numerical analysis (for students in mathematics and in computer science, 1990–1991)
Discrete mathematics (for students in mathematics and in informatics, 1993– )
Combinatorics of set systems (for students in teaching mathematics, 2002)
Complexity theory (for students in computer science, 2003)
Data mining (2003– )
Random walks in graphs (1995)
Combinatorial probability theory (2001)

Other professional activity:
Over 8 years of teaching experience
Guest reseracher in several universities (Univ. Köln, Inst. für Informatik, 1992-1993,
Montanuniv. Leoben, Inst. für Ang. Math., 1994-1995, CWI Amsterdam, 1998-2000)
Research position in the Research Laboratory of the Computer and Automation Institute
(1995– )


Up to 5 selected publications from the past 5 years:
Bounded contraction of graphs with polynomial growth (with N. Seifter), European Journal of
Combinatorics 22 (1) (2001), no. 1, 85-90. (IF=0,335)
High density compression of log files (with B. Rácz), Proceedings of the Data Compression
Conference 2004, Snowbird, UT, USA. IEEE Computer Society
Generating random elements of abelian groups, Random Structures and Algorithms,
várhatóan 2005. (IF=0,759)

The five most important publications:
Lattices in graphs with polynomial growth (with N. Seifter), Discrete Math. 186 (1998), no. 1-
3, 227-236. (IF=0,301)
On local expansion of vertex-transitive graphs, Combin. Probab. Comput. 7 (1998), no. 2,
205-209. (IF=0,512)
Bounded contraction of graphs with polynomial growth (with N. Seifter), European Journal of
Combinatorics 22 (1) (2001), no. 1, 85-90. (IF=0,335)
Approximate representation of groups (2004) (with László Babai and Katalin Friedl) (kézirat)
Generating random elements of abelian groups, Random Structures and Algorithms,
várhatóan 2005. (IF=0,759)

Activity in the scientific community, international relations



                                             Personal data
96                        MSc program in mathematics: personal data


member of the Bolyai Mathematical Society (1993– ), Institute of Combinatorics and its
Applications (1995– ),
technical editor of Combinatorica (996–1998)
member of the organizing committee of the 2nd European Congress of Mathematics (1996)

Internatonal relations: CWI Amsterdam, Cambridge Univ., Montanuniv. Leoben.




                                        Personal data
                               MSc program in mathematics: personal data                    97


Name: Gergely Mádi-Nagy

Date of birth: 1973
Highest degree (discipline): diploma in mathematics, BSc in economics
Present employer, position: BUTE, assistant professor, Eötvös University, part-time assistant
professor
Scientific degree (discipline): PhD (applied mathematics)
Major Hungarian scholarships:

Teaching activity (with list of courses taught so far):
Eötvös University (1997– ):
Operations Research, Decision Theory, Nonlinear Programming
BUTE (2000– )
Calculus, Linear Algebra, Operations Research, Probability Theory, Statistics

Other professional activity:
10 years of teaching experience, 1 National Student Research Conference (OTDK)
supervisions (2nd place), 10 talks at international conferences, seminars;
5 refereed publications; 6 research reports;

Up to 5 selected publications from the past 5 years:
Prékopa, A. and G. Mádi-Nagy (2008). A Class of Multiattribute Utility Functions. Economic
   Theory, 34 (3), pp. 591-602
Mádi-Nagy, G. (2005). A method to find the best bounds in a multivariate discrete moment
  problem if the basis structure is given. Studia Scientiarum Mathematicarum Hungarica 42
  (2), pp. 207 - 226.
Mádi-Nagy, G. and A. Prékopa (2004).On Multivariate Discrete Moment Problems and their
  Applications to Bounding Expectations and Probabilities. Mathematics of Operations
  Research 29(2), pp. 229-258.
Mádi-Nagy G. és Prékopa A. (2004). Egy többváltozós hasznossági függvény. (A
  Mulitivariate Utility Function, with english abstract) Alkalmazott Matematikai Lapok 21,
  23-34.


The five most important publications:
Prékopa, A. and G. Mádi-Nagy (2007). A Class of Multiattribute Utility Functions. Economic
   Theory, 34 (3), pp. 591-602
Mádi-Nagy, G. (2005). A method to find the best bounds in a multivariate discrete moment
  problem if the basis structure is given. Studia Scientiarum Mathematicarum Hungarica 42
  (2), pp. 207 - 226.
Mádi-Nagy, G. and A. Prékopa (2004).On Multivariate Discrete Moment Problems and their
  Applications to Bounding Expectations and Probabilities. Mathematics of Operations
  Research 29(2), pp. 229-258.



                                             Personal data
98                           MSc program in mathematics: personal data


Mádi-Nagy G. és Prékopa A. (2004). Egy többváltozós hasznossági függvény. (A
  Mulitivariate Utility Function, with english abstract) Alkalmazott Matematikai Lapok 21,
  23-34.
Nagy G. és Prékopa A. (2000). Többváltozós diszkrét függvények féloldalas approximációja
   polinomokkal. (One-sided Approximation of Multivariate Discrete Functions by
   Polynomials, with english abstract) Alkalmazott Matematikai Lapok 20, 195-215.


Activity in the scientific community, international relations
     member of Hungarian Operations Research Society
     coauthors from USA;
     visiting reseracher at universities in Germany, USA;




                                           Personal data
                              MSc program in mathematics: personal data                        99




Name: László Márkus

Date of birth: 1961
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös Loránd University, associate professor
Scientific degree (discipline): CSc (mathematics)
Major Hungarian scholarships: -

Teaching activity (with list of courses taught so far):
Eötvös University (1990- ):
Time Series Analysis (lecture, for students in mathematics/applied mathematics)
Spectral and Parameter estimation of Stochastic Processes(lecture, for students in
mathematics)
Analysis of financial processes I-II. (lecture, for students in mathematics/applied
mathematics)
Probability Theory (practice/tutorial, for students in mathematics/applied mathematics)
Mathematical Statistics (practice/tutorial, for students in mathematics/applied mathematics)
Advanced Probability Theory (lecture, for students in informatics)
Advanced Mathematical Statistics (lecture, for students in informatics)
Probability Theory (lecture, for students in geophysics; astronomy;)
Mathematical Statistics (lecture, for students in geophysics, astronomy; )

Other professional activities in the last 5 years:
18 years of teaching experience,
12 diploma thesis supervisions, supervision of the work of 4 Ph.D. students
Over 30 lectures at international conferences; 32 publications, 18 of them in peer reviewed
journals;

2000 - 2003: Head of an international thematic research project, funded by the Hungarian
National Scientific Research Fund (OTKA) (10 participants, of them two British, two
German).
2001-2004: Co-ordinator of time series modelling in a National Research and Development
Project for estimating flood risks of Tisza River2002-2004: Participant in the PRO-ENBIS
project of the EU for establishing the European Network for Business and Industrial Statistics
(ENBIS).
2004 - 2007: Head of an international thematic research project: funded by the Hungarian
National Scientific Research Fund (OTKA) (12 participants, of them two British, one
German-Canadian).
2005-2007: Research projects at Eötvös University funded by different international insurance
companies. Co-ordinator of 3 of those projects Participant in 3 further projects.

Up to 5 selected publications from the past 5 years:
László Márkus, Péter Elek: A long range dependent model with nonlinear innovations for
simulating daily river flows, Natural Hazards in Earth System Sciences, 2004., Vol.2.,
pp.277-283.
László Márkus, József Kovács, Gábor Halupka: Dynamic Factor Analysis for Quantifying
Aquifer Vulnerability, Acta Geologica Hungarica, 2004. Vol. 47. No.1. pp.1-17.

                                            Personal data
100                          MSc program in mathematics: personal data


Ian Dryden, László Márkus, Charles Taylor, József Kovács: Non-Stationary spatio-temporal
analysis of karst water levels Journal of the Royal Statistical Society, Series C-Applied
Statistics 2005.,Vol.54., No.3., pp. 673-690.
Péter Elek, László Márkus: A light-tailed conditionally heteroscedastic model with
applications to river flows, Journal of Time Series Analysis, 2008. Vol. 29, No.1, 14-36.
Krisztina Vasas, Péter Elek, László Márkus: A two state regime switching autoregressive
model with application to river flow analysis, Journal of Statistical Planning and Inference,
137 (2007) pp. 3113 - 3126.

The five most important publications:
László Márkus: On a stability problem of the forecast of Lévy's Brownian motion, Probability
Theory and Its Applications, 1997. Vol. 42., No. 2, pp.407-409.
László Márkus, Olaf Berke, József Kovács and Wolfgang Urfer Spatial Prediction of the
Intensity of Latent Effects Governing Hydrogeological Phenomena Environmetrics, 1999. Vol
10. pp. 633-654.
Ian Dryden, László Márkus, Charles Taylor, József Kovács: Non-Stationary spatio-temporal
analysis of karst water levels Journal of the Royal Statistical Society, Series C-Applied
Statistics 2005.,Vol.54., No.3., pp. 673-690.
Krisztina Vasas, Péter Elek, László Márkus: A two state regime switching autoregressive
model with application to river flow analysis, Journal of Statistical Planning and Inference,
137 (2007) pp. 3113 - 3126.
Péter Elek, László Márkus: A light-tailed conditionally heteroscedastic model with
applications to river flows, Journal of Time Series Analysis, 2008. Vol. 29, No.1, 14-36.

Activity in the scientific community, international relations
MEMBERSHIP IN SCIENTIFIC ORGANISATIONS:
Bernoulli Society for Probability Theory and Statistics 1990-present
European Regional Committee of the Bernoulli Society elected member for 2008-2012
INTECOL - Society for International Ecological Sciences1998-present
EGU - European Geological Union 1997-2005
The Applied Stochastic Models and Data Analysis International Society 2006-present

REFEREE for the journals: Journal of Time Series Analysis, Water Resources Research
ORGANIZER of two international conferences




                                           Personal data
                               MSc program in mathematics: personal data                    101


Name: György Michaletzky

Date of birth: 1950
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, professor, head of department
Scientific degree (discipline): DSc (mathematics)
Major Hungarian scholarships: Széchenyi scholarship (1997–2001)

Teaching activity (with list of courses taught so far):
Probability Theory, Statistics, Multidimensional statistical analysis, Stochastic processes,
control and filtering, Stochastic differential equations, Birth and death processes, Queueing
systems, Stationary stochastic processes, Risk processes, Markov-processes, Distribution of
the eigenvalues of random matrices, Hankel-approximation, Sampling theory, System theory.


Other professional activity:
33 years of teaching experience, over 30 lectures at international conferences;
53 publications

Up to 5 selected publications from the past 5 years:
~, Quasi-similarity of compressed shift operators, Acta Sci. Math., Szeged, 69(2003), 223-239
~, Kockázati folyamatok, Eötvös Kiadó, Jegyzet, 2. átdolgozott kiadás, 2001.
~, L. Gerencsér, BIBO--stability of switching systems, IEEE Trans. on Automatic Control,
47/11, 2002, 1895-1898.
I. Gyöngy – ~, On the Wong-Zakai approximations with delta martingales,
Proc. R. Soc. London, A. 460(2003), 309-324.
L. Gerencsér, ~ , Zs. Vágó, Risk sensitive identification of linear stochastic systems, accepted
Mathematics of Control, Signals and Systems 17 (2005), 77-100.

The five most important publications:
A. Lindquist, Gy. Michaletzky – G. Picci, Zeros of spectral factors, the geometry of splitting
subspaces, and the algebraic Riccati inequality, SIAM J. Control, Vol. 33. No. 2. pp. 365-401,
1995.
Gy. Michaletzky, J. Bokor, P. Várlaki, Representability of Stochastic Systems, Akadémiai
Kiadó, 1998.
Gy. Michaletzky – A. Ferrante, Splitting subspaces and acausal spectral factors, J. Math.
Systems, Estim. and Control Vol. 5. No. 3.pp.363-366, 1995.
A. Lindquist – Gy. Michaletzky, Output-induced subspaces, invariant directions and
interpolation in linear discrete time stochastic systems, SIAM J. Control, 35/3 pp.810-859,
1997.
M. Bolla - Gy. Michaletzky - G. Tusnády - M. Ziermann, Extrema of sums of heterogeneous
quadratic forms, Linear Algebra and Applic. 269 1998, 331-365.

Activity in the scientific community, international relations




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102                            MSc program in mathematics: personal data


Name: Tamás F. Móri

Date of birth: 1953
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös Loránd University, associate professor
Scientific degree (discipline): CSc (mathematics)
Major Hungarian scholarships: Széchenyi Professor scholarship (1998–2001)

Teaching activity (with list of courses taught so far):
Eötvös Loránd University (1978– ):
Probability theory (for students in mathematics, applied mathematics, and informatics;
lecture, practice)
Mathematical statistics (for students in mathematics, applied mathematics, informatics, and
geophysics; lecture, practice)
Stochastics (for students in mathematics; lecture)
Foundations of statistics 1-2 (for students in mathematics, and applied mathematics; lecture)
Discrete parameter martingales (for students in mathematics; lecture)
Analysis of survival data (for students in mathematics, and applied mathematics; lecture)
Measure and integral (in English, for MSc students)
Advanced probability theory (in English, for MSc students)
Foundations of statistics (in English, for MSc students)
Analysis of survival data (in English, for MSc students)

Other professional activity:
30 years of teaching experience, 14 diploma thesis supervisions, 2 PhD thesis supervisions.
Textbooks, lecture notes (in Hungarian):
Multivariate Statistical Analysis (Műszaki Könyvkiadó, Budapest, 1986), Editor
Teaching software for PC in mathematics (complex function theory), also in English and
   German, 1987–90
Mathematical statistics (Tankönyvkiadó, Budapest, 1995), Ch.II. Estimations
Problem book in mathematical statistics (ELTE Eötvös Kiadó, Budapest, 1997) (with L.
   Szeidl and A. Zempléni)
Discrete parameter martingales (ELTE, 1999)
Analysis of survival data. Available online http://www.math.elte.hu/~mori/elettartam.pdf
Activities in other institutions, visits:
1985-1991 Research fellow, Mathematical Institute of the HAS
2006-2010 Associated member, Alfréd Rényi Institute of Mathematics
1992 University of Sheffield, Department of Probability and Statistics, one month visit,
   TEMPUS individual mobility grant

Up to 5 selected publications from the past 5 years:
Almost sure convergence of weighted partial sums. Acta Math. Hungar., 99 (2003), 285–303.
   (with B. Székely)
The maximum degree of the Barabási random tree. Comb. Probab. Computing, 13 (2004)
The convexity method of proving moment–type inequalities. Statist. Probab. Lett., 66 (2004),
   303–313. (with V. Csiszár)


                                             Personal data
                             MSc program in mathematics: personal data                    103


A new class of scale free random graphs. Statist. Probab. Lett.76 (2006), 1587–1593. (with Z.
   Katona)
Degree distribution nearby the origin of a preferential attachment graph. Electron. Comm.
Probab., 12 (2007), 276–282.


The five most important publications:
On the rate of convergence in the martingale central limit theorem. Studia Sci. Math. Hungar.
   12 (1977) 413–417.
Asymptotic behaviour of symmetric polynomial statistics. Ann. Probab. 10 (1982) 124–131.
   (with G. J. Székely)
A note on the background of several Bonferroni–Galambos type inequalities. J. Appl. Probab.
   22 (1985) 836–843. (with G. J. Székely)
On the waiting time till each of some given patterns occurs as a run. Probab. Th. Rel. Fields
   87 (1991) 313–323.
Covering with blocks in the non-symmetric case. J. Theor. Probab. 8 (1995) 139–164.

Activity in the scientific community, international relations:
1979– member of the J. Bolyai Mathematical Society, 2006–2009 secretary of the Ethical
   Committee
1979– member of the Bernoulli Society for Probability Theory and Mathematical Statistics,
   2000–2004 member of the European Regional Committee
2002–2005 member of the mathematical jury of OTKA




                                           Personal data
104                            MSc program in mathematics: personal data


Name: Gábor Moussong

Date of birth: 1957
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, assistant professor
Scientific degree (discipline): PhD (mathematics)
Major Hungarian scholarships: Széchenyi scholarship (2000–2003)


Teaching activity (with list of courses taught so far):
Eötvös University (1982– ):
geometry, differential geometry, topology, algebraic topology (for students in mathematics,
lecture, practice)
mathematics (for students in cartography; lecture)
Universiteit Gent (1991):
algebraic topology (for students in mathematics, lecture)
BSM (1997– )
topics in geometry (lecture, practice)
The Ohio State University (1997-1998):
calculus and analytic geometry
topics in geometry

Other professional activity:
26 years of teaching experience, 20 diploma thesis supervisions;
over 15 lectures at international conferences;
11 publications;

Up to 5 selected publications from the past 5 years:
1. Moussong, G., Prassidis, S.: Equivariant rigidity theorems, New York J. Math. 10 (2004),
151-167.
2. Moussong, G.: Models of hyperbolic geometry, in: Bolyai memorial volume, ed. by K.
Kapitány, G. Németh, V. Silberer, Vince Kiadó (2004), 143-165 (in Hungarian).
3. Csikós, B., Moussong, G.: On the Kneser-Poulsen Conjecture in Elliptic Space,
Manuscripta Math., 121 (2006), 481-489.


The five most important publications:
1. Moussong, G.: Hyperbolic Coxeter Groups, Ph.D. Dissertation, The Ohio State University,
1988.
2. Moussong, G.: Some non-symmetric manifolds. Differential geometry and its applications,
Coll. Math. Soc. J. Bolyai 56, North Holland, Amsterdam (1992), 535-546.
3. Charney, R., Davis, M. W., Moussong, G.: Nonpositively curved, piecewise Euclidean
structures on hyperbolic manifolds, Michigan Math. J. 44 (1997) no. 1., 201-208.
4. Davis, M. W., Moussong, G.: Notes on Nonpositively Curved Polyhedra. Low
Dimensional Topology, eds. K. Böröczky Jr., W. Neumann, A. Stipsicz, Bolyai Society Math.
Studies Nr. 8 (1999), 11-94.


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                             MSc program in mathematics: personal data                  105


5. Moussong, G., Prassidis, S.: Equivariant rigidity theorems, New York J. Math. 10 (2004),
   151-167.

Activity in the scientific community, international relations
   member of the Bolyai Mathematical Society, 1982– ;
   organizer of five international conferences;
   member of editorial board for Periodica Math. Hung., 1991-1997;
   committee member for the National Mathematical Competition for Secondary Schools,
   1990-;
   program manager for Budapest Semesters in Mathematics, 1989-1991;
   coauthors from USA;
   visiting professor at universities in Belgium, USA.




                                           Personal data
106                            MSc program in mathematics: personal data


Name: András Némethi

Date of birth: 1959
Highest degree (discipline): diploma in mathematics
Present employer, position: Alfréd Rényi Institute of Mathematics, researcher
Scientific degree (discipline): Doctor of Science (mathematics)
Major Hungarian scholarships: –

Teaching activity (with list of courses taught so far):
OSU Columbus, Ohio, USA (1991–2006):
Algebra, Geometry, Analysis, Algebraic Geometry, Algebraic Topology
CEU (2004– )
Algebraic Geometry, Hodge Theory

Other professional activity:
1985-1990, Researcher, National Institute for Science and Technical Research, Bucharest,
Romania.
1991-1995, Instructor, Ohio State University, USA
1995-1998, Assistant Professor, Ohio State University, USA
1998-2002, Associate Professor, Ohio State University, USA
2002-2006, Professor, Ohio State University, USA
2004 óta, Researcher, Alfréd Rényi Institute of Mathematics, Budapest (head of the Algebraic
Geometry and Differential Topology research division).


Up to 5 selected publications from the past 5 years:
1. Némethi, A.: Invariants of normal surface singularities, Contemporary Mathematics, 354
    (2004), 161-208.
2. Mendris, R. and Némethi, A.: The link of f(x,y)+zn=0 and Zariski’s Conjecture,
    Compositio Math., 141 (2005), 502-524.
3. Némethi, A.: On the Ozsváth-Szabó invariant of negative definite plumbed 3-manifolds,
    Geometry and Topology, 9 (2005), 873-883.
4. McNeal, J.D., Némethi, A.: The order of contact of a holomorphic ideal in C2, Math.
    Zeitschrift, 250(4) (2005), 873-883
5. J.F. de Bobadilla, Luengo, I., Melle-Hernández, A. and Némethi, A.: On rational cuspidal
    projective plane curves, Proc. of London Math. Society, 92 (2006), 99-138.

The five most important publications:
1. Némethi, A. and Steenbrink, J.: Extended Hodge bundles for Abelian, Annals of
   Mathematics, 143 (1996), 131-148.
2. Némethi, A.: ``Weakly‖ Elliptic Gorenstein singularities of surfaces, Inventiones Math.,
137 (1999), 145-167.
3. Némethi, A. and Nicolaescu, L.I.: Seiberg-Witten invariants and surface singularities,
   Geometry and Topology, 6 (2002), 269-328.
4. Némethi, A.: On the Heegaard Floer homology of S3-d(K) and unicuspidal rational plane
   curves, Fields Institute Communications, 47 (2005), 219-234.

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                            MSc program in mathematics: personal data                  107


5. Luengo, I., Melle-Hernández, A. and Némethi, A.: Links and analytic invariants of
   superisolated singularities, Journal of Algebraic Geometry, 14 (2005), 543-565.

Activity in the scientific community, international relations

Editor of the journals Periodica Mathematica Hungarica and
  Studia Scientiarium Math. Hungarica;
  Organizer of eight international conferences;
  Visiting positions at
   – Math. Inst. of the Hungarian Academy of Sciences, Budapest, Hungary (March 1990-
     May 1990)
   – University of Utrecht and Nijmegen, the Netherlands (Sept. 1990-Dec. 1990)
   – University of Toronto, Canada (July 1991)
  – MSRI, Berkeley (May 1993)
  – University of Nice, France (July 1993)
  – University of Nijmegen, the Netherlands (Sept. 1993-June 1994)
  – E´cole Polytechnique, Palaiseau, France (Oct. 1996-Dec. 1996)
  – University of Nice, France (June 15-July 15, 1997)
  – University of Nantes, France (June 01-30, 1998)
  – University of Bordeaux, France (November 01-30, 1999)
  – Rényi Institute of Mathematics, Budapest, Hungary (July 1999-June 2000)
  – University of Hannover, Germany (October 01-30, 2005).
  Coauthors from several countries;




                                          Personal data
108                            MSc program in mathematics: personal data


Name: Péter P. Pálfy

Date of birth: 1955
Highest degree (discipline): diploma in mathematics
Present employer, position: Alfréd Rényi Institute of Mathematics, director;
     Eötvös University, professor
Scientific degree (discipline): DSc (mathematics),
     corresponding member of the Hungarian Academy of Sciences (2004)
Major Hungarian scholarships: Széchenyi professor’s scholarship (1998–2001)

Teaching activity (with list of courses taught so far):
Eötvös University (1978– ):
     Algebra, Algebra and number theory, Linear algebra, Group theory, Lie algebras,
     Lattice theory, Permutation groups, Simple groups of Lie type, Group representation
     theory, Seminar in algebra
Vanderbilt University (1983):
      Linear algebra, Group theoretic methods in universal algebra
University of Hawaii (1986):
       Caluculus III, Probability theory
Technische Hochschule Darmstadt (1991-1992):
       Lineare Algebra, Gruppentheorie

Other professional activity:
      30 years of teaching experience, 8 diploma thesis supervisions, 2 Ph.D. thesis
      supervisions;
      over 80 lectures at international conferences;
      57 publications;

Up to 5 selected publications from the past 5 years:
1.    C.H. Li, Z.P. Lu, P.P. Pálfy, Further restrictions on the structure of finite CI-groups, J.
      Algebraic Comb. 26 (2007), 161-181.
2.    P.P. Pálfy, Maximal clones and maximal permutation groups, Discuss. Math. Gen.
      Algebra Appl. 27 (2007), 277-291.
3.    P.P. Pálfy, A non-power-hereditary congruence lattice representation of M3, Publ. Math.
      Debrecen 69 (2006), 361-366.
4.    P. Hegedűs, P.P. Pálfy, Finite modular congruence lattices, Algebra Universalis 54
      (2005), 105-120.
5.    P.P. Pálfy, Groups and lattices, London Math. Soc. LNS vol. 305, 428-454.

The five most important publications:
1.    P.P. Pálfy, Isomorphism problem for relational structures with a cyclic automorphism,
      Europ. J. Combinatorics 8 (1987), 35-43.
2.    P.P. Pálfy, Unary polynomials in algebras, I, Algebra Universalis 18 (1984), 262-273.
3.    L. Babai, P.J. Cameron, P.P. Pálfy, On the orders of primitive groups with restricted
      composition factors, J. Algebra 79 (1982), 161-168.


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                             MSc program in mathematics: personal data                  109


4.   P.P. Pálfy, A polynomial bound for the orders of primitive solvable groups, J. Algebra
     77 (1982), 127-137.
5.   P.P. Pálfy, P. Pudlák, Congruence lattices of finite algebras and intervals in subgroup
     lattices of finite groups, Algebra Universalis 11 (1980), 22-27.

Activity in the scientific community, international relations
     Mathematics committee of the Hungarian Academy of Sciences: member since 1985,
     secretary 1990-1996, chairman since 2005;Board of the Bolyai research fellowship:
     member 2004-2006, chairman since 2007;
     chairman of the mathematics granting committee of the Hungarian NSRF (OTKA),
     2001–2003;
     member of the Hungarian Accreditation Committee (1997-2000 and 2007-);
     member of the Scientific Council of the International Banach Center (Warsaw) since
     2006;
     member of the committee for the Bolyai prize (2007);
     editor-in-chief of Studia Scientiarum Mathematicarum Hungarica (since 2007)
     coauthors from Czechoslovakia, England, USA, Australia, China;
     visiting professor at Vanderbilt University (USA, 1983), the University of Hawaii
     (USA, 1986) and Technische Hochschule Darmstadt (Germany, 1991-1992).




                                           Personal data
110                            MSc program in mathematics: personal data


Name: Katalin Pappné Kovács

Date of birth: 1955
Highest degree (discipline): diploma in mathematical education
Present employer, position: Eötvös University, associate professor
Scientific degree (discipline): CSc (mathematics)

Teaching activity (with list of courses taught so far):
Eötvös University (1987– ):
     algebra (for students in mathematics; lecture, practice)
     number theory (for students in mathematics; lecture, practice)
     linear algebra (for student in informatics; practice)
     algebra and number theory, teaching algebra and number theory (for PhD students of
     the Math. Education PhD program of the University of Debrecen)
University of Illinois (1993–1995 )
     linear algebra, differential equation (lecture, practice)

Other professional activity:
      32 diploma thesis supervisions;
      over 10 lectures at international conferences;
      27 publications

Up to 5 selected publications from the past 5 years:
1.    On the characterization of n-polyadditive functions, Publ. Math. Debrecen, 2006 (1-7)
2.    On triples of consecutive integers, Annales Univ. Sci. 49 (2007), 143-147

The five most important publications:
1.    On the characterization of additive functions with monotonic norm, Journal of Number
      Theory, Vol 24, no.3, 1986, 298-304
2.    On a conjecture concerning additive arithmetical functions II, Publ. Math. Debrecen 50,
      1997, 1-3
3.    On the haracterization of additive functions on Gaussian integers, Publ. Math. Debrecen
      58 (1-2) (2001), 73-78
4.    On the characterization of n-polyadditive functions, Publ. Math. Debrecen, 2006 (1-7)
5.    On triples of consecutive integers, Annales Univ. Sci. 49 (2007), 143-147

Activity in the scientific community, international relations
     Bolyai János Math. Society membership
     MR-reviewer (for 15 years)




                                             Personal data
                               MSc program in mathematics: personal data                    111


Name: József Pelikán

Date of birth: 1947
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, associate professor
Scientific degree (discipline): doctoral degree with distinction (mathematics)
Major Hungarian scholarships:

Teaching activity (with list of courses taught so far):
Eötvös University (1969– ):
     algebra and number theory (for students in mathematics; lecture, practice) introductory
     courses,
     various topics in algebra (for students in mathematics; lecture) advanced courses
BSM (1988– )
    various algebra and number theory courses

short courses in various foreign universities (in English, French and German)

Other professional activity:
39 years of teaching experience, over 10 diploma thesis supervisions; over 10 lectures at
international conferences;
16 publications;

Up to 5 selected publications from the past 5 years:
1.   Discrete Mathematics. Springer, New York, 2003., x+290 pp., ISBN: 0-387-95584-4
     (co-authors: L. Lovász, K. Vesztergombi)
2.   On the running time of the Adleman-Pomerance-Rumely primality test. Publ. Math.
     Debrecen 56 (2000) 523-534. (co-authors: J. Printz, E. Szemerédi)

The five most important publications:
1.   Discrete Mathematics. Springer, New York, 2003., x+290 pp., ISBN: 0-387-95584-4
     (co-authors: L. Lovász, K. Vesztergombi)
2,   Finite groups with few non-linear irreducible characters. Acta Math. Acad. Sci. Hungar.
     25 (1974), 223-226.
3,   On semigroups, in which products are equal to one of the factors. Period. Math.
     Hungar. 4 (1973), 103-106.
4,   Properties of balanced incomplete block designs. Combin. Theory and its Appl. (Proc.
     Colloq. Balatonfüred, 1969) vol. III. 869-889., North- Holland, Amsterdam, 1970.
5,   Valency conditions for the existence of certain subgraphs. Theory of Graphs (Proc.
     Colloq. Tihany, 1966) 251-258., Academic Press, New York, 1968.

Activity in the scientific community, international relations
     Various leading positions in the János Bolyai Mathematical Society
     Member of Board of Editors of Matematikai Lapok
     Leader of the Hungarian team at the International Mathematical Olympiad (IMO),
     1988–
     Member of the Advisory Board of the IMO (since 1992),

                                             Personal data
112                        MSc program in mathematics: personal data


      Chairman of the Advisory Board of the IMO (since 2002)




                                         Personal data
                               MSc program in mathematics: personal data                     113


Name: Tamás Pfeil

Date of birth: 1967
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, assistant professor
Scientific degree (discipline): PhD (mathematics)
Major Hungarian scholarships: -

Teaching activity (with list of courses taught so far):
Eötvös University (1989– ):
mathematics (for students in biology; lecture, practice)
analysis (for students in mathematics and meteorology; practice)
partial differential equations (for students in mathematics and meteorology; practice)
ordinary differential equations (for students in mathematics; practice)


Other professional activity:
18 years of teaching experience, 1 diploma thesis supervision, lecture and poster at
international conferences;
7 publications;

Up to 5 selected publications from the past 5 years:
Pfeil, T., Shape-preserving signal forms in heat conduction, Appl. Math. Modelling, 32
    (2008), 1599-1606.

The five most important publications:
1. Faragó, I., Haroten, H., Komáromi, N., Pfeil, T., A hővezetési egyenlet és numerikus
megoldásának kvalitatív tulajdonságai. I. A másodfokú közelítés nemnegativitása, a mximum
elv és az oszcillációmentesség, Alk. Mat. Lapok, 17 (1993), 123-141.
2. Faragó, I., Haroten, H., Komáromi, N., Pfeil, T., A hővezetési egyenlet és numerikus
megoldásának kvalitatív tulajdonságai. I. Az elsőfokú közelítések nemnegativitása, Alk. Mat.
Lapok, 17 (1993), 101-121.
3. Pfeil, T., On the time-monotonicity of the solutions of linear second order homogeneous
parabolic equations, Annales Univ. Sci. Budapest., 36 (1993), 139-146.
4. Pfeil, T., An elementary proof for the time-monotonicity of the solutions of linear parabolic
equations, Publ. Math. Debrecen, 46 (1995), 71-77.
5. Faragó, I., Pfeil, T., Preserving concavity in initial-boundary value problems of parabolic
type and its numerical solution, Per. Math. Hungar., 30 (1995), 135-139.


Activity in the scientific community, international relations
   member of the committee of Arany Dániel competition of the Bolyai Mathematical
   Society;




                                             Personal data
114                            MSc program in mathematics: personal data


Name: Vilmos Prokaj

Date of birth: 1966
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, associate professor
Scientific degree (discipline): PhD (mathematics)
Major Hungarian scholarships: Bolyai scholarship (2000–2003)

Teaching activity (with list of courses taught so far):
Eötvös University:
Analysis 1993-1997 (for students in mathematics; practice)
Functional analysis 1996-1997 (for students in mathematics; practice)
Probability and statistics 1991-1993, 1997-,(for students in mathematics, informatics;
practice)
Stochastic processes 2001-, (for students in mathematics; practice)
Stochastic analysis, Stochastic dinamical systems, Filtering of stochastic processes,
Reinsurance 2000-, (for students in mathematics; lecture)

Other professional activity:
15 years of teaching experience, 4 diploma thesis supervisions;
12 publications;

Up to 5 selected publications from the past 5 years:
1. A characterization of singular measures. Real Anal. Exchange 29 (2003/04), no. 2, 805--
812.


The five most important publications:
1. A characterization of singular measures. Real Anal. Exchange 29 (2003/04), no. 2, 805--
812.
2. On a construction of J. Tkadlec concerning sigma-porous sets. Real Anal. Exchange,
27(1):269 273, 2001/02.
3. Márton Elekes, Tamás Keleti, and Vilmos Prokaj.
The composition of derivatives has a fixed point. Real Anal. Exchange, 27(1):131 140,
2001/02.
4. Monotone and discrete limits of continuous functions. Real Anal. Exchange, 25(2):879 885,
1999/00.
5. Restrictions of self-adjoint partial isometries. Period. Math. Hungar., 35(3):211 214, 1997.


Activity in the scientific community, international relations
      member of the Bolyai Mathematical Society;



                                             Personal data
                             MSc program in mathematics: personal data                      115


Name: Tamás Pröhle

Date of birth: 1952
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös Loránd University, assistant
Scientific degree (discipline): –
Major Hungarian scholarships: –

Teaching activity (with list of courses taught so far):
Application of multivariate statistical methods
Statistical computing
Probability theory and statistics
– more than 25 years of teaching experience

Other professional activity: In connection with statistical computing. Main field of interest
includes statistical analysis of multivariate data and time series. Prepared teaching materials
for statistical softwares such as SPSS, SAS, and MATLAB. Applies mathematical statistics in
a wide range of fields in science, law, and technology (environmental management,
hydrology, psychology, jurisdiction, medicine, anthropology, design of experiments etc.)



Up to 5 selected publications from the past 5 years:
I. László, T. Pröhle et al.: A Method for Clustering Satellite Images Using Segments,
   Annales Univ. Sci. Budapest, Sect. Comp. 23 (2004), 163-178.

The five most important publications:
I. László, T. Pröhle et al.: A Method for Clustering Satellite Images Using Segments,
    Annales Univ. Sci. Budapest, Sect. Comp. 23 (2004), 163-178.
Gy. Gyenis, T. Pröhle et al.: Body Composition in Puberty Period, In: Puberty: Variabiliy of
    Changes and Complexity of Factors, Eötvös Univ. Press, Budapest 2000, pp 75-82.
B. Rojkovich, T. Pröhle et al.: Urinary excretion of thial components in patient with
    rheumatoid arthritis. Clin. Diagn. Lab. Immunol. 1999, 6, 683-685.



Activity in the scientific community, international relations:
Member of the Hungarian Association for Image Analysis and Pattern Recognition, and of the
John von Neumann Computer Society. Active member of Users Groups of several statistical
software packages (MATLAB, SPSS, SAS, STATISTICA), where he regularly holds lectures.




                                           Personal data
116                           MSc program in mathematics: personal data


Name: András Recski

Date of birth: 1948
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, professor (part time) and
    Budapest University of Technology and Economics, professor (full time)
Scientific degree (discipline): DSc (mathematics)
Major Hungarian scholarships: Széchenyi scholarship (2000–2004)

Teaching activity (with list of courses taught so far):
Eötvös University (1972– ):
algebra (for students in mathematics; lecture, practice)
discrete mathematics (for students in mathematics and informatics)

Budapest University of Technology and Economics (1990– )
analysis and discrete mathematics (for students in electrical engineering
   and informatics; lecture, practice)

Other professional activities:
36 years of teaching experience, about 6 diploma thesis supervisions,
    5 Ph.D. thesis supervisions; over 70 lectures at international conferences;
approx. 110 publications.

Up to 5 selected publications from the past 5 years:
1. T. Jordán – A. Recski – D. Szeszlér: System optimization, Typotex, Budapest, 2004.
2. A. Recski: Maps of matroids with applications, Discrete Math. 303 (2005) 175-185.
3. A. Recski – D. Szeszlér: The evolution of an idea – Gallai’s algorithm, Bolyai Soc. Math.
    Studies 15 (2006) 317-328.
4. A. Recski – J. Szabó: On the generalization of the matroid parity problem, Graph Theory,
    Trends in Mathematics, Birkhauser, 2006, 347-354.
5. K. Friedl – A. Recski – G. Simonyi: Graph theory exercises, Typotex, Budapest, 2006.

The five most important publications:
1. L. Lovász – A. Recski: On the sum of matroids, Acta Math. Acad. Sci. Hungar. 24 (1972)
   329-333.
2. M. Iri – A. Recski: What does duality really mean? Circuit Th. Appl. 8 (1980) 317-324.
3. A. Recski: Matroid theory and its applications in electric engineering and in statics,
   Springer, Berlin, 1989.
4. A. Recski: Combinatorics in electric engineering and statics, Handbook of Combinatorics,
   Elsevier, Amsterdam, 1995, 1911-1924.
5. A. Recski: Some polynomially solvable subcases of the detailed routing problem in VLSI
   design, Discrete Applied Math. 115 (2001) 199-208.

Activity in the scientific community, international relations
      member of the editorial board of 5 math journals;
      organizer of several international conferences;

                                            Personal data
                        MSc program in mathematics: personal data   117


general secretary of the János Bolyai Mathematical Society;




                                      Personal data
118                            MSc program in mathematics: personal data


Name: András Sárközy

Date of birth: 1941
Highest degree (discipline): diploma in mathematics (1963)
Present employer, position: Eötvös University, professor
Scientific degree (discipline): DSc (mathematics), 1982;
     regular member of the Hungarian Academy of Sciences, 2004
Major Hungarian Scholarships: Széchenyi Professor’s Scholarship (1999-2002)

Teaching activity:
Eötvös University (1963– ):
     algebra, number theory, algebra and number theory, computational number theory,
     linear algebra, combinatorial number theory, applications of exponential sums in
     number theory, additive number theory
University of Illinois (1972/73, 1989/90), UCLA (1983), University of Georgia (1985/1986),
     The City University of New York, Baruch College (1986/1987), University of Waterloo
     (1990/91), The University of Memphis (2007/2008):
     calculus, linear algebra, linear programming, complex analysis, algebraic number
     theory, combinatorial number theory, elementary analytical number theory

Other professional activity:
      researcher: Rényi Institute (1971-1994), 6 years in USA, Canada, France, Germany,
      England
      220 research papers and 4 books

5 selected publications from the past 5 years:
1.    L. Goubin, C. Mauduit and A. Sárközy, Construction of large families of pseudorandom
      binary sequences, J. Number Theory 106 (2004), 56-69.
2.    R. Ahlswede, L. Khachatrian and A. Sárközy, On the density of primitive sets, J.
      Number Theory 109 (2004), 319-361.
3.    C. Mauduit and A. Sárközy, Construction of pseudorandom binary sequences by using
      the multiplicative inverse, Acta Math. Hungar. 108 (2005), 239-252.
4.    A. Sárközy, On sums and products of residues modulo p, Acta Arith. 118 (2005), 403-
      409.
5.    P. Hubert, C. Mauduit and A. Sárközy, On pseudorandom binary lattices, Acta Arith.
      125 (2006), 51-62.

A tudományos életmű szempontjából legfontosabb 5 publikáció:
1.    A. Sárközy, On difference sets of sequences of integers, 1, Acta Math. Acad. Sci.
      Hungar. 31 (1978), 125-149.
2.    A. Sárközy, On divisors of binomial coefficients, 1., J. Number Theory 20 (1985), 70-
      80.
3.    A. Sárközy and C. L. Stewart, On divisors of sums of integers, II, l. Reine Angew.
      Math. 365 (1986), 171-191.
4.    A. Sárközy, Finite addition theorems, II., J. Number Theory 48 (1994),197-218.
5.    C. Mauduit and A. Sárközy, On finite pseudorandom binary sequences, 1, Measure of
      pseudorandomness, the Legendre symbol, Acta Arith. 82 (1997), 365-377.

                                             Personal data
                             MSc program in mathematics: personal data           119




Activity in the scientific community, international relations
     President of the Mathematical Committee of the Hungarian Academy of Sciences
     (2003-2006)
     President of the mathematical jury of the HNFSR (OTKA), 1999-2001
     Editor of 5 mathematical journals
     Visiting professor, resp. researcher in USA, Canada, UK, Germany and France for
     altogether 11 years
     56 coauthors from 10 countries




                                           Personal data
120                            MSc program in mathematics: personal data


Name: Zoltán Sebestyén

Date of birth: 1943
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, Institute of Mathematics, full professor
Scientific degree (discipline): DSc (mathematics)
Major Hungarian scholarships: Széchenyi scholarship (1997–2001)

Teaching activity (with list of courses taught so far):
Eötvös University (1967– ):
analysis(for students in mathematics, physic, geophysic, chemistry; lecture, practice)
functional analysis (for students in mathematics; lecture, practice)

Other professional activity:
40 years of teaching experience, 20 diploma thesis supervisions, 10 Ph.D. thesis supervisions;
over 20 lectures at international conferences;
over 60 publications;

Up to 5 selected publications from the past 5 years:
1. On Krein-von Neumann and Friedrichs extensions, Acta Sci. Math. (Szeged) 69 (2003),
323-336., /with E. Sikolya/.
2. On products of unbounded operators, Acta Math. Hung. 100 (1-2)(2003), 105-129.,
/with J. Stochel/.
3. Sebestyén Moment Problem: the multidimensional case, Amer. Math. Soc. 132 (2004)
1029-1035. (with Dan Popovici)
4. Reflection Symmetry and Symmetrizability of Hilbert space operators, Amer. Math. Soc.
133 (2005) 1727-1731 (with J. Stochel)
5. On the nonnegativity of operator products, Acta Math. Hung. 109(2005), 1-14.
(with S. Hassi, H. de Snoo)


The five most important publications:
Every C*-seminorm is automatically submultiplicative Per. Math. Hung. 10 (1979), 1-8.
On the definition of C*-algebras II., Can. J. Math. 37 (1985), 664-681.
Restrictions of positive selfadjoint operators, Acta Sci. Math. (Szeged) 55 (1991), 149-154.
Operator extensions on Hilbert space, Acta Sci. Math. (Szeged) 57 (1993), 233-248.
Anticommutant lifting and anticommutant dilation, PAMS 121 (1995), 133-136.


Activity in the scientific community, international relations
Member of the Bolyai Math. Soc., Amer. Math. Soc.
Co-president of seven international conferences



                                             Personal data
                               MSc program in mathematics: personal data                      121


Name: István Sigray

Date of birth: 1964
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, assistant
Scientific degree (discipline):
Major Hungarian scholarships:

Teaching activity (with list of courses taught so far):
Eötvös University (1988– ):
Analysis, and complex analysis (for students in mathematics; lecture, practice)
Riemann surfaces and Special functions (for students in mathematics; lecture)
Applyed complex analysis (for students in physics)
BSM (1995)
chapters from complex analysis (lecture, practice)

Other professional activity:
20 years of teaching experience, 4 diploma thesis supervisions, 2 lectures at international
conferences;
2 publications;

Up to 5 selected publications from the past 5 years:
1. Solution of the polynomial equation kp’q–lpq’ = cpm, Stud. Sci. Math. Hung. 45 (2008),
   161–195..


The five most important publications:
1. On the monodromy representation of polynomial maps in n variables, Stud. Sci. Math.
Hung. 39 (2002), 361–367.
2. Solution of the polynomial equation kp’q–lpq’ = cpm, Stud. Sci. Math. Hung. 45 (2008),
161–195..


Activity in the scientific community, international relations




                                             Personal data
122                            MSc program in mathematics: personal data


Name: Eszter Sikolya

Date of birth: 1976
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, assistant
Scientific degree (discipline): PhD (mathematics)
Major Hungarian scholarships: Magyary Zoltán Postdoctoral Scholarship (2006–2007)

Teaching activity (with list of courses taught so far):
Eötvös Loránd University (1998-2002, 2005– ):
analysis (for students in mathematics; lecture, practice)
partial differential equations (for students in physics; practice)
infinite dimensional dynamical systems (for students in mathematics; lecture)

University of Tübingen (2002-2004):
Functionalanalysis (for students in mathematics, parctice)

Other professional activity:
10 years of teaching experience, 1 diploma thesis supervisions;
10 lectures at international conferences;
9 publications;
3 international patents

Up to 5 selected publications from the past 5 years:
K.-J. Engel, M. Kramar Fijavž, R. Nagel, E. Sikolya, Vertex control of flows in networks.
Networks and Heterogeneous Media, to appear.

E. Sikolya, A functional analytic method for the analysis of general partial differential
equations. Probl. Program. 2006, no. 2-3, 669–673.

T. Mátrai and E. Sikolya, Asymptotic behavior of flows in networks. Forum Math. 19 (2007),
429–461.

M. Kramar and E. Sikolya, Spectral properties and asymptotic peridocity of flows in
networks. Math. Z. 249 (2005), 139–162.

E. Sikolya, Simultaneous observability of networks of strings and beams. Bol. Soc. Paran.
Mat. 21 Nr. 1/2 (2003), 1–11.

The five most important publications:
K.-J. Engel, M. Kramar Fijavž, R. Nagel, E. Sikolya, Vertex control of flows in networks.
Networks and Heterogeneous Media, to appear.

M. Kramar, D. Mugnolo and E. Sikolya, Variational and semigroup methods for waves and
diffusion in networks. Appl. Math. Optim. 55 (2007), 219–240.



                                             Personal data
                             MSc program in mathematics: personal data                      123


T. Mátrai and E. Sikolya, Asymptotic behavior of flows in networks. Forum Math. 19 (2007),
429–461.

M. Kramar and E. Sikolya, Spectral properties and asymptotic peridocity of flows in
networks. Math. Z. 249 (2005), 139–162.

E. Sikolya, Simultaneous observability of networks of strings and beams. Bol. Soc. Paran.
Mat. 21 Nr. 1/2 (2003), 1–11.



Activity in the scientific community, international relations
Strasbourg, Prof. Komornik Vilmos (see the paper Simultaneous observability of networks of
strings and beams)
Tübingen, Prof. Rainer Nagel (see the paper Spectral properties and asymptotic peridocity of
flows in networks)
Rome, Prof. Klaus-Jochen Engel




                                           Personal data
124                            MSc program in mathematics: personal data


Name: László Simon

Date of birth: 1940.
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, full professor
Scientific degree (discipline): DSc (mathematics)
Major Hungarian scholarships:

Teaching activity (with list of courses taught so far):
Eötvös University (1963– ):
Partial differential equations (for students in mathematics; lecture, practice)
analysis (for students in physics)

Other professional activity:
45 years of teaching experience, 8 diploma thesis supervisions, 7 Ph.D. thesis supervisions;
over 30 lectures at international conferences;
65 publications;

Up to 5 selected publications from the past 5 years:
1. W. Jäger, L. Simon: On nonlinear perturbations of the Schrödinger equation with
    discontinuous coefficients, Acta Math. Hung. 98 (2003), 227-243.
2. L. Simon: On approximation of solutions of parabolic functional differential equations in
    unbounded domains, Proceedings of the Conference FSDONA Teistungen, 2001, 439-
    451.
3. L. Simon: On nonlinear parabolic functional differential equations with nonlocal linear
    contact conditions, Funct. Diff. Equations 11(2004), 153-162.
4. On contact problems for nonlinear parabolic functional differential equations, Electronic J.
    of Qualitative Theory of Diff. Equations, 2004, 22, 1-11.
5. L. Simon, W. Jäger, On a system of quasilinear parabolic functional differential equations,
    Acta Math. Hung. 112 (2006), 39-55.

The five most important publications:
1. L. Simon: On approximation of solutions of boundary value problems in domains with
    unbounded boundary, Mat. Sbornik 91 (1973), 488-493.

2. L. Simon: On strongly nonlinear elliptic equations in unbounded domains, Differ.
    Uravneniya 22 (1986), 472-483.

3. L. Simon: Radiation conditions and the principle of limiting absorption for quasilinear
    elliptic equations, DAN SSSR 288 (1986), 316-319.

4. L. Simon: On strongly nonlinear elliptic equations with weak coercivity condition. Publ.
    Math. Barcelona 36 (1992), 175-188.

5. L. Simon: On nonlinear hyperbolic functional differential equations, Math. Nachr. 217
    (2000), 175-186.


                                             Personal data
                             MSc program in mathematics: personal data          125


Activity in the scientific community, international relations
   organizer of five international conferences;
   member of the Mathematical Commitee of the Hungarian Academy of Sciences;
   member of the granting committee of the Hungarian NSRF (OTKA), 1999–2003;
   coauthor from Germany;
   visiting professor at universities in Germany, Spain, Finland and Belgium.




                                           Personal data
126                            MSc program in mathematics: personal data


Name: Péter Simon

Date of birth: 1966
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös Loránd University, associate professor
Scientific degree (discipline): PhD (mathematics)
Major Hungarian scholarships: Bolyai scholarship (2000–2001 and 2003-2005)

Teaching activity (with list of courses taught so far):
Eötvös Loránd University (1990– ):
Differential equations (for students in mathematics and applied mathematics; lecture, practice)
Dynamical systems (for students in mathematics and applied mathematics; lecture, practice)
Mathematical modelling (for students in applied mathematics; practice)
Analysis (for students in physics; lecture, practice)
Analysis (for students in mathematics and applied mathematics; practice)
Calculus (for students in physics; lecture, practice)
BSM (2003– )
Dynamical systems
Real functions and measures

Other professional activity:
18 years of teaching experience, 6 diploma thesis supervisions, 2 Ph.D. thesis supervisions;
over 25 lectures at international conferences;
53 publications;
International collaborations (Leeds, Vienna)

Up to 5 selected publications from the past 5 years:
1. J. Karátson, P.L. Simon, Exact multiplicity for degenerate two-point boundary value
      problems with p-convex nonlinearity, , J. Nonlin. Anal., 52 (6), 1569-1590 (2003).
2. P. L. Simon, On the structure of of spectra of travelling waves, E. J. Qualitative Theory of
      Diff. Equ., 15, 1-19, (2003).
3. Tóth, J., Simon P.L., Differenciálegyenletek; Bevezetés az elméletbe és az alkalmazásokba,
      Typotex, (2005).
4. Simon, P.L., Classification of positive convex functions according to focal equivalence,
      IMA J. Appl. Math., 71, 519-533 (2006).
5. Simon, P.L., Volford, A., Detailed study of limit cycles and global bifurcations in a
      circadian rhythm model, Int. J. Bif. Chaos,16 (2), 349-367 (2006).

The five most important publications:
B.M. Garay, P.L. Simon, The local flow-box theorem for discretizations. The analytic case, J.
      Difference Eqns. Appl., 7, 345-381, (2001).
J. Karátson, P.L. Simon, On the linearized stability stability of positive solutions of
      quasilinear problems with p-convex or p-concave nonlinearity, J. Nonlin. Anal., 47,
      4513-4520, (2001).
J. Hofbauer, P.L. Simon, An existence theorem for parabolic equations on ${\bf R}^N$ with
      discontinuous nonlinearity, E. J. Qualitative Theory of Diff. Equ., No. 8., 1-9 (2001).


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                             MSc program in mathematics: personal data                      127


Simon, P.L., Kalliadasis, S., Merkin, J.H., Scott, S.K., Stability of flames in an exothermic-
      endothermic system, IMA J. Appl. Math., 69, 175-203, (2004).
J. Hernandez, J. Karátson, P.L. Simon, Multiplicity for semilinear elliptic equations involving
      singular nonlinearity, J. Nonlin. Anal., 65 (2), 265-283 (2006).

Activity in the scientific community, international relations
Collaboration with J. Hofbauer (Vienna) 1997-2001.
Bolyai János Fellowship: 2000-2001, 2003-2005.
Research Fellowship at the University of Leeds: 2001-2002.
OTKA (Hungarian Science Foundation) grant: 1997-2000, 2001-2004.




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Name: András Stipsicz

Date of birth: 1966
Highest degree: diploma in mathematics,
Present employer: Alfréd Rényi Mathematical Institute, scientific advisor
Scientific degree: DSc (mathematics)
Major Hungarian Scholarship: Széchenyi István Scholarship: 2001
     Bolyai János Scholarship, 1999-2002

Teaching activity (with list of courses taught so far):
Eötvös University (1997-2002):
Analysis, algebraic topology, differential topology
BSM (Budapest Semester in Mathematics) 1997-
analysis, toplogy

Other professional activity:
Research in mathematics since 1990
Over 10 years of teaching

Up to 5 selected publications from the past 5 years:
Ozsváth-Szabó invariants and tight contact 3-manifolds I (Paolo Lisca-val közösen) Geom.
Topol. 8 (2004) 925-945.
An exotic smooth structure on CP2#6CP2-bar (Szabó Zoltánnal közösen) Geom. Topol. 9
(2005) 813-832
Ont he geography of Stein fillings of certain 3-manifolds, Michigan Math. J. 51 (2003) 327-
337
Seifert fibered contact 3-manifolds via surgery (Paolo Lisca-val közösen) Algebr. Geom.
Topol. 4 (2004) 199-217.
Tight, non-fillable contact circle bundles (Paolo Lisca-val közösen) Math. Ann. 328 (2004)
285-298.


The five most important publications:
Ozsváth-Szabó invariants and tight contact 3-manifolds I (Paolo Lisca-val közösen)Geom.
Topol. 8 (2004) 925-945.
4-manifolds and Kirby calculus (Robert Gompf-fal közösen)
AMS Graduate Studies in Math. Vol. 20 (1999)
Seifert fibered contact 3-manifolds via surgery (Paolo Lisca-val közösen)
Algebr. Geom. Topol. 4 (2004) 199-217.
Tight, non-fillable contact circle bundles (Paolo Lisca-val közösen)
Math. Ann. 328 (2004) 285-298.

Activity in the scientific community, international relations




                                             Personal data
                        MSc program in mathematics: personal data                     129


Guest professor/reseracher at several universities ( (UC Irvine, MSRI Berkeley, Princeton
University, IAS Princeton, Warwick University, Max-Planck-Institute Bonn, Columbia
University),
Invited address at several conferences
Organizer of several conferences and summer schools




                                      Personal data
130                          MSc program in mathematics: personal data


Name: Csaba Szabó

Date of birth: 1965
Highest degree: diploma in mathematics,
Present employer: Associate Professor, ELTE, Dept of Algebra and Number Theory
Scientific degree: DSc (mathematics)
Major Hungarian Scholarship: Széchenyi István Scholarship: 2001
     Bolyai János Scholarship, 1998-2001

Teaching activity:
Eötvös University (1986– )
     algebra, algebra and number theory, linear algebra
Abroad:
    calculus I-II., linear algebra
Budapest Semesters in Mathematics (1998– )
    algebra, Galois theory, number Theory

Other professional activity:
       3x1 years Post Doctoral Fellowship

Up to 5 selected publications from the past 5 years:
1.    Pluhár Gabriella; Szabó Csaba The free spectrum of the varieties of bands, Semigroup
      Forum, Vol. 76, (2008) No. 3. 576-578
2.    Kátai-Urbán, Kamilla; Szabó, Csaba On the free spectrum of the variety generated by
      the combinatorial completely 0-simple semigroups. Glasg. Math. J. 49 (2007), no. 1,
      93–98.
3.    Horváth, Gábor; Lawrence, John; Mérai, László; Szabó, Csaba The complexity of the
      equivalence problem for nonsolvable groups. Bull. Lond. Math. Soc. 39 (2007), no. 3,
      433–438.
4.    Kátai-Urbán, Kamilla; Szabó, Csaba Free spectrum of the variety generated by the five
      element combinatorial Brandt semigroup. Semigroup Forum 73 (2006),
5.    Szabó, Csaba On rings with few orbits. Comm. Algebra 34 (2006), no. 6, 2251–2260.

The five most important publications:
1.    Cs. Szabó és P. J. Cameron, Independence algebras, J. London Math.Soc. (2) 61 (2000)
      321–334.
2.    Cs. Szabó és R. W. Quackenbush, Nilpotent groups are not dualizable, Journal of
      Australian Mathematical Society, 73 (2002) 173–179.
3.    Cs. Szabó és R. W. Quackenbush, Strong duality for metacyclic groups, Journal of
      Australian Mathematical Society 72 (2002) 377–392.
4.    Cs. Szabó et al., Natural dualities for quasi-varieties generated by a finite commutative
      ring, The Victor Aleksandrovich Gorbunov memorial issue Algebra Universalis, 46
      (2001), 285–320.
5.    Cs. Szabó, Nilpotent rings are not dualizable, Algebra Universalis, 42 (1999) 293–298.




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                               MSc program in mathematics: personal data                 131


Name: István Szabó

Date of birth: 1948
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös Loránd University, associate professor
Scientific degree (discipline): CSc (mathematics)
Major Hungarian Scholarships:

Teaching activity (with list of courses taught so far):
Eötvös Loránd University (1991– ):
Applied information theory and algebra (for students in mathematics, for student for
informatics; lecture, practice):
Data Compression, Cryptography

Other professional activity:
20 years of teaching experience;
20 publications;
1 technical book revision
1 Hungarian patent;
Expert titles: Electronic signature service expert

Up to 5 selected publications from the past 5 years:
- I. Szabó: System of courses and tools in the field of technological security evaluation
     methodology, HISEC’2004 (Hungarian Information Security Conference), 2004.
-. I. Szabó: Common Criteria – Educational curriculum, Published by Ministry of Informatics
     and Telecommunication, 2004
-. I. Szabó: IT security and covert channels, SAP’2006 Conference, 2006
-. P.Papp, I. Szabó: Different approaches to the security of cryptography- based security
     mechanisms, Journal of Applied Mathematics, 23 (2006) .207-294


The five most important publications:
―On matrix characterizations of primitive regular semigroups‖, Coll. Math.Soc.,39, 461-469
―On a class of lattice ordered semigroups‖, Acta Math. Ac.Sci. Hung.,30,141-147
―Laws, Organisations, Recommendations and Practice‖, Global IT Security, Österreichische
   Computer Gesellschaft, Proceedings of the XV. IFIP World Computer Congress, 1998
Book-like publications (in many copies, published on Internet by governmental organisation)
   determining educational and professional orientation, revised by wide audience:
„Common Criteria Methodology for security evaluation of IT products and systems‖,
   Recommendation document No 16 by MEH ITB, www.itb.hu/ajanlasok/a16 , 1998.,
   Published by the Interministerial Committee on Informatics of the Prime Minister’s Office
„IT Security Sectorial Strategy of Hungarian Information Society Strategy ‖, Published by
   Ministry of Informatics and Telecommunication, 2004
STUDY on the possible tasks of the National Communications Authority regarding the IT
   Security Sectorial Strategy of Hungarian Information Society Strategy, 2004

Activity in the scientific community, international relations

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Member of the following professional associations: John von Neumann Computer Society,
  Hungarian Electronic Signature Association.
Presentations, participation at different conferences.




                                           Personal data
                               MSc program in mathematics: personal data                     133


Name: Mihály Szalay.


Date of birth: 1947
Highest degree (discipline): M.Ed. in Mathematics and Physics
Present employer: Eötvös University, associate professor
Scientific degree (discipline): CSc (mathematics)

Teaching activity (with list of courses taught so far):
Eötvös University (1970– ):
     algebra and number theory (for students in mathematic and physics; practice)
     linear algebra and geometry (for students in informatics; lecture, practice)
     number theory (for student in mathematics; lecture, practice)
     group theory (for students in physics; lecture)
     analytic number theory (for students in mathematics; lecture)
     power sum method and its applications; statistical theory of partitions; statistical theory
     of groups; chapters from number theory (special courses (lectures) for students in
     mathematics).

Other professional activity:
       37 years of teaching experience.
       24 research papers, 2 survey papers, 1 textbook.

Up to 5 selected publications from the past 5 years:
1.   Nicolas, J.-L., Szalay, M.: Popularity of sets represented by the partitions of n, The
     Ramanujan Journal 8 (2004), 147–175.
2.   Dartyge, C., Sárközy, A., Szalay, M.: On the distribution of the summands of partitions
     in residue classes, Acta Math. Hunmgar. 109 (2005), 215–237.
3.   Dartyge, C., Sárközy, A., Szalay, M.: On the number of prime factors of summands of
     partitions, Journal de Théorie des Nombres de Bordeaux 18 (2006), 73–87.
4.   Dartyge, C., Sárközy, A., Szalay, M.: On the distribution of the summands of unequal
     partitions in residues classes, Acta Math. Hungar. 110 (2006), 323–335.
5.   Dartyge, C., Szalay, M.: Dominant residue classes concerning the summands of
     partitions, Functiones et Approximatio 37 (2007), 65–96.

The five most important publications:
1.   Szalay, M., Turán, P.: On some problems of the statistical theory of partitions with
     application to characters of the symmetric group, I, Acta Math. Acad. Sci. Hungar. 29
     (1977), 361–379.
2.   Erdős, P., Szalay, M.: On some problems of J. Dénes and P. Turán, in: Studies in Pure
     Mathematics (to the Memory of Paul Turán), Akadémiai Kiadó, Budapest, 1983, 187–
     212.
3.   Erdős, P, Szalay, M.: On the statistical theory of partitions, in: Coll. Math. Soc. J.
     Bolyai, 34 (Topics in Classical Number Theory, Budapest, 1981), 397–450.
4.   Erdős, P, Nicolas, J.-L., Szalay, M.: Partitions into parts which are unequal and large, in:
     Lecture Notes in Mathematics 1380 (Number Theory, Ulm, 1987), Springer, Berlin–
     Heidelberg–New York, 1989, 19–30.


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5.    Dartyge, C., Szalay, M.: Dominant residue classes concerning the summands of
      partitions, Functiones et Approximation 37 (2007), 65–96.


Activity in the scientific community, international relations
      Matematikai Lapok (technical editor), 1985–1990;
      Network ERBCI PACT 92-4022 (ELTE–coordinator), 1992–1995;
      Mathematical Reviews (reviewer), 1987–;
      Zentralblatt für Mathematik (reviewer), 1987–;
      coauthors from France, U.K., U.S.A.;
      invited professor at the University Henri Poincaré, Nancy 1.




                                           Personal data
                               MSc program in mathematics: personal data                       135


Name: Péter Sziklai

Date of birth: 1968
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, associate professor
Scientific degree (discipline): CSc (mathematics)
Major Hungarian scholarships: Bolyai scholarship, Eötvös scholarship, Magyary postdoctoral
fellowship, OTKA postdoctoral grant

Teaching activity (with list of courses taught so far):
Discrete mathematics, practice/lecture (for students in teaching of math., mathematics,
applied math.): since 1989 (15 years, 3-4 years missed)
Geometry practice (for students in teaching of math.): 1989-91 (2 years)
Set theory and logic practice (for students in teaching of math.): 4 years
Finite geometry seminar: 10 years approx.
Introduction to finite geometry, lecture: 4 years
Symmetric structures, lecture (students in mathematics): 2 év
Graphs and algorithms lecture (for students in teaching of math.): 3 years
Introduction to computer science, lecture, practice (BTU, stutents in informatics): 5 years
Elements of computer science, lecture (BTU ): 2 years
Calculus (CEU, Environmental studies): 3 years


Other professional activity:
19 years of teaching experience, 7 diploma thesis supervisions, 1 Ph.D. thesis supervisions;
over 20 lectures at international conferences;
25 publications;
2 patents pending

Up to 5 selected publications from the past 5 years:
1. J. Eisfeld, L. Storme and P. Sziklai, On the spectrum of the sizes of maximal partial
   spreads in PG(2n,q), q>=3, Des. Codes Cryptogr., 36 (2005), 101-110.
2. P. Sziklai, Partial flocks of the quadratic cone, J. Combin. Th. Ser. A, 113 (2006), 698-702.
3. P. L. Erdős, P. Ligeti, P. Sziklai, D. Torney, Subwords in reverse complement order,
   Annals of Comb., 10 (2006), 415-430.
4. S. Ball, A. Blokhuis, A. Gács, P. Sziklai and Zs. Weiner, On linear codes whose weights
   and length have a common divisor, Advances in Mathematics 211 (2007), 94-104.
5. P. Sziklai, A conjecture and a bound on the number of points of a plane curve, Finite Fieds
   Appl., 14 (2008), 41-43.

The five most important publications:
1. J. Eisfeld, L. Storme and P. Sziklai, On the spectrum of the sizes of maximal partial
   spreads in PG(2n,q), q>=3, Des. Codes Cryptogr., 36 (2005), 101-110.

2. P. Sziklai, Partial flocks of the quadratic cone, J. Combin. Th. Ser. A, 113 (2006), 698-702.




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3. P. L. Erdős, P. Ligeti, P. Sziklai, D. Torney, Subwords in reverse complement order,
   Annals of Comb., 10 (2006), 415-430.
4. S. Ball, A. Blokhuis, A. Gács, P. Sziklai and Zs. Weiner, On linear codes whose weights
   and length have a common divisor, Advances in Mathematics 211 (2007), 94-104.
5. P. Sziklai, A conjecture and a bound on the number of points of a plane curve, Finite Fieds
   Appl., 14 (2008), 41-43.

Activity in the scientific community, international relations
Combinatorica (Springer-Bolyai), Managing Editor
organizer of two international conferences;
member of Hungarian-Spanish/Flemish/Italian/Slovenian/Dutch bilateral projects in past
member of the granting committee of the Rényi Kató Prize;
head of ELTECRYPT research group




                                           Personal data
                               MSc program in mathematics: personal data                    137


Name: Róbert Szőke

Date of birth: 1958
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, associate professor
Scientific degree (discipline): CSc (mathematics), Ph.D(mathematics)
Major Hungarian scholarships: Széchenyi professor scholarship (2000–2003)

Teaching activity (with list of courses taught so far):
Notre Dame University (1985-1990)
Calculus, (for undergraduate students, practice)
Ordinary Differential equations (for undegraduate students, practice),
Since January 1, 1991 I teach at the Department of Analysis at Eötvös University, except
certain short periods, see below.
Eötvös University (1991– ):
analysis (for students in mathematics; mathematics- physics or technology education;
informatics-physics; astronomy; geophysics; lecture, practice)
complex analysis (for tudents in mathematics;mathematics or physics education;astronomy;
lecture, practice)
several complex variables (for tudents in mathematics; lecture)
complex manifolds (for PhD students, lecture)
BSM (2004 Spring semester)
Basic Algebraic geometry (lecture)
CEU (2004 Fall semester)
Complex manifolds (Reading course)

Purdue University
Linear algebra and ordinary differential equations (1997 Spring semester, for students in
engineering, lecture)
 Ordinary differential equations (2005 Spring semester, for students in engineering, lecture)
Linear algebra (2007 Fall semester, for students in engineering, lecture)

Other professional activity:
Sept 1977- June 1978: computer operator in the Computer center of the Ministry of Labour
Nov. 1983- Aug. 1984 and Aug.-Dec. 1990: scientific coworker, Computer center of the
Medical University
Sept. 1984- Aug. 1985: guest researcher at the Mathematical Institute of the Hungarian
Academy of Sciences,
Aug. 1985- Aug. 1990: graduate student at the University of Notre Dame
October 1992- Aug. 1994: guest researcher at the Max Planck Institut für Mathematik, Bonn
Sept. -Dec. 1999: guest researcher (with an Eötvös fellowship) at the Mathematical Institute
of Oxford University
 Feb.- Dec. 2008: guest researcher at the Rényi Institute of Mathematics

Up to 5 selected publications from the past 5 years:


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1. R. Szőke: Canonical complex structures associated to connections and complexifications
   of Lie groups (Math. Ann. 329, 553-591, 2004)
2. R. Szőke: Többváltozós komplex függvénytan (egyetemi jegyzet, 2003, ELTE, Eötvös
   kiadó)
3. R. Szőke: Complex crowns of symmetric spaces (Int. J. Math. 16, 889-902, 2005)
4. A. Korányi, R. Szőke: On Weyl group equivariant maps (Proc. AMS, 134, 3449-3456,
   2006)
5. R. Szőke: On isometries of Kahler manifolds (Acta Math. Hung. 111, 77-79, 2006)


The five most important publications:
1. L. Lempert-R. Szőke: Global solutions of the homogeneous Monge-Ampere equation and
   complex structures on the tangent bundles of Riemannian manifolds (Math. Ann. 290,
   689-712, 1991)
2. R. Szőke: Complex structures on the tangent bundle of Riemannian manifolds (Math.
   Ann. 291, 409-428, 1991)
3. A. Dancer- R. Szőke: Symmetric spaces, adapted complex structures and hyperkahler
   structures (Q. J. Math., 48, 27-38, 1997)
4. R. Szőke: Involutive structures on the tangent bundle of symmetric spaces (Math. Ann.,
    319, 319-348, 2001)
5. R. Szőke: Canonical complex structures associated to connections and complexifications
   of Lie groups (Math. Ann. 329, 553-591, 2004)

Activity in the scientific community, international relations
Member of the Bolyai Mathematical Society and the AMS.
Referee of NSF and OTKA proposals and international math journals.




                                           Personal data
                               MSc program in mathematics: personal data                     139


Name: Tamás Szőnyi

Date of birth: 1957
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, professor, Computer and Automation
      Research Institute, Hungarian Academy of Sciences, research advisor (part time)
Scientific degree (discipline): DSc (mathematics)
Major Hungarian scholarships: Széchenyi scholarship (1997–2000), Pál Erdős Prize of the
      Hungarian Academy (1997).


Teaching activity (with list of courses taught so far):
Eötvös University (1987– ):
Discrete mathematics (for students in mathematics; lecture, practice; also for students in
informatics)
Symmetric structures, finite geometry, Mathematical games, Extremal set systems,
Enumeration, Error correcting codes,
Finite geometry seminar (research seminar 1986--)

University of Szeged (1994--1997)
Geometries and their models, Algebraic methods in combinatorics, Plane curves, Codes and
geometries (for students in mathematics)

Technical University Budapest (1982--1993)
Mathematics I,II,III, IV (for students in transportation engineering)

Other professional activity:
25 years of teaching experience, 15 diploma thesis supervisions, 7 Ph.D. thesis supervisions;
over 30 lectures at international conferences; 1 book in Hungarian,
65 publications
Visiting professor Yale, TUE Eindhoven, University of Sussex, University of Ghent,
University of Perugia, University of Basilicata (in total roughly 26 months)

Up to 5 selected publications from the past 5 years:
A. Gács, T. Szőnyi , Zs. Weiner, On the spectrum of minimal blocking sets, J. of Geometry,
76 (2003), 256-281
A. Gács , T. Szőnyi, On maximal partial spreads on PG(n,q), Designs, Codes, and
Cryptography 29 (2003), 123-129
E. Boros, T. Szőnyi, K. Tichler. Defining sets for PG(2,q), Discrete Mathematics 30
(2005), 17—31.
J. Barát, F. Pambianco, S. Marcugini, T. Szőnyi, On disjoint blocking sets, J.
Comb. Designs 14 (2006), 149—158.
A. Blokhuis, L. Lovász, L. Storme, T. Szőnyi, On multiple blocking sets in Galois planes,
Advances in Geometry 7 (2007), 39—53.

The five most important publications:
E. Boros, T. Szőnyi, On the sharpness of a theorem of B. Segre, Combinatorica 6 (1986),
261-268

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L. Rónyai, T. Szőnyi, Planar functions over finite fields, Combinatorica 9 (1989), 315-320
T. Szőnyi, Blocking sets in Desarguesian affine and projective planes, Finite Fields and Appl.
2 (1997), 187-202
T. Szőnyi, On the embedding of (k,p)-arcs in maximal arcs, Designs, Codes, and
Cryptography 18 (1999), 235-246
A. Blokhuis, L. Storme, T. Szőnyi, Multiple blocking sets in Desarguesian planes,
J. London Math. Soc.60 (1999), 321-332

Activity in the scientific community, international relations
member of the J. Bolyai Math. Society, reviewer of Mathematical Reviews,
secretary and later vice president of the Mathematical Committee of the Hungarian
Academy of Sciences (1999--), member of the OTKA Jury in mathematics
(1998—2001),
Editor of Combinatorica, Innovations in Incidence Geometry, Abh. Math. Sem.
Univ. Hamburg, Contributions to Discrete Mathematics, Annales Univ. Eötvös,
Sect Math.
Organizer of 4 international conferences, editor of 3 conference proceedings
International relations: TUE Eindhoven, Universities of Ghent, Perugia, Potenza,
Sussex.




                                           Personal data
                               MSc program in mathematics: personal data               141


Name: András Szűcs

Date of birth: 1950
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, full professor
Scientific degree (discipline): DSc (mathematics)
Major Hungarian scholarships: Széchenyi scholarship (1997—2000)

Teaching activity (with list of courses taught so far):
Eötvös University (1981– ):
geometry, analysis, complex analysis, topology
BSM (1988)
Algebraic topology

Other professional activity:
30 years of teaching experience, many diploma thesis supervisions, 2 Ph.D. thesis
supervisions;
over 10 invited (1 hour) lectures at international conferences;
51 publications;

Up to 5 selected publications from the past 5 years:
1) with T. Ekholm: Geometric formulas for Smale invariants of codimension two
   immersions, Topology 42 (2003) 171 – 196
2) with G. Lippner: A new proof of the Herbert multiple-point formula (Russian) Fundam.
   Prikl. Mat. 11 (2005) no 5, 107 – 116; translation in J. Math. Sci (N.Y.) 146 (2007), no
   11, 5523 – 5529.
3) Elimination of Singularities by Cobordism, Real and complex singularities, 301 – 324,
   Contemporary Mathematics Volume 354, Amer Math. Soc., Providence, RI, 2004
4) with T. Ekholm and T. Terpai: Cobordism of fold maps and maps with prescribed number
   of cusps. Kyushu J. Math. 61 (2007), no 2, 395 – 414.
5) Cobordism of singular maps, Geometry and Topology 12 (2008) 2379-2452.

The five most important publications:
1) Analogue of the Thom space for mapping with singularity of type Sigma1, Math. Sb. (N.
   S.) 108 (150) (1979) no. 3 438 – 456 (in Russian); English translation: Math. USSR-Sb.
   36 (1979) no. 3. 405 – 426 (1980)
2) Cobordism group of immersions of oriented manifolds; Acta Math. Hungar. 64 (2) (1994),
   191 – 230
3) with R. Rimanyi: Pontrjagin – Thom type construction for maps with singularities,
   Topology 37 (1998), 1177 – 1191
4) with T. Ekholm: Geometric formulas for Smale invariants of codimension two
   immersions, Topology 42 (2003) 171 – 196
5) Cobordism of singular maps, Geometry and Topology 12 (2008) 2379 – 2452.

Activity in the scientific community, international relations:
Secretary of the Doctoral Committee of the Hungarian Academy of Siences (5 years)

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142                       MSc program in mathematics: personal data


Secretary of the Hungarian Topology Conference (20 years)
Member of the doctoral committee on a large number of occasions
Editor of Mathematica Slovaca.




                                        Personal data
                               MSc program in mathematics: personal data                      143


Name: Árpád Tóth

Date of birth: 1964
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, associate professor
Scientific degree (discipline): PhD (mathematics)
Major Hungarian scholarships: Bolyai Fellowship

Teaching activity (with a selection of courses taught so far):
Eötvös University (2003– ):
Analysis (for students in math, math ed; lecture, practice)
Calculus (for students in physics education; lecture, practice)
Ordinary Differential Equations (for students in physics edutacttion; lecture, practice)
Modular Forms (for students in math, lecture)
Several Complex Variables (for students in math, lecture)
Topology (for students in math, lecture)

BSM (2004– )
Topology (lecture, practice)
Analytic Number Theory (lecture, practice)

Fordham University (2001-2003)
Calculus (for students in math, business, life sciences; lecture, practice)
Linear Algebra (for students in math; lecture, practice)
Finte Math with Probability (for liberal arts students; lecture, practice)

University of Michigan (1997-2000)

Calculus ((various versions) for students in math, engineering, business, life sciences; lecture,
practice)
Linear Algebra (for students in engineering; lecture, practice)
Ordinary Differential Equations (for students in engineering; lecture, practice, computer lab)
Advanced Vector Calculus (for graduate students in engineering; lecture, practice)
Number Theory (for students in math; lecture, practice)
Modular Forms (for PhD students in math, lecture)

Rutgers University (1992-1997)

Calculus (for students in math, engineering, business, life sciences; lecture, practice)
Vector Calculus (for students in physics, engineering; lecture, practice)
Ordinary Differential Equations (for students in engineering; practice)
Advanced Vector Calculus (for master students in applied math; practice)

Other professional activity:
More than 15 years of teaching experience, over 15 lectures at international conferences;
8 publications;

Up to 5 selected publications from the past 5 years:

                                             Personal data
144                         MSc program in mathematics: personal data


1.    Toth A., Varolin D. Holomorphic diffeomorphisms of semisimple homogeneous spaces.
      Compos. Math. 142 (2006), no. 5, 1308—1326.
2.    Elekes M., Toth A. Covering locally compact groups by less than $2\sp \omega$ many
      translates of a compact nullset. Fund. Math. 193 (2007), no. 3, 243--257.
3.    Toth A. On the Steinberg module of Chevalley groups. Manuscripta Math. 116 (2005),
      no. 3, 277--295.
4.    Toth A., On the evaluation of Salié sums. Proc. Amer. Math. Soc. 133 (2005), no. 3,
      643--645
5.    Duke W., Toth A. The splitting of primes in division fields of elliptic curves.
      Experiment. Math. 11 (2002), 555--565

The five most important publications:
1. Toth A., Varolin D. Holomorphic diffeomorphisms of semisimple homogeneous spaces.
      Compos. Math. 142 (2006), no. 5, 1308—1326.
2. Toth A., Roots of quadratic congruences. Internat. Math. Res. Notices 2000, no. 14, 719--
    739.
 3. Toth A. On the Steinberg module of Chevalley groups. Manuscripta Math. 116 (2005),
    no. 3, 277--295.
 4. Toth A., On the evaluation of Salié sums. Proc. Amer. Math. Soc. 133 (2005), no. 3, 643--
    645
 5. Duke W., Toth A. The splitting of primes in division fields of elliptic curves. Experiment.
    Math. 11 (2002), no. 4, 555--565




                                          Personal data
                               MSc program in mathematics: personal data                145


Name: László Verhóczki

Date of birth: 1961
Highest degree (discipline): diploma in mathematics and physics
Present employer, position: Eötvös University, associate professor
Scientific degree (discipline): PhD (mathematics)
Major Hungarian scholarships: –

Teaching activity (with list of courses taught so far):
Technical University of Budapest (1985–1997):
Geometry (all levels, lecture, practice)
Descriptive Geometry (lecture, practice)
Differential Geometry (lecture, practice)
Calculus (practice)
Eötvös University (1997– )
Geometry (all levels, lecture, practice)
Differential Geometry (all levels, lecture, practice)

Other professional activity:
23 years of teaching experience, 11 diploma thesis supervisions;
over 13 lectures at international conferences;
15 publications.

Up to 5 selected publications from the past 5 years:
1. Verhóczki, L.: Special cohomogeneity one isometric actions on irreducible symmetric
   spaces of types I and II, Beiträge Algebra Geom. 44 (2003), 57–74.
2. Csikós, B., Verhóczki, L.: Tubular structures of compact symmetric spaces associated
   with the exceptional Lie group F4, Geometriae Dedicata 109 (2004), 239–252.
3. Verhóczki, L.: The exceptional compact symmetric spaces G2 and G2/SO(4) as tubes,
   Monatshefte für Mathematik 141 (2004), 323–335.
4. Csikós, B., Németh, B., Verhóczki, L.: Volumes of principal orbits of isotropy subgroups
   in compact symmetric spaces, Houston J. Math. 33 (2007), 719–734.
5. Csikós, B., Verhóczki, L.: Classification of Frobenius Lie algebras of dimension ≤6,
   Publicationes Math. Debrecen 70 (2007), 427–451.


The five most important publications:
1. Verhóczki, L.: Reflections of Riemannian manifolds, Publicationes Math. Debrecen
   38 (1991), 19–31.
2. Verhóczki, L.: Special isoparametric orbits in Riemannian symmetric spaces,
   Geometriae Dedicata 55 (1995), 305–317.
3. Verhóczki, L.: Shape operators of orbits of isotropy subgroups in Riemannian symmetric
   spaces of the compact type, Beiträge Algebra Geom. 36 (1995), 155–170.
4. Berndt, J., Vanhecke, L., Verhóczki, L.: Harmonic and minimal unit vector fields on
   Riemannian symmetric spaces, Illinois J. Math. 47 (2003), 1273–1286.
5. Csikós, B., Németh, B., Verhóczki, L.: Volumes of principal orbits of isotropy subgroups


                                             Personal data
146                           MSc program in mathematics: personal data


  in compact symmetric spaces, Houston J. Math. 33 (2007), 719–734.

Activity in the scientific community, international relations
      organizer of three international conferences;
      member of the Bolyai Mathematical Society (1988–);
      coauthors from Belgium and Germany;
      visiting professor at universities in Belgium and Germany.




                                            Personal data
                               MSc program in mathematics: personal data                  147


Name: Katalin Vesztergombi

Date of birth: 1948
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös Lorand University, associate professor
Scientific degree (discipline): CSc (mathematics) 1987
Major Hungarian scholarships:

Teaching activity (with list of courses taught so far): Algorithmic geometry, discrete
mathematics, discrete programing, combinatorial optimization, discrete mathematical models,
calculus, differential equations, complex analysis, graphtheory, linear algebra, numerical
methods, ALGOL; 32 years



Other professional activity:
Teaching and research: ELTE, JATE, BME, Rutgers University, Yale University, University
of Washington, Microsoft Research (Redmond)
1 international patent

Up to 5 selected publications from the past 5 years:
Geometric representations of graphs (with L. Lovász), Paul Erdős and his Mathematics, (ed.
G. Halász, L. Lovász, M. Simonovits, V.T. Sós), Bolyai Society--Springer Verlag (2004).

Quadrilaterals and k-sets (with L. Lovász, U. Wagner, E. Welzl) in: Towards a Theory of
Geometric Graphs, (J. Pach, Ed.), AMS Contemporary Mathematics 342 (2004) 139-148.

Graph limits and parameter testing (with C.Borgs, J.Chayes, L.Lovász, V.T.Sós, B.Szegedy)
STOC 2006

Counting graph homomorphisms (with C.Borgs, J.Chayes, L.Lovász, V.T.Sós) in: Topics in
Discrete Mathematics (ed. M.Klazar, J.Kratochvil, M.Loebl, J.Matousek,R.Thomas, P.Valtr)
Springer (2006), 315-371



The five most important publications:


Activity in the scientific community, international relations




                                             Personal data
148                         MSc program in mathematics: personal data


Name: András Zempléni


Date of birth: 1960
Highest degree (discipline): diploma in mathematics
Present employer, position: Eötvös University, associate professor
Scientific degree (discipline): CSc (mathematics)



Teaching activity (with list of courses taught so far):
Eötvös University (1982– ):
Probability theory (for students in applied mathematics, informatics, meteorology, geology;
lecture, practice)
Mathematical statistics (for students in applied mathematics, informatics, meteorology,
geology; lecture, practice)
Industrial statistics (for students in applied mathematics)
Modelling environmental data (for PhD students in mathematics)
Teaching experience: 25 years
Lecture note: Móri F. Tamás, Szeidl László, Zempléni András: Mathematical statistics
exercises (Budapest, 1997, ELTE Eötvös Press)

Other professional activity:
25 years of teaching experience, 20 diploma thesis supervisions, 1 Ph.D. thesis supervision
Over 20 lectures at international conferences
52 publications
Coordinator of several major projects in applied statistics
Head of the Applied Statistical Consulting Group (1998-)
Teaching in German: KVIF, Statistics, 2002-
Participation in the English MSc courses held at Eötvös University, Department of Probability
Theory and Statistics
Grants: Royal Society Postdoctoral Fellowship (Sheffield, 1991/92), Bolyai János research
grant (1998-2000), DAAD grant (München, 2003)


Up to 5 selected publications from the past 5 years:
Taylor, C.C., Zempléni, A.: Chain Plot: a Tool for Exploiting Bivariate Temporal
       Structures Computational Statistics and Data Analysis, 2004, pp 141 -153
Zempléni, A., Véber, M., Duarte, B. and Saraiva, P.: Control Charts: a cost -
       optimization approach for processes with random shifts. Appl. Stoch. Models
       in Business and Industry, 20, p.185-200, 2004 .
Dryden, I.L., Zempléni, A.: Extreme shape analysis. J. Roy. Stat. Soc., Ser. C, 55, part 1, p.
       103-121. 2006.
Arató, N.M., Bozsó,D., Elek, P., Zempléni, A.: Forecasting and simulating mortality tables.
       Accepted, Mathematical and Computer Modelling, 2008.
Elek, P., Zempléni, A.: Tail behaviour and extremes of two-state Markov-switching
       autoregressive models. Computers and Mathematics, with applications, 55, p. 2839-
       2855, 2008.


The five most important publications:

                                          Personal data
                            MSc program in mathematics: personal data                       149


Zempléni, A.: On the heredity of Hun and Hungarian property, J. of Theoretical
       Probability Vol 3. No.4. 1990, p. 599-609.
Zempléni, A.: Inference for bivariate extreme value distributions. Journa l of
       Applied Statistical Science 1996, 4, No. 2/3, p. 107 -122.
Taylor. C.C., Zempléni, A.: Chain Plot: a Tool for Exploiting Bivariate Temporal
       Structures. Computational Statistics and Data Analysis 46, p. 141 -153, 2004
Dryden, I.L., Zempléni, A.: Extreme shape analysis. J. Roy. Stat. Soc., Ser. C, 55, part 1, p.
       103-121. 2006.
Elek, P., Zempléni, A. Tail behaviour and extremes of two-state Markov-switching
       autoregressive models. Computers and Mathematics, with applications, 55, p. 2839-
       2855, 2008.


Activity in the scientific community, international relations:
Coordinator of several EU projects
Member of the European Regional Committee of the Bernoulli Society (2004-)
Coauthors from the United Kingdom, the Netherlands
Organisor of 3 conferences




                                          Personal data
150                      MSc program in mathematics: language proficiency



            MSc in Mathematics: Language proficiency
István Ágoston
       1. Language proficiency examination (high level): 1985
       2. Teaching experience: Carleton University, Ottawa (1991, 1996, 2002, 2004: four
       semesters), Budapest Semesters in Mathematics (2 semesters)
       3. Studies abroad: Ph.D. studies, Carleton University, Ottawa, 1986–1990
       4. Talks delivered in English: over 20 conference talks

Miklós Arató
       1. Language proficiency examination (high level):
       2. Teaching experience:
       3. Studies abroad:
       4. Talks delivered in English: over 15 conference talks

András Bátkai
      1. Language proficiency examination (high level):
      2. Teaching experience:
      3. Studies abroad:
      4. Talks delivered in English: over 20 conference talks

András A. Benczúr
      1. Language proficiency examination (high level):
      2. Teaching experience:
      3. Studies abroad: Ph. D. Studies, MIT (graduation in 1997)
      4. Talks delivered in English: over 15 conference lectures

Károly Bezdek
       1. Language proficiency examination (high level):
       2. Teaching experience: University of Calgary (2004– )
       3. Studies abroad:
       4. Talks delivered in English: over 20 conference lectures

Károly Böröcyky Jr.
       1. Language proficiency examination (high level):
       2. Teaching experience: Budapest Semesters in Mathematics (1994– )
       3. Studies abroad:
       4. Talks delivered in English: over 20 conference lectures

Zoltán Buczolich
       1. Language proficiency examination (high level):
       2. Teaching experience: University of Calfornia, Davis (1989–1990), University of
       Wisconsin, Milwaukee (1994), Michigan State University (2001–2002), University of
       North Texas (2003)
       3. Studies abroad:
       4. Talks delivered in English: over 25 invited talks

Balázs Csikós

                                      Language proficiency
                         MSc program in mathematics: language proficiency              151


       1. Language proficiency examination (high level): 1984
       2. Teaching experience: Budapest Semesters in Mathematics (1990– )
       3. Studies abroad:
       4. Talks delivered in English: over 26 conference lectures

Villő Csiszár
       1. Language proficiency examination (high level): 1999
       2. Teaching experience:
       3. Studies abroad: University of Sheffield (1 year)
       4. Talks delivered in English:

Piroska Csörgő
       1. Language proficiency examination (high level):
       2. Teaching experience:
       3. Studies abroad:
       4. Talks delivered in English: over 20 conference talks

Csaba Fábián
       1. Language proficiency examination (high level):
       2. Teaching experience:
       3. Studies abroad:
       4. Talks delivered in English: over 10 conference talks

István Faragó
        1. Language proficiency examination (high level):
        2. Teaching experience:
        3. Studies abroad:
        4. Talks delivered in English: over 40 conference talks

László Fehér
       1. Language proficiency examination (high level):
       2. Teaching experience: Universityof Notre Dame (1993–1998)
       3. Studies abroad: Ph.D. studies at University of Notre Dame (1992–1998)
       4. Talks delivered in English:

Alice Fialowski
       1. Language proficiency examination (high level):
       2. Teaching experience: Univ. of Pennsylvania, Philadelphia (1987–1989), Univ. of
       California, Davis (1990–1995),
       3. Studies abroad:
       4. Talks delivered in English: over 20 conference talks

András Frank
      1. Language proficiency examination (high level):
      2. Teaching experience: University of Bonn (1984–1986, 1989–1993)
      3. Studies abroad:
      4. Talks delivered in English: over 60 conference talks



                                      Language proficiency
152                      MSc program in mathematics: language proficiency


Róbert Freud
       1. Language proficiency examination (high level): 1975
       2. Teaching experience: Ohio State University, Columbus and UCLA, Los Angeles
       (1982–1983, sixteen months)
       3. Studies abroad:
       4. Talks delivered in English: over 10 conference talks

Katalin Fried
       1. Language proficiency examination (high level): 1980
       2. Teaching experience:
       3. Studies abroad:
       4. Talks delivered in English:

Róbert Fullér
       1. Language proficiency examination (high level):
       2. Teaching experience: Universityof Helsinki (2008, 9 months)
       3. Studies abroad:
       4. Talks delivered in English:

Vince Grolmusz
       1. Language proficiency examination (high level):
       2. Teaching experience: University of Chicago (1999, over 6 months)
       3. Studies abroad:
       4. Talks delivered in English:

Katalin Gyarmati
       1. Language proficiency examination (high level):
       2. Teaching experience:
       3. Studies abroad:
       4. Talks delivered in English: over 16 conference talks

Gábor Halász
      1. Language proficiency examination (high level): 1967
      2. Teaching experience: University of Illinois (1978–1979)
      3. Studies abroad:
      4. Talks delivered in English:

Norbert Hegyvári
       1. Language proficiency examination (high level):
       2. Teaching experience:
       3. Studies abroad:
       4. Talks delivered in English: over 15 conference lectures

Péter Hermann
       1. Language proficiency examination (high level):
       2. Teaching experience: Budapest Semesters in Mathematics (over 15 years), CEU
       (over 3 years)
       3. Studies abroad:
       4. Talks delivered in English:
                                      Language proficiency
                         MSc program in mathematics: language proficiency               153




Tibor Illés
        1. Language proficiency examination (high level):
        2. Teaching experience: University of Edinburgh (2007–2008, 12 months)
        3. Studies abroad:
        4. Talks delivered in English:

Ferenc Izsák
       1. Language proficiency examination (high level):
       2. Teaching experience:
       3. Studies abroad:
       4. Talks delivered in English: over 10 conference lectures

Tibor Jordán
       1. Language proficiency examination (high level):
       2. Teaching experience: University of Odense (1996–1998), University of Aarhus
       (1999)
       3. Studies abroad:
       4. Talks delivered in English: over 50 conference lectures

Alpár Jüttner
       1. Language proficiency examination (high level):
       2. Teaching experience:
       3. Studies abroad:
       4. Talks delivered in English: over 10 conference lectures

János Karátson
       1. Language proficiency examination (high level):
       2. Teaching experience:
       3. Studies abroad:
       4. Talks delivered in English: over 10 conference lectures

Gyula Károlyi
      1. Language proficiency examination (high level): 1996
      2. Teaching experience: ETH Zurich (2001–2002), University of Memphis (2005)
      3. Studies abroad:
      4. Talks delivered in English: over 40 conference talks

Tamás Keleti
      1. Language proficiency examination (high level):
      2. Teaching experience:Budapest Semesters in Mathematics (1999– , 9 years)
      3. Studies abroad:
      4. Talks delivered in English: over 20 conference talks

Tamás Király
      1. Language proficiency examination (high level):
      2. Teaching experience:
      3. Studies abroad:
      4. Talks delivered in English: over 10 conference talks
                                      Language proficiency
154                       MSc program in mathematics: language proficiency




Zoltán Király
       1. Language proficiency examination (high level):
       2. Teaching experience:
       3. Studies abroad:
       4. Talks delivered in English: over 10 conference talks (www.cs.elte.hu/~kiraly)

Emil Kiss
      1. Language proficiency examination (high level): 1981
      2. Teaching experience: La Trobe University, Australia (1986, 3 semesters), University of
       Illinois, Chicago (1990, 2 semesters), Budapest Semesters in Mathematics (2 courses)
       3. Studies abroad:
       4. Talks delivered in English: over 10 conference talks

György Kiss
      1. Language proficiency examination (high level):
      2. Teaching experience:
      3. Studies abroad:
      4. Talks delivered in English: over 20 conference lectures

Péter Komjáth
       1. Language proficiency examination (high level): 1982
       2. Teaching experience:
       3. Studies abroad:
       4. Talks delivered in English:

Géza Kós
      1. Language proficiency examination (high level):
      2. Teaching experience:
      3. Studies abroad:
      4. Talks delivered in English: over 10 lectures

Antal Kováts
       1. Language proficiency examination (high level):
       2. Teaching experience:
       3. Studies abroad:
       4. Talks delivered in English: over 10 conference lectures

János Kristóf
       1. Language proficiency examination (high level):
       2. Teaching experience: Central European University (2006–2007, over 1 year)
       3. Studies abroad:
       4. Talks delivered in English:

Miklós Laczkovich
       1. Language proficiency examination (high level):
       2. Teaching experience: Michigan State University (1983), University of California
       (Santa Barbara (1984), University College, London (2001–, 3 months/year)
       3. Studies abroad:

                                       Language proficiency
                         MSc program in mathematics: language proficiency                 155


       4. Talks delivered in English: over 10 invited addresses during the last 8 years

Gyula Lakos
       1. Language proficiency examination (high level): 2003
       2. Teaching experience: Northwestern University (2003–2004)
       3. Studies abroad: Ph.D. studies at MIT (1998–2003)
       4. Talks delivered in English:

László Lovász
       1. Language proficiency examination (high level):
       2. Teaching experience: Yale University (1999, over six months)
       3. Studies abroad:
       4. Talks delivered in English:

András Lukács
      1. Language proficiency examination (high level):
      2. Teaching experience: Univ. Köln, Inst. für Informatik, 1992-1993, Montanuniv.
      Leoben, Inst. für Ang. Math., 1994-1995, CWI Amsterdam, 1998-2000
      3. Studies abroad:
      4. Talks delivered in English: over 10 conference talks

Gergely Mádi-Nagy
       1. Language proficiency examination (high level):
       2. Teaching experience:
       3. Studies abroad:
       4. Talks delivered in English: 10 conference talks

László Márkus
       1. Language proficiency examination (high level):
       2. Teaching experience:
       3. Studies abroad:
       4. Talks delivered in English: over 30 conference talks

György Michaletzky
      1. Language proficiency examination (high level):
      2. Teaching experience:
      3. Studies abroad:
      4. Talks delivered in English: over 30 conference lectures

Tamás Móri
      1. Language proficiency examination (high level):
      2. Teaching experience:
      3. Studies abroad:
      4. Talks delivered in English: over 20 conference lectures

Gábor Moussong
      1. Language proficiency examination (high level): 1988



                                      Language proficiency
156                      MSc program in mathematics: language proficiency


       2. Teaching experience: Ohio State University (1997–1998), Budapest Semesters in
       Mathematics (1997– )
       3. Studies abroad: Ph.D. Studies at Ohio State University (1985–1988)
       4. Talks delivered in English: over 15conference lectures

András Némethi
      1. Language proficiency examination (high level): 1991
      2. Teaching experience: Ohio State University (1991–2006)
      3. Studies abroad:
      4. Talks delivered in English: over 10 conference lectures

Péter P. Pálfy
        1. Language proficiency examination (high level): 1984
        2. Teaching experience: Vanderbilt University (1983, 1 semester), University of
        Hawaii (1986, 1 semester)
        3. Studies abroad:
        4. Talks delivered in English: over 80 conference talks

Katalin Pappné Kovács
       1. Language proficiency examination (high level):
       2. Teaching experience: University of Illinois, Urbana (1993–1995)
       3. Studies abroad:
       4. Talks delivered in English: over 10 conference talks

József Pelikán
       1. Language proficiency examination (high level): 1972
       2. Teaching experience: Budapest Semesters in Mathematics (over 10 years)
       3. Studies abroad:
       4. Talks delivered in English: over 10 talks

Tamás Pfeil
      1. Language proficiency examination (high level):
      2. Teaching experience: Eötvös University, English program in biology (over 10
      years)
      3. Studies abroad:
      4. Talks delivered in English:

Vilmos Prokaj
      1. Language proficiency examination (high level):
      2. Teaching experience: ELTE English MSc program (2003, 2005, over eight months)
      3. Studies abroad:
      4. Talks delivered in English:

Tamás Pröhle
      1. Language proficiency examination (high level):
      2. Teaching experience: ELTE English MSc program (2003, 2005, over eight months)
      3. Studies abroad:
      4. Talks delivered in English:


                                      Language proficiency
                         MSc program in mathematics: language proficiency            157


András Recski
      1. Language proficiency examination (high level):
      2. Teaching experience: Yale Universit (1994, over six months)
      3. Studies abroad:
      4. Talks delivered in English:

András Sárközy
      1. Language proficiency examination (high level): 1967
      2. Teaching experience: University of Illinois (1972/73, 1989/90), UCLA (1983),
      University of Georgia (1985/1986), The City University of New York, Baruch College
      (1986/1987), University of Waterloo (1990/91), The University of Memphis
      (2007/2008):
      3. Studies abroad:
      4. Talks delivered in English: a large number of conference talks

Zoltán Sebestyén
       1. Language proficiency examination (high level):
       2. Teaching experience:
       3. Studies abroad:
       4. Talks delivered in English: over 20 conference lectures

István Sigray
        1. Language proficiency examination (high level): 1988
        2. Teaching experience:
        3. Studies abroad:
        4. Talks delivered in English:

Eszter Sikolya
       1. Language proficiency examination (high level):
       2. Teaching experience: University of Tübingen (2002–2004, 2 years)
       3. Studies abroad:
       4. Talks delivered in English: 10 conference talks

László Simon
       1. Language proficiency examination (high level):
       2. Teaching experience:
       3. Studies abroad:
       4. Talks delivered in English: over 30 conference lectures

Péter Simon
        1. Language proficiency examination (high level):
        2. Teaching experience: Budapest Semesters in Mathematics (2003– ,5 years)
        3. Studies abroad:
        4. Talks delivered in English: over 25 conference lectures

András Stipsicz
      1. Language proficiency examination (high level):



                                      Language proficiency
158                      MSc program in mathematics: language proficiency


       2. Teaching experience: Budapest Semesters in Mathematics (over 10 years), UC
       Irvine, MSRI Berkeley, Princeton University, IAS Princeton, Warwick University,
       Columbia University,
       3. Studies abroad: Ph.D. studies
       4. Talks delivered in English: over 20 conference talks

Csaba Szabó
       1. Language proficiency examination (high level):
       2. Teaching experience: McMaster University, Hamilton (1997–1998), Budapest
       Semesters in Mathematics (over 10 years)
       3. Studies abroad:
       4. Talks delivered in English: over 25 conference talks

István Szabó
        1. Language proficiency examination (high level):
        2. Teaching experience:
        3. Studies abroad:
        4. Talks delivered in English: over 10 conference lectures

Mihály Szalay
      1. Language proficiency examination (high level):
      2. Teaching experience:
      3. Studies abroad:
      4. Talks delivered in English: over 10 conference talks

Péter Sziklai
       1. Language proficiency examination (high level): 1986
       2. Teaching experience:
       3. Studies abroad:
       4. Talks delivered in English:

Róbert Szőke
       1. Language proficiency examination (high level): 1991
       2. Teaching experience: University of Notre Dame (1986–1990), Purdue University
       (1997, 2005, 2007 –1 semester each year), Budapest Semesters in Mathematics
       (2004), CEU (2004)
       3. Studies abroad: Ph.D. Studies at University of Notre Dame(1985–1990)
       4. Talks delivered in English: over 10 conference talks

Szőnyi Tamás:
       1. Language proficiency examination (high level):
       2. Teaching experience:
       3. Studies abroad:
       4. Talks delivered in English: over 10 conference talks (www.cs.elte.hu/~szonyi)

András Szűcs
      1. Language proficiency examination (high level):
      2. Teaching experience: Budapest Semesters in Mathematics (1988, 1 semester)
      3. Studies abroad:
                                      Language proficiency
                         MSc program in mathematics: language proficiency               159


       4. Talks delivered in English: over 10 invited 1 hour lectures

Árpád Tóth
      1. Language proficiency examination (high level):
      2. Teaching experience: Rutgers University (1992–1997), University of Michigan,
      Ann Arbour (1997–2000), Princeton University (2000–2001), Fordham University,
      New York (2001–2003)
      3. Studies abroad: Ph.D. studies at Rutgers University (1992–1997)
      4. Talks delivered in English: over 10 conference talks (see at www.cs.elte.hu/~toth)

László Verhóczki
       1. Language proficiency examination (high level):
       2. Teaching experience:
       3. Studies abroad:
       4. Talks delivered in English: over 10 conference lectures

Katalin Vesztergombi
       1. Language proficiency examination (high level):
       2. Teaching experience: Yale University (1999, over six months)
       3. Studies abroad:
       4. Talks delivered in English:

András Zempléni
      1. Language proficiency examination (high level):
      2. Teaching experience: ELTE English MSc program (2003, 2005, over eight months)
      3. Studies abroad:
      4. Talks delivered in English: over 20 conference talks




                                      Language proficiency
160                       MSc program in mathematics: course descriptions



              MSc in Mathematics: Course descriptions
Title of the course:                  Algebraic and differential topology

Number of contact hours per week:     4+2
Credit value:                         6+3
Course coordinator(s):                András Szűcs
Department(s):                        Department of Analysis
Evaluation:                           oral examination + grade for problem solving
Prerequisites:                        Algebraic Topology course in BSC

A short description of the course:
Characteristic classes and their applications, computation of the cobordism ring of manifolds,
Existence of exotic spheres.

Textbook:
Further reading:
1) J. W. Milnor, J. D. Stasheff: Characteristic Classes, Princeton, 1974.
2) R. E. Stong: Notes on Cobordism Theory, Princeton, 1968.




                                        Course descriptions
                          MSc program in mathematics: course descriptions              161


Title of the course:                  Algebraic Topology (basic material)

Number of contact hours per week:     2+0
Credit value:                         2
Course coordinator(s):                András Szűcs
Department(s):                        Department of Analysis
Evaluation:                           oral examination
Prerequisites:                        Algebraic Topology course in the BSC

A short description of the course:
Homology groups, cohomology ring, homotopy groups, fibrations, exact sequences, Lefschetz
fixpoint theorem.


Textbook:
none
Further reading: R. M. Switzer: Algebraic Topology, Homotopy and Homology, Springer-
Verlag, 1975.




                                        Course descriptions
162                       MSc program in mathematics: course descriptions


Title of the course:                  Algorithms I

Number of contact hours per week:     2+2
Credit value:                         2+3
Course coordinator(s):                Zoltán Király
Department(s):                        Department of Computer Science
Evaluation:                           oral examination and tutorial mark
Prerequisites: none

A short description of the course:
Sorting and selection. Applications of dynamic programming (maximal interval-sum,
knapsack, order of multiplication of matrices, optimal binary search tree, optimization
problems in trees).
Graph algorithms: BFS, DFS, applications (shortest paths, 2-colorability, strongly connected
orientation, 2-connected blocks, strongly connected components). Dijkstra’s algorithm and
applications (widest path, safest path, PERT method, Jhonson’s algorithm). Applications of
network flows. Stable matching. Algorithm of Hopcroft and Karp.
Concept of approximation algorithms, examples (Ibarra-Kim, metric TSP, Steiner tree, bin
packing). Search trees. Amortization time. Fibonacci heap and its applications.
Data compression. Counting with large numbers, algorithm of Euclid, RSA. Fast Fourier
transformation and its applications. Strassen’s method for matrix multiplication.


Textbook:
Further reading:
T. H. Cormen, C. E. Leiserson, R. L. Rivest, C. Stein: Introduction to Algorithms, McGraw-
Hill, 2002




                                        Course descriptions
                          MSc program in mathematics: course descriptions                163


Title of the course:                  Analysis IV (for mathematicians)

Number of contact hours per week:     4+2
Credit value:                         4+2
Course coordinator(s):                János Kristóf
Department(s):                        Department of Applied Analysis and Computational
                                      Mathematics, Department of Analysis
Evaluation:                           oral or written examination, tutorial mark
Prerequisites:

A short description of the course:
Abstract measures and integrals. Measurable functions. Outer measures and the extensions of
measures. Abstract measure spaces. Lebesgue- and Lebesgue-Stieltjes measure spaces.
Charges and charges with bounded variation. Absolute continuous and singular measures.
Radon-Nycodym derivatives. Lebesgue decomposition of measures. Density theorem of
Lebesgue. Absolute continuous and singular real functions. Product of measure spaces.
Theorem of Lebesgue-Fubini. L^p spaces. Convolution of functions.

Textbook: none
Further reading:
1) Bourbaki, N.: Elements of Mathematics, Integration I, Chapters 1-6, Springer-Verlag, New
York-Heidelberg-Berlin, 2004.
2) Dieudonné, J.: Treatise On Analysis, Vol. II, Chapters XIII-XIV, Academic Press, New
York-San Fransisco-London, 1976.
3) Halmos, Paul R.: Measure Theory, Springer-Verlag, New York-Heidelberg-Berlin, 1974.
4) Rudin, W.: Principles of Mathematical Analysis, McGraw-Hill Book Co., New York-San
Fransisco-Toronto-London, 1964.
5) Dunford, N.- Schwartz, T.J.: Linear operators. Part I: General Theory, Interscience
Publishers, 1958.




                                        Course descriptions
164                       MSc program in mathematics: course descriptions


Title of the course:                  Analysis of time series

Number of contact hours per week:     2+2
Credit value:                         3+3
Course coordinator(s):                László Márkus
Department(s):                        Department of Probability Theory and Statistics
Evaluation:                           Oral examination
Prerequisites:                        Probability theory and Statistics,
                                      Stationary processes

A short description of the course:
Basic notions of stationary processes,weak, k-order, strict stationarity, ergodicity,
convergence to stationary distribution. Interdependence structure: autocovariance,
autocorrelation, partial autocorrelation functions and their properties, dynamic copulas.
Spectral representation of stationary processes by an orthogonal stochastic measure, the
spectral density function, Herglotz’s theorem.
Introduction and basic properties of specific time series models: Linear models: AR(1), AR(2)
AR(p), Yule-Walker equations, MA(q), ARMA(p,q), ARIMA(p,d,q) conditions for the
existence of stationary solutions and invertibility, the spectral density function. Nonlinear
models: ARCH(1), ARCH(p), GARCH(p,q), Bilinear(p,q,P,Q), SETAR, regime switching
models. Stochastic recursion equations, stability, the Ljapunov-exponent and conditions for
the existence of stationary solutions, Kesten-Vervaat-Goldie theorem on stationary solutions
with regularly varying distributions. Conditions for the existence of stationary ARCH(1)
process with finite or infinite variance, the regularity index of the solution.
Estimation of the mean. Properties of the sample mean, depending on the spectral measure.
Estimation of the autocovariance function. Bias, variance and covariance of the estimator.
Estimation of the discrete spectrum, the periodogram. Properties of periodogram values at
Fourier frequencies. Expectation, variance, covariance and distribution of the periodogram at
arbitrary frequencies. Linear processes, linear filter, impulse-response and transfer functions,
spectral density and periodogram transformation by the linear filter. The periodogram as
useless estimation of the spectral density function. Windowed periodogram as spectral density
estimation. Window types. Bias and variance of the windowed estimation. Tayloring the
windows. Prewhitening and CAT criterion.


Textbook: none
Further reading:
Priestley, M.B.: Spectral Analysis and Time Series, Academic Press 1981
Brockwell, P. J., Davis, R. A.: Time Series: Theory and Methods. Springer, N.Y. 1987
Tong, H. : Non-linear time series: a dynamical systems approach, Oxford University Press,
1991.
Hamilton, J. D.: Time series analysis, Princeton University Press, Princeton, N. J. 1994
Brockwell, P. J., Davis, R. A.: Introduction to time series and forecasting, Springer. 1996.
Pena, D., Tiao and Tsay, R.: A Course in Time Series Analysis, Wiley 2001.




                                        Course descriptions
                          MSc program in mathematics: course descriptions          165


Title of the course:                  Applications of Operations Research

Number of contact hours per week:     2+0
Credit value:                         3+0
Course coordinator(s):                Gergely Mádi-Nagy
Department(s):                        Department of Operations Research
Evaluation:                           oral or written examination
Prerequisites: -

A short description of the course:
Applications in economics. Inventory and location problems. Modeling and solution of
complex social problems. Transportation problems. Models of maintenance and production
planning. Applications in defense and in water management.

Textbook: none
Further reading: none




                                        Course descriptions
166                       MSc program in mathematics: course descriptions


Title of the course:                  Applied discrete mathematics seminar

Number of contact hours per week:     0+2
Credit value:                         2
Course coordinator(s):                Zoltán Király
Department(s):                        Department of Computer Science
Evaluation:                           giving a presentation
Prerequisites: none

A short description of the course:
Study and presentation of selected journal papers.


Textbook:
Further reading:




                                        Course descriptions
                          MSc program in mathematics: course descriptions                167


Title of the course:                  Approximation algorithms

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator(s):                Tibor Jordán
Department(s):                        Department of Operations Research
Evaluation:                           oral or written examination
Prerequisites:

A short description of the course:
approximation algorithms for NP-hard problems, basic techniques,
 LP-relaxations. Set cover, primal-dual algorithms. Vertex cover, TSP, Steiner tree, feedback
vertex set, bin packing, facility location, scheduling problems, k-center, k-cut, multicut,
multiway cut, multicommodity flows, minimum size k-connected subgraphs, minimum
superstring, minimum max-degree spanning trees.

Textbook: V.V. Vazirani, Approximation algorithms, Springer, 2001.
Further reading:




                                        Course descriptions
168                       MSc program in mathematics: course descriptions


Title of the course:                  Basic algebra (reading course)

Number of contact hours per week:     0+2
Credit value:                         5
Course coordinator(s):                Péter Pál Pálfy
Department(s):                        Department of Algebra and Number Theory
Evaluation:                           oral or written examination
Prerequisites:

A short description of the course:
Basic group theory. Permutation groups. Lagrange’s Theorem. Homomorphisms and normal
subgroups. Direct product, the Fundamental theorem of finite Abelian groups. Free groups
and defining relations.
Basic ring theory. Ideals. Chain conditions. Integral domains, PID’s, euclidean domains.
Fields, field extensions. Algebraic and transcendental elements. Finite fields.
Linear algebra. The eigenvalues, the characterisitic polynmial and the minimal polynomial of
a linear transformation. The Jordan normal form. Transformations of Euclidean spaces.
Normal and unitary transformations. Quadratic forms, Sylvester’s theorem.


Textbook: none
Further reading:
     I.N. Herstein: Abstract Algebra. Mc.Millan, 1990
     P.M. Cohn: Classic Algebra. Wiley, 2000
     I.M. Gel’fand: Lectures on linear algebra. Dover, 1989




                                        Course descriptions
                          MSc program in mathematics: course descriptions                 169


Title of the course:                  Basic Geometry (reading course)

Number of contact hours per week:     0+2
Credit value:                         5
Course coordinator(s):                Gábor Moussong
Department(s):                        Department of Geometry
Evaluation:                           oral or written examination
Prerequisites:

A short description of the course:
Non-euclidean geometries: Classical non-euclidean geometries and their models. Projective
spaces. Transformation groups.
Vector analysis: Differentiation, vector calculus in dimension 3. Classical integral theorems.
Space curves, curvature and torsion.
Basic topology: The notion of topological and metric spaces. Sequences and convergence.
Compactness and connectedness. Fundamental group.

Textbooks:
1. M. Berger: Geometry I–II (Translated from the French by M. Cole and S. Levy).
   Universitext, Springer-Verlag, Berlin, 1987.
2. P.C. Matthews: Vector Calculus (Springer Undergraduate Mathematics Series). Springer,
   Berlin, 2000.
3. W. Klingenberg: A Course in Differential Geometry (Graduate Texts in Mathematics).
   Springer-Verlag, 1978.
4. M. A. Armstrong: Basic Topology (Undergraduate Texts in Mathematics), Springer-
   Verlag, New York, 1983.
Further reading:




                                        Course descriptions
170                       MSc program in mathematics: course descriptions


Title of the course:                  Business economics

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator(s):                Róbert Fullér
Department(s):                        Department of Operations Research
Evaluation:                           oral or written examination
Prerequisites:

A short description of the course:
Monopoly, Lerner index; horizontal differentiation, the effect of advertisement and service;
vertical differentiation; price discrimination; vertical control; Bertrand’s paradox, repeated
games; price competition; tacit collusion; the role of R&D in the competition.


Textbook:
Jean Tirole, The Theory of Industrial Organization, The MIT Press, Cambridge, 1997.
Further reading:




                                        Course descriptions
                          MSc program in mathematics: course descriptions                   171


Title of the course:                  Chapters of Complex Function Theory

Number of contact hours per week:     4+0
Credit value:                         6
Course coordinator(s):                Gábor Halász
Department(s):                        Department of Analysis
Evaluation:                           oral examination, home work and participation
Prerequisites:                        Complex Functions (BSc),
                                      Analysis IV. (BSc)

A short description of the course:
The aim of the course is to give an introduction to various chapters of functions of a complex
variable. Some of these will be further elaborated on, depending on the interest of the
participants, in lectures, seminars and practices to be announced in the second semester. In
general, six of the following, essentially self-contained topics can be discussed, each taking
about a month, 2 hours a week.
Topics:
Phragmén-Lindelöf type theorems.
Capacity. Tchebycheff constant. Transfinite diameter. Green function. Capacity and
Hausdorff measure. Conformal radius.
Area principle. Koebe’s distortion theorems. Estimation of the coefficients of univalent
functions.
Area-length principle. Extremal length. Modulus of quadruples and rings. Quasiconformal
maps. Extension to the boundary. Quasisymmetric functions. Quasiconformal curves.
Divergence and rotation free flows in the plane. Complex potencial. Flows around fixed
bodies.
Laplace integral. Inversion formuli. Applications to Tauberian theorems, quasianalytic
functions, Müntz’s theorem.
Poisson integral of L_p functions. Hardy spaces. Marcell Riesz’s theorem. Interpolation
between L_p spaces. Theorem of the Riesz brothers.
Meromorphic functions in the plane. The two main theorems of the Nevanlinna theory.


Textbook:
Further reading:
M. Tsuji: Potential Theory in Modern Function Theory, Maruzen Co., Tokyo, 1959.
L.V. Ahlfors: Conformal Invariants, McGraw-Hill, New York, 1973.
Ch. Pommerenke: Univalent Functions, Vandenhoeck & Ruprecht, Göttingen, 1975.
L.V. Ahlfors: Lectures on Quasiconformal Mappings, D. Van Nostrand Co., Princeton, 1966.
W.K.Hayman: MeromorphicFunctions, Clarendon Press, Oxford 1964.
P. Koosis: Introduction to Hp Spaces, University Press, Cambridge 1980.
G. Polya and G. Latta: Complex Variables, John Wiley & Sons, New York, 1974.




                                        Course descriptions
172                       MSc program in mathematics: course descriptions


Title of the course:                  Codes and symmetric structures

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator(s):                Tamás Szőnyi
Department(s):                        Department of Computer Science
Evaluation:                           oral or written examination
Prerequisites:

A short description of the course:
Error-correcting codes; important examples: Hamming, BCH (Bose, Ray-Chaudhuri,
Hocquenheim) codes. Bounds for the parameters of the code: Hamming bound and perfect
codes, Singleton bound and MDS codes. Reed-Solomon, Reed-Muller codes. The Gilbert-
Varshamov bound. Random codes, explicit asymptotically good codes (Forney's concatenated
codes, Justesen codes). Block designs t-designs and their links with perfect codes. Binary and
ternary Golay codes and Witt designs. Fisher's inequality and its variants. Symmetric designs,
the Bruck-Chowla-Ryser condition. Constructions (both recursive and direct) of block
designs.

Textbook: none
Further reading:
P.J. Cameron, J.H. van Lint: Designs, graphs, codes and their links Cambridge Univ. Press,
1991.
J. H. van Lint: Introduction to Coding theory, Springer, 1992.
J. H. van Lint, R.J. Wilson, A course in combinatorics, Cambridge Univ. Press, 1992; 2001




                                        Course descriptions
                          MSc program in mathematics: course descriptions             173


Title of the course:                  Combinatorial algorithms I.

Number of contact hours per week:     2+2
Credit value:                         3+3
Course coordinator(s):                Tibor Jordán
Department(s):                        Department of Operations Research
Evaluation:                           oral or written examination and tutorial mark
Prerequisites:

A short description of the course:
Search algorithms on graphs, maximum adjacency ordering, the algorithm of Nagamochi and
Ibaraki. Network flows. The Ford Fulkerson algorithm, the algorithm of Edmonds and Karp,
the preflow push algorithm. Circulations. Minimum cost flows. Some applications of flows
and circulations. Matchings in graphs. Edmonds` algorithm, the Gallai Edmonds structure
theorem. Factor critical graphs. T-joins, f-factors. Dinamic programming. Minimum cost
arborescences.

Textbook:
A. Frank, T. Jordán, Combinatorial algorithms, lecture notes.
Further reading:




                                        Course descriptions
174                       MSc program in mathematics: course descriptions


Title of the course:                  Combinatorial algorithms II.

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator(s):                Tibor Jordán
Department(s):                        Department of Operations Research
Evaluation:                           oral or written examination
Prerequisites:

A short description of the course:
Connectivity of graphs, sparse certificates, ear decompositions. Karger`s algorithm for
computing the edge connectivity. Chordal graphs, simplicial ordering. Flow equivalent trees,
Gomory Hu trees. Tree width, tree decomposition. Algorithms on graphs with small tree
width. Combinatorial rigidity. Degree constrained orientations. Minimum cost circulations.

Textbook:
A. Frank, T. Jordán, Combinatorial algorithms, lecture notes.
Further reading:




                                        Course descriptions
                          MSc program in mathematics: course descriptions                    175


Title of the course:                  Combinatorial Geometry

Number of contact hours per week:     2+1
Credit value:                         2+2
Course coordinator:                   György Kiss
Department:                           Department of Geometry
Evaluation:                           oral or written examination and tutorial mark
Prerequisites:

A short description of the course:
Combinatorial properties of finite projective and affine spaces. Collineations and polarities,
conics, quadrics, Hermitian varieties, circle geometries, generalized quadrangles.
Point sets with special properties in Euclidean spaces. Convexity, Helly-type theorems,
transversals.
Polytopes in Euclidean, hyperbolic and spherical geometries. Tilings, packings and coverings.
Density problems, systems of circles and spheres.


Textbook: none
Further reading:
1. Boltyanski, V., Martini, H. and Soltan, P.S.: Excursions into Combinatorial Geometry,
   Springer-Verlag, Berlin-Heidelberg-New York, 1997.
2. Coxeter, H.S.M.: Introduction to Geometry, John Wiley & Sons, New York, 1969.
3. Fejes Tóth L.: Regular Figures, Pergamon Press, Oxford-London-New York-Paris, 1964.




                                        Course descriptions
176                       MSc program in mathematics: course descriptions




Title of the course:                  Combinatorial number theory.

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator(s):                András Sárközy
Department(s):                        Department of Algebra and Number Theory
Evaluation:                           oral or written examination
Prerequisites:                        Number theory 2

A short description of the course:
Brun's sieve and its applications. Schnirelmann's addition theorems, the primes form an
additive basis. Additive and multiplicative Sidon sets. Divisibility properties of sequences,
primitive sequences. The "larger sieve", application. Hilbert cubes in dense sequences,
applications. The theorems of van der Waerden and Szemeredi on arithmetic progressions.
Schur's theorem on the Fermat congruence.

Textbook: none
Further reading:
     H. Halberstam, K. F. Roth: Sequences.
     C. Pomerance, A. Sárközy: Combinatorial Number Theory (in: Handbook of
     Combinatorics)
     P. Erdős, J. Surányi: Topics in number theory.




                                        Course descriptions
                          MSc program in mathematics: course descriptions               177


Title of the course:                  Combinatorial structures and algorithms

Number of contact hours per week:     0+2
Credit value:                         3
Course coordinator(s):                Tibor Jordán
Department(s):                        Department of Operations Research
Evaluation:                           tutorial mark
Prerequisites:

A short description of the course:
Solving various problems from combinatorial optimization, graph theory, matroid theory, and
combinatorial geometry.



Textbook: none
Further reading: L. Lovász, Combinatorial problems and exercises, North Holland 1979.




                                        Course descriptions
178                       MSc program in mathematics: course descriptions


Title of the course:                  Commutative algebra

Number of contact hours per week:     2+2
Credit value:                         3+3
Course coordinator(s):                József Pelikán
Department(s):                        Department of Algebra and Number Theory
Evaluation:                           oral or written examination and tutorial mark
Prerequisites:                        Rings and Algebras

A short description of the course:
Ideals. Prime and maximal ideals. Zorn's lemma. Nilradical, Jacobson radical. Prime
spectrum.
Modules. Operations on submodules. Finitely generated modules. Nakayama's lemma. Exact
sequences. Tensor product of modules.
Noetherian rings. Chain conditions for mudules and rings. Hilbert's basis theorem. Primary
ideals. Primary decomposition, Lasker-Noether theorem. Krull dimension. Artinian rings.
Localization. Quotient rings and modules. Extended and restricted ideals.
Integral dependence. Integral closure. The 'going-up' and 'going-down' theorems. Valuations.
Discrete valuation rings. Dedekind rings. Fractional ideals.
Algebraic varieties. 'Nullstellensatz'. Zariski-topology. Coordinate ring. Singular and regular
points. Tangent space.
Dimension theory. Various dimensions. Krull's principal ideal theorem. Hilbert-functions.
Regular local rings. Hilbert's theorem on syzygies.

Textbook: none
Further reading:
     Atiyah, M.F.–McDonald, I.G.: Introduction to Commutative Algebra. Addison–Wesley,
     1969.




                                        Course descriptions
                          MSc program in mathematics: course descriptions                   179


Title of the course:                  Complex Functions

Number of contact hours per week:     3+2
Credit value:                         3+3
Course coordinator(s):                Gábor Halász
Department(s):                        Department of Analysis
Evaluation:                           oral examination and tutorial mark
Prerequisites:                        Analysis 3 (BSc)

A short description of the course:
Complex differentiation. Power series. Elementary functions. Cauchy’s integral theorem and
integral formula. Power series representation of regular functions. Laurent expansion. Isolated
singularities. Maximum principle. Schwarz lemma and its applications. Residue theorem.
Argument principle and its applications. Sequences of regular functions. Linear fractional
transformations. Riemann’s conformal mapping theorem. Extension to the boundary.
Reflection principle. Picard’s theorem. Mappings of polygons. Functions with prescribed
singularities. Integral functions with prescribed zeros. Functions of finite order. Borel
exceptional values. Harmonic functions. Dirichlet problem for a disc.


Textbook:
Further reading:
L. Ahlfors: Complex Analysis, McGraw-Hill Book Company, 1979.




                                        Course descriptions
180                       MSc program in mathematics: course descriptions


Title of the course:                  Complex manifolds

Number of contact hours per week:     3+2
Credit value:                         4+3
Course coordinator(s):                Róbert Szőke
Department(s):                        Department of Analysis
Evaluation:                           oral or written examination and tutorial mark
Prerequisites:                        complex analysis (BSc)
                                      real analysis and algebra (BSc)
                                      Some experience with real manifolds and differential
                                      forms is useful.

A short description of the course:
Complex and almost complex manifolds, holomorphic fiber bundles and vector bundles, Lie
groups and transformation groups, cohomology, Serre duality, quotient and submanifolds,
blowup, Hopf-, Grassmann and projective algebraic manifolds, Weierstrass' preparation and
division theorem, analytic sets, Remmert-Stein theorem, meromorphic functions, Siegel, Levi
and Chow's theorem, rational functions.

Objectives of the course: the intent of the course is to familiarize the students with the most
important methods and objects of the theory of complex manifolds and to do this as simply as
possible. The course completely avoids those abstract concepts (sheaves, coherence, sheaf
cohomology) that are subjects of Ph.D. courses. Using only elementary methods (power
series, vector bundles, one dimensional cocycle) and presenting many examples, the course
introduces the students to the theory of complex manifolds and prepares them for possible
future Ph.D. studies.

Textbook: Klaus Fritzsche, Hans Grauert: From holomorphic functions to complex manifolds,
Springer Verlag, 2002
Further reading:
K. Kodaira: Complex manifolds and deformations of complex structures, Springer Verlag,
2004
1.Huybrechts: Complex geometry: An introduction, Springer Verlag, 2004




                                        Course descriptions
                          MSc program in mathematics: course descriptions                 181


Title of the course:                  Complexity theory

Number of contact hours per week:     2+2
Credit value:                         3+3
Course coordinator(s):                Vince Grolmusz
Department(s):                        Department of Computer Science
Evaluation:                           oral examination and tutorial mark
Prerequisites:

A short description of the course: finite automata, Turing machines, Boolean circuits. Lower
bounds to the complexity of algorithms. Communication complexity. Decision trees, Ben-
Or’s theorem, hierarchy theorems. Savitch theorem. Oracles. The polynomial hierarchy.
PSPACE. Randomized complexity classes. Pseudorandomness. Interactive protocols.
IP=PSPACE. Approximability theory. The PCP theorem. Parallel algorithms. Kolmogorov
complexity.


Textbook: László Lovász: Computational Complexity
(ftp://ftp.cs.yale.edu/pub/lovasz.pub/complex.ps.gz)
Further reading:
Papadimitriou: Computational Complexity (Addison Wesley, 1994)
Cormen. Leiserson, Rivest, Stein: Introduction to Algorithms; MIT Press and McGraw-Hill.




                                        Course descriptions
182                      MSc program in mathematics: course descriptions


Title of the course:                 Complexity theory seminar

Number of contact hours per week:    0+2
Credit value:                        2
Course coordinator(s):               Vince Grolmusz
Department(s):                       Department of Computer Science
Evaluation:                          oral examination or tutorial mark
Prerequisites:                       Complexity theory

A short description of the course: Selected papers are presented in computational complexity
theory


Textbook: none
Further reading:
STOC and FOCS conference proceedings
The Electronic Colloquium on Computational Complexity (http://eccc.hpi-web.de/eccc/)




                                       Course descriptions
                          MSc program in mathematics: course descriptions               183


Title of the course:                  Computational methods in operations research

Number of contact hours per week:     0+2
Credit value:                         0+3
Course coordinator(s):                Gergely Mádi-Nagy
Department(s):                        Department of Operations Research
Evaluation:                           tutorial mark
Prerequisites: -

A short description of the course:
Implementation questions of mathematical programming methods.
Formulation of mathematical programming problems, and interpretation of solutions: progress
from standard input/output formats to modeling tools.
The LINDO and LINGO packages for linear, nonlinear, and integer programming. The
CPLEX package for linear, quadratic, and integer programming.
Modeling tools: XPRESS, GAMS, AMPL.

Textbook: none
Further reading: Maros, I.: Computational Techniques of the Simplex Method, Kluwer
Academic Publishers, Boston, 2003




                                        Course descriptions
184                      MSc program in mathematics: course descriptions


Title of the course:                 Continuous Optimization

Number of contact hours per week:   3+2
Credit value:                       3+3
Course coordinator(s):               Tibor Illés
Department(s):                       Department of Operations Research
Evaluation:                          oral or written examination
Prerequisites:

A short description of the course: Linear inequality systems: Farkas lemma and other
alternative theorems, The duality theorem of linear programming, Pivot algorithms (criss-
cross, simplex), Interior point methods, Matrix games: Nash equilibrium, Neumann theorem
on the existence of mixed equilibrium, Convex optimization: duality, separability, Convex
Farkas theorem, Kuhn-Tucker-Karush theorem, Nonlinear programming models, Stochastic
programming models.


Textbook: none
Further reading:
1. Katta G. Murty: Linear Programming. John Wiley & Sons, New York, 1983.
2. Vašek Chvátal: Linear Programming. W. H. Freeman and Company, New York, 1983.
3. C. Roos, T. Terlaky and J.-Ph. Vial: Theory and Algorithms for Linear Optimization: An
   Interior Point Approach. John Wiley & Sons, New York, 1997.
4. Béla Martos: Nonlinear Programming: Theory and Methods. Akadémiai Kiadó, Budapest,
   1975.
5. M. S. Bazaraa, H. D. Sherali and C. M. Shetty: Nonlinear Programming: Theory and
   Algorithms. John Wiley & Sons, New York, 1993.
6. J.-B. Hiriart-Urruty and C. Lemaréchal: Convex Analysis and Minimization Algorithms I-
   II. Springer-Verlag, Berlin, 1993.




                                       Course descriptions
                          MSc program in mathematics: course descriptions             185


Title of the course:                  Convex Geometry

Number of contact hours per week:     4+2
Credit value:                         6+3
Course coordinator(s):                Károly Böröczky, Jr.
Department(s):                        Department of Geometry
Evaluation:                           oral or written examination and tutorial mark
Prerequisites:

A short description of the course:
Convex polytopes, Euler and Dehn–Sommerville formulas, upper bound theorem.
Mean projections. Isoperimetric, Brunn-Minkowski, Alexander-Fenchel, Rogers–Shephard
and Blaschke-Santalo inequalities.
Lattices in Euclidean spaces. Successive minima and covering radius. Minkowski,
Minkowski–Hlawka and Mahler theorems. Critical lattices and finiteness theorems. Reduced
basis.

Textbook: none
Further reading:
1) B. Grünbaum: Convex polytopes, 2nd edition, Springer-Verlag, 2003.
2) P.M. Gruber: Convex and Discrete Geometry, Springer-Verlag, 2006.
3) P.M. Gruber, C.G. Lekkerkerker: Geometry of numbers, North-Holland, 1987.




                                        Course descriptions
186                       MSc program in mathematics: course descriptions


Title of the course:                  Cryptography

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator(s):                István Szabó
Department(s):                        Department of Probability Theory and Statistics
Evaluation:                           C type examination
Prerequisites:                        Probability and statistics

A short description of the course:
Data Security in Information Systems. Confidentiality, Integrity, Authenticity, Threats
    (Viruses, Covert Channels), elements of the Steganography and Cryptography;
Short history of Cryptography (Experiences, Risks);
Hierarchy in Cryptography: Primitives, Schemes, Protocols, Applications;
Random- and Pseudorandom Bit-Generators;
Stream Ciphers: Linear Feedback Shift Registers, Stream Ciphers based on LFSRs, Linear
    Complexity, Stream Ciphers in practice (GSM-A5, Bluetooth-E0, WLAN-RC4), The
    NIST Statistical Test Suite;
Block Ciphers: Primitives (DES, 3DES, IDEA, AES), Linear and Differential Cryptanalysis;
Public-Key Encryption: Primitives (KnapSack, RSA, ElGamal public-key encryption, Elliptic
    curve cryptography,…), Digital Signatures, Types of attacks on PKS (integer factorisation
    problem, Quadratic/Number field sieve factoring, wrong parameters,…);
Hash Functions and Data Integrity: Requirements, Standards and Attacks (birthday, collisions
    attacks);
Cryptographic Protocols: Modes of operations, Key management protocols, Secret sharing,
    Internet protocols (SSL-TLS, IPSEC, SSH,…)
Cryptography in Information Systems (Applications): Digital Signatures Systems (algorithms,
    keys, ETSI CWA requirements, Certification Authority, SSCD Protection Profile, X-
    509v3 Certificate,…), Mobile communications (GSM), PGP, SET,…;
Quantum Cryptography (quantum computation, quantum key exchange, quantum
    teleportation).

Textbook: none
Further reading:
Bruce Schneier: Applied Cryptography. Wiley, 1996
Alfred J. Menezes, Paul C. van Oorshchor, Scott A. Vanstone: Handbook of Applied
Cryptography, CRC Press, 1997, http://www.cacr.math.uwaterloo.ca/hac/




                                        Course descriptions
                          MSc program in mathematics: course descriptions             187


Title of the course:                  Current topics in algebra

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator:                   Emil Kiss
Department:                           Department of Algebra and Number Theory
Evaluation:                           oral or written examination
Prerequisites:

A short description of the course:
This subject of this course is planned to change from year to year. Some possible topics:
algebraic geometry, elliptic curves, p-adic numbers, valuation theory, Dedekind-domains,
binding categories.


Textbook: none
Further reading:
       depends on the subject




                                        Course descriptions
188                       MSc program in mathematics: course descriptions


Title of the course:                  Data mining

Number of contact hours per week:     2+2
Credit value:                         3+3
Course coordinator:                   András Lukács
Department:                           Department of Computer Science
Evaluation:                           oral or written examination and tutorial mark
Prerequisites:

A short description of the course:
Basic concepts and methodology of knowledge discovery in databases and data mining.
Frequent pattern mining, association rules. Level-wise algorithms, APRIORI. Partitioning and
Toivonen algorithms. Pattern growth methods, FP-growth. Hierarchical association rules.
Constraints handling. Correlation search.
Dimension reduction. Spectral methods, low-rank matrix approximation. Singular value
decomposition. Fingerprints, fingerprint based similarity search.
Classification. Decision trees. Neural networks. k-NN, Bayesian methods, kernel methods,
SVM.
Clustering. Partitioning algorithms, k-means. Hierarchical algorithms. Density and link based
clustering, DBSCAN, OPTICS. Spectral clustering.
Applications and implementation problems. Systems architecture in data mining. Data
structures.

Textbook:

Further reading:
Jiawei Han és Micheline Kamber: Data Mining: Concepts and Techniques, Morgan
Kaufmann Publishers, 2000, ISBN 1558604898,
Pang-Ning Tan, Michael Steinbach, Vipin Kumar: Introduction to Data Mining, Addison-
Wesley, 2006, ISBN 0321321367.
 T. Hastie, R. Tibshirani, J. H. Friedman: The Elements of Statistical Learning: Data Mining,
Inference, and Prediction, Springer-Verlag, 2001.




                                        Course descriptions
                          MSc program in mathematics: course descriptions                     189


Title of the course:                  Descriptive set theory

Number of contact hours per week:     3+2
Credit value:                         4+3
Course coordinator(s):                Miklos Laczkovich
Department(s):                        Department of Analysis
Evaluation:                           oral or written examination and tutorial mark
Prerequisites:                        Analysis 4,
                                      Introduction to topology

A short description of the course:
Basics of general topology. The Baire property. The tranfinite hierarchy of Borel sets. The
Baire function classes. The Suslin operation. Analytic and coanalytic sets. Suslin spaces.
Projective sets.


Textbook: none
Further reading:
K. Kuratowski: Topology I, Academic Press, 1967.
A. Kechris: Classical descriptive set theory, Springer, 1998.




                                        Course descriptions
190                       MSc program in mathematics: course descriptions


Title of the course:                  Design, analysis and implementation of algorithms and
                                      data structures I

Number of contact hours per week:     2+2
Credit value:                         3+3
Course coordinator(s):                Zoltán Király
Department(s):                        Department of Computer Science
Evaluation:                           oral examination
Prerequisites:                        Algorithms I

A short description of the course:
Maximum adjacency ordering and its applications. Sparse certificates for connectivity.
Minimum cost arborescence. Degree constrained orientations of graphs. 2-SAT. Tree-width,
applications. Gomory-Hu tree and its application. Steiner tree and traveling salesperson.
Minimum cost flow and circulation, minimum mean cycle.
Matching in non-bipartite graphs, factor-critical graphs, Edmonds’ algorithm. Structure
theorem of Gallai and Edmonds. T-joins, the problem of Chinese postman.
On-line algorithms, competitive ratio.


Textbook: none
Further reading:
T. H. Cormen, C. E. Leiserson, R. L. Rivest, C. Stein: Introduction to Algorithms, McGraw-
Hill, 2002.
A. Schrijver: Combinatorial Optimization, Springer-Verlag, 2002.
Robert Endre Tarjan: Data Structures and Network Algorithms , Society for Industrial and
Applied Mathematics, 1983.
Berg-Kreveld-Overmars-Schwarzkopf: Computational Geometry: Algorithms and
Applications , Springer-Verlag, 1997.




                                         Course descriptions
                          MSc program in mathematics: course descriptions                    191


Title of the course:                  Design, analysis and implementation of algorithms and
                                      data structures II

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator(s):                Zoltán Király
Department(s):                        Department of Computer Science
Evaluation:                           oral examination
Prerequisites:                        Design, analysis and implementation of algorithms and
                                      data structures I

A short description of the course:
Data structures for the UNION-FIND problem. Pairing and radix heaps. Balanced and self-
adjusting search trees.
Hashing, different types, analysis. Dynamic trees and their applications.
Data structures used in geometric algorithms: hierarchical search trees, interval trees, segment
trees and priority search trees.


Textbook: none
Further reading:
T. H. Cormen, C. E. Leiserson, R. L. Rivest, C. Stein: Introduction to Algorithms, McGraw-
Hill, 2002.
A. Schrijver: Combinatorial Optimization, Springer-Verlag, 2002.
Robert Endre Tarjan: Data Structures and Network Algorithms , Society for Industrial and
Applied Mathematics, 1983.
Berg-Kreveld-Overmars-Schwarzkopf: Computational Geometry: Algorithms and
Applications , Springer-Verlag, 1997.




                                        Course descriptions
192                       MSc program in mathematics: course descriptions


Title of the course:                  Differential Geometry I

Number of contact hours per week:     2+2
Credit value:                         2+3
Course coordinator(s):                László Verhóczki (associate professor)
Department(s):                        Department of Geometry
Evaluation:                           oral or written examination and tutorial mark
Prerequisites:

A short description of the course:
Smooth parameterized curves in the n-dimensional Euclidean space Rn. Arc length
parameterization. Distinguished Frenet frame. Curvature functions, Frenet formulas.
Fundamental theorem of the theory of curves. Signed curvature of a plane curve. Four vertex
theorem. Theorems on total curvatures of closed curves.
Smooth hypersurfaces in Rn. Parameterizations. Tangent space at a point. First fundamental
form. Normal curvature, Meusnier’s theorem. Weingarten mapping, principal curvatures and
directions. Christoffel symbols. Compatibility equations. Theorema egregium. Fundamental
theorem of the local theory of hypersurfaces. Geodesic curves.

Textbook:
M. P. do Carmo: Differential geometry of curves and surfaces. Prentice Hall, Englewood
       Cliffs, 1976.
Further reading:
B. O’Neill: Elementary differential geometry. Academic Press, New York, 1966.




                                        Course descriptions
                          MSc program in mathematics: course descriptions                    193


Title of the course:                  Differential Geometry II

Number of contact hours per week:     2+0
Credit value:                         2
Course coordinator(s):                László Verhóczki
Department(s):                        Department of Geometry
Evaluation:                           oral or written examination
Prerequisites:

A short description of the course:
Differentiable manifolds. Smooth mappings between manifolds. Tangent space at a point.
Tangent bundle of a manifold. Lie bracket of two smooth vector fields. Submanifolds.
Covariant derivative. Parallel transport along a curve. Riemannian manifold, Levi-Civita
connection. Geodesic curves. Riemannian curvature tensor field. Spaces of constant
curvature. Differential forms. Exterior product. Exterior derivative. Integration of differential
forms. Volume. Stokes’ theorem.

Textbooks:
1. F. W. Warner: Foundations of differentiable manifolds and Lie groups. Springer-Verlag
   New York, 1983.
2. M. P. do Carmo: Riemannian geometry. Birkhäuser, Boston, 1992.
Further reading:




                                        Course descriptions
194                       MSc program in mathematics: course descriptions


Title of the course:                  Differential Topology (basic material)

Number of contact hours per week:     2+0
Credit value:                         2
Course coordinator(s):                András Szűcs
Department(s):                        Department of Analysis
Evaluation:                           oral examination
Prerequisites:                        Algebraic Topology course in BSC

A short description of the course:
Morse theory, Pontrjagin construction, the first three stable homotopy groups of spheres,
Proof of the Poincare duality using Morse theory, immersion theory.

Textbook:
Further reading:
M. W. Hirsch: Differential Topology, Springer-Verlag, 1976.




                                        Course descriptions
                          MSc program in mathematics: course descriptions         195


Title of the course:                  Differential Topology Problem solving

Number of contact hours per week: 0+2
Credit value:                      3
Course coordinator(s):             András Szűcs
Department(s):                     Department of Analysis
Evaluation:                        oral examination
Prerequisites:                     BSc Algebraic Topology Course

A short description of the course:
See at the courses of Differential and Algebraic Topology of the basic material


Textbook:
Further reading:
1) J. W. Milnor J. D Stasheff: Characteristic Classes, Princeton, 1974.
2) R. E. Stong: Notes on Cobordism theory, Princeton 1968.




                                        Course descriptions
196                       MSc program in mathematics: course descriptions


Title of the course:                  Discrete Dynamical Systems

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator(s):                Zoltán Buczolich
Department(s):                        Department of Analysis
Evaluation:                           oral examination
Prerequisites:                        Measure and integration theory (BSc Analysis 4)

A short description of the course:
Topologic transitivity and minimality. Omega limit sets. Symbolic Dynamics. Topologic
Bernoulli shift. Maps of the circle. The existence of the rotation number. Invariant measures.
Krylov-Bogolubov theorem. Invariant measures and minimal homeomorphisms. Rotations of
compact Abelian groups. Uniquely ergodic transformations and minimality. Unimodal maps.
Kneading sequence. Eventually periodic symbolic itinerary implies convergence to periodic
points. Ordering of the symbolic itineraries. Characterization of the set of the itineraries.
Equivalent definitions of the topological entropy. Zig-zag number of interval maps. Markov
graphs. Sharkovskii’s theorem. Foundations of the Ergodic theory. Maximal and Birkhoff
ergodic theorem.


Textbook: none
Further reading:
A. Katok, B.Hasselblatt: Introduction to the modern theory of dynamical
systems.Encyclopedia of Mathematics and its Applications, 54. Cambridge University
Press,Cambridge, 1995.


W. de Melo, S. van Strien, One-dimensional dynamics, Springer Verlag, New York (1993).


I. P. Cornfeld, S. V. Fomin and Ya. G. Sinai, Ergodic Theory, Springer Verlag, New York,
(1981).




                                        Course descriptions
                          MSc program in mathematics: course descriptions                  197


Title of the course:                  Discrete Geometry

Number of contact hours per week:     3+2
Credit value:                         4+3
Course coordinator(s):                Károly Bezdek
Department(s):                        Department of Geometry
Evaluation:                           oral or written examination and tutorial mark
Prerequisites:

A short description of the course:
Packings and coverings in E2. Dowker theorems. The theorems of L. Fejes Tóth and Rogers
on densest packing of translates of a convex or centrally symmetric convex body.
Homogeneity questions. Lattice-like arrangements. Homogeneous packings (with group
actions). Space claim, separability.
Packings and coverings in (Euclidean, hyperbolic or spherical space) Ad. Problems with the
definition of density. Densest circle packings (spaciousness), and thinnest circle coverings in
A2. Tammes problem. Solidity. Rogers’ density bound for sphere packings in Ed. Clouds,
stable systems and separability. Densest sphere packings in A3. Tightness and edge tightness.
Finite systems. Problems about common transversals.

Textbook: none
Further reading:
1. Fejes Tóth, L.: Regular figures, Pergamon Press, Oxford–London–New York–Paris, 1964.
2. Fejes Tóth, L.: Lagerungen in der Ebene auf der Kugel und im Raum, Springer-Verlag,
  Berlin–Heidelberg–NewYork, 1972.
3. Rogers, C. A.: Packing and covering, Cambridge University Press, 1964.
4. Böröczky, K. Jr.: Finite packing and covering, Cambridge Ubiversity Press, 2004.




                                        Course descriptions
198                       MSc program in mathematics: course descriptions


Title of the course:                  Discrete Mathematics

Number of contact hours per week:     2+2.
Credit value:                         2+3
Course coordinator(s):                László Lovász
Department(s):                        Department of Computer Science
Evaluation:                           oral or written examination and tutorial grade
Prerequisites:

A short description of the course:
Graph Theory: Colorings of graphs and.hypergraphs, perfect graphs.Matching Theory.
Multiple connectivity. Strongly regular graphs, integrality condition and its application.
Extremal graphs. Regularity Lemma. Planarity, Kuratowski’s Theorem, drawing graphs on
surfaces, minors, Robertson-Seymour Theory.

Fundamental questions of enumerative combinatorics. Generating functions, inversion
formulas for partially ordered sets, recurrences. Mechanical summation.Classical counting
problems in graph theory, tress, spanning trees, number of 1-factors.

Randomized methods: Expectation and second moment method. Random graphs, threshold
functions.

Applications of fields: the linear algebra method, extremal set systems. Finite fields, error
correcting codes, perfect codes.

Textbook: none
Further reading:
J. H. van Lint, R.J. Wilson, A course in combinatorics, Cambridge Univ. Press, 1992; 2001.
L. Lovász: Combinatorial Problems and Exercises, AMS, Providence, RI, 2007
R. L. Graham, D. E. Knuth, O. Patashnik, Concrete Mathematics,




                                        Course descriptions
                          MSc program in mathematics: course descriptions               199


Title of the course:                  Discrete Mathematics II

Number of contact hours per week:     4+0
Credit value:                         6
Course coordinator(s):                Tamás Szőnyi
Department(s):                        Department of Computer Science
Evaluation:                           oral examination
Prerequisites:                        Discrete Mathematics I

A short description of the course:

Probabilistic methods: deterministic improvement of a random object. Construction of graphs
with large girth and chromatic number.
Random graphs: threshold function, evolution around p=logn/n. Pseudorandom graphs.
Local lemma and applications.
Discrepancy theory. Beck-Fiala theorem.
Spencer’s theorem. Fundamental theorem on the Vapnik-Chervonenkis dimension.

Extremal combinatorics
Non- bipartite forbidden subgraphs: Erdős-Stone-Simonovits and Dirac theorems.
Bipartite forbidden subgraphs: Turan number of paths and K(p,q). Finite geometry and
algebraic constructions.
Szemerédi’s regularity lemma and applications. Turán-Ramsey type theorems.
Extremal hypergraph problems: Turán’s conjecture.

Textbook:

Further reading:
Alon-Spencer: The probabilistic method, Wiley 2000.




                                        Course descriptions
200                       MSc program in mathematics: course descriptions


Title of the course:                  Discrete optimization

Number of contact hours per week:     3+2
Credit value:                         3+3
Course coordinator:                   András Frank
Department:                           Dept. Of Operations research
Evaluation:                           oral exam + tutorial mark
Prerequisites:

A short description of the course:
Basic notions of graph theory and matroid theory, properties and methods (matchings, flows
and circulations, greedy algorithm). The elements of polyhedral combinatorics (totally
unimodular matrices and their applications). Main combinatorial algorithms (dynamic
programming, alternating paths, Hungarian method). The elements of integer linear
programming (Lagrangian relaxation, branch-and-bound).

Textbook:
András Frank: Connections in combinatorial optimization (electronic notes).

Further reading:
W.J. Cook, W.H. Cunningham, W.R. Pulleybank, and A. Schrijver, Combinatorial
Optimization, John Wiley and Sons, 1998.

B. Korte and J. Vygen, Combinatorial Optimization: Theory and Algorithms, Springer, 2000.

E. Lawler, Kombinatorikus Optimalizálás: hálózatok és matroidok, Műszaki Kiadó, 1982.
(Combinatorial Optimization: Networks and Matroids).

A. Schrijver, Combinatorial Optimization: Polyhedra and efficiency, Springer, 2003. Vol. 24
of the series Algorithms and Combinatorics.

R. K. Ahuja, T. H. Magnanti, J. B. Orlin: Network flows: Theory, Algorithms and
Applications, Elsevier North-Holland, Inc., 1989




                                        Course descriptions
                          MSc program in mathematics: course descriptions                 201


Title of the course:                  Discrete parameter martingales

Number of contact hours per week:     2+0
Credit value:                         2
Course coordinator(s):                Tamás F. Móri
Department(s):                        Department of Probability Theory and Statistics
Evaluation:                           oral examination
Prerequisites:                        Probability and statistics

A short description of the course:
Almost sure convergence of martingales. Convergence in Lp, regular martingales.
Regular stopping times, Wald’s theorem.
Convergence set of square integrable martingales.
Hilbert space valued martingales.
Central limit theory for martingales.
Reversed martingales, U-statistics, interchangeability.
Applications: martingales in finance; the Conway algorithm; optimal strategies in favourable
   games; branching processes with two types of individuals.

Textbook: none
Further reading:
Y. S. Chow – H. Teicher: Probability Theory – Independence, Interchangeability,
Martingales. Springer, New York, 1978.
J. Neveu: Discrete-Parameter Martingales. North-Holland, Amsterdam, 1975.




                                        Course descriptions
202                       MSc program in mathematics: course descriptions


Title of the course:                  Dynamical Systems

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator(s):                Zoltán Buczolich
Department(s):                        Department of Analysis
Evaluation:                           oral examination
Prerequisites:                        Differential equations (BSc)

A short description of the course:
Contractions, fixed point theorem. Examples of dynamical systems: Newton’s method,
interval maps, quadratic family, differential equations, rotations of the circle. Graphic
analysis. Hyperbolic fixed points. Cantor sets as hyperbolic repelleres, metric space of code
sequences. Symbolic dynamics and coding. Topologic transitivity, sensitive dependence on
the initial conditions, chaos/chaotic maps, structural stability, period three implies chaos.
Schwarz derivative. Bifuraction theory. Period doubling. Linear maps and linear differential
equations in the plane. Linear flows and translations on the torus. Conservative systems.


Textbook: none
Further reading:
B. Hasselblatt, A. Katok: A first course in dynamics. With a panorama of
recentdevelopments. Cambridge University Press, New York, 2003.
A. Katok, B.Hasselblatt: Introduction to the modern theory of dynamical
systems.Encyclopedia of Mathematics and its Applications, 54. Cambridge University
Press,Cambridge, 1995.
Robert L. Devaney: An introduction to chaotic dynamical systems. Second edition.
AddisonWesley Studies in Nonlinearity. AddisonWesley Publishing Company, Advanced
Book Program, Redwood City, CA, 1989.




                                        Course descriptions
                          MSc program in mathematics: course descriptions                     203


Title of the course:                  Dynamical systems and differential equations

Number of contact hours per week:     4+2
Credit value:                         6+3
Course coordinator(s):                Péter Simon
Department(s):                        Dept. of Appl. Analysis and Computational Math.
Evaluation:                           oral or written examination and tutorial mark
Prerequisites:                        Differential equations (BSc)

A short description of the course:
Topological equivalence, classification of linear systems. Poincaré normal forms,
classification of nonlinear systems. Stable, unstable, centre manifolds theorems, Hartman -
Grobman theorem. Periodic solutions and their stability. Index of two-dimensional vector
fields, behaviour of trajectories at infinity. Applications to models in biology and chemistry.
Hamiltonian systems. Chaos in the Lorenz equation.
Bifurcations in dynamical systems, basic examples. Definitions of local and global
bifurcations. Saddle-node bifurcation, Andronov-Hopf bifurcation. Two-codimensional
bifurcations. Methods for finding bifurcation curves. Structural stability. Attractors.
Discrete dynamical systems. Classification according to topological equivalence. 1D maps,
the tent map and the logistic map. Symbolic dynamics. Chaotic systems. Smale horseshoe ,
Sharkovski’s theorem. Bifurcations.



Textbook: none
Further reading:
L. Perko, Differential Equations and Dynamical systems, Springer




                                        Course descriptions
204                       MSc program in mathematics: course descriptions


Title of the course:                  Dynamics in one complex variable

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator(s):                István Sigray
Department(s):                        Department of Analysis
Evaluation:                           oral or written examination and tutorial mark
Prerequisites:

A short description of the course:
Julia és Fatou sets. Smooth Julia sets. Attractive fixpoints, Koenigs linearization theorem.
Superattractive fixpoints Bötkher theorem. Parabolic fixpoints, Leau-Fatou theorem. Cremer
points és Siegel discs. Holomorphic fixpoint formula. Dense subsets of the Julia set.. Herman
rings. Wandering domains. Iteration of Polynomials. The Mandelbrot set. Root finding by
iteration. Hyperbolic mapping. Local connectivity.


Textbook:
John Milnor: Dynamics in one complex variable, Stony Brook IMS Preprint #1990/5

Further reading:
M. Yu. Lyubich: The dynamics of rational transforms, Russian Math Survey, 41 (1986) 43–
117
A. Douady: Systeme dynamique holomorphes, Sem Bourbaki , Vol 1982/83, 39-63,
Asterisque, 105–106




                                        Course descriptions
                          MSc program in mathematics: course descriptions                  205


Title of the course:                  Ergodic theory

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator(s):                Zoltán Buczolich
Department(s):                        Department of Analysis
Evaluation:                           oral examination
Prerequisites: :                      Measure and integration theory (BSc Analysis 4) ,
                                      Functional analysis 1.

A short description of the course:
Examples. Constructions. Von Neumann L2 ergodic theorem. Birkhoff-Khinchin pointwise
ergodic theorem. Poincaré recurrence theorem and Ehrenfest’s example. Khinchin’s theorem
about recurrence of sets. Halmos’s theorem about equivalent properties to recurrence.
Properties equivalent to ergodicity. Measure preserving property and ergodicity of induced
maps. Katz’s lemma. Kakutani-Rokhlin lemma. Ergodicity of the Bernoulli shift, rotations of
the circle and translations of the torus. Mixing (definitions). The theorem of Rényi about
strongly mixing transformations. The Bernoulli shift is strongly mixing. The Koopman von
Neumann lemma. Properties equivalent to weak mixing. Banach’s principle. The proof of the
Ergodic Theorem by using Banach’s principle. Differentiation of integrals. Wiener’s local
ergodic theorem. Lebesgue spaces and properties of the conditional expectation. Entropy in
Physics and in information theory. Definition of the metric entropy of a partition and of a
transformation. Conditional information and entropy. ``Entropy metrics‖. The conditional
expectation as a projection in L2. The theorem of Kolmogorv and Sinai about generators.
Krieger’s theorem about generators (without proof).


Textbook: none
Further reading:
K. Petersen, Ergodic Theory,Cambridge Studies in Advanced Mathematics 2, Cambridge
University Press, (1981).
I. P. Cornfeld, S. V. Fomin and Ya. G. Sinai, Ergodic Theory, Springer Verlag, New York,
(1981).




                                        Course descriptions
206                        MSc program in mathematics: course descriptions


Title of the course:                   Exponential sums in number theory.

Number of contact hours per week:      2+0
Credit value:                          3
Course coordinator(s):                 András Sárközy
Department(s):                         Department of Algebra and Number Theory
Evaluation:                            oral or written examination
Prerequisites:

A short description of the course:
Additive and multiplicative characters, their connection, applications. Vinogradov's lemma
and its dual. Gaussian sums. The Pólya-Vinogradov inequality. Estimate of the least quadratic
nonresidue. Kloosterman sums. The arithmetic and character form of the large sieve,
applications. Irregularities of distribution relative to arithmetic progressions, lower estimate of
character sums. Uniform distribution. Weyl's criterion. Discrepancy. The Erdős-Turán
inequality. Van der Corput's method.

Textbook: none
Further reading:
       I. M. Vinogradov: Elements of number theory
       L. Kuipers, H. Niederreiter: Uniform Distribution of Sequences.
       S. W. Graham, G. Kolesnik: Van der Corput’s Method of Exponential Sums.
       H. Davenport: Multiplicative Number Theory.




                                         Course descriptions
                          MSc program in mathematics: course descriptions                   207


Title of the course:                  Finite Geometries

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator:                   György Kiss (associate professor)
Department:                           Department of Geometry
Evaluation:                           oral examination
Prerequisites:

A short description of the course:
The axiomams of projective and affine planes, examples of finite planes, non-desarguesian
planes. Collineations, configurational theorems, coordinatization of projective planes. Higher
dimensional projective spaces.
Arcs, ovals, Segre’s Lemma of Tangents. Estimates on the number of points on an algebraic
curve. Blocking sets, some applications of the Rédei polynomial. Arcs, caps and ovoids in
higher dimensional spaces.
Coverings and packings, linear complexes, generalized polygons. Hyperovals.
Some applications of finite geometries to graph theory, coding theory and cryptography.

Textbook: none
Further reading:
1. Hirschfeld, J:W.P.: Projective Geometries over Finite Fields, Clarendon Press, Oxford,
  1999.
2. Hirschfeld, J.W.P.: Finite Projective Spaces of Three Dimensions, Clarendon Press,
  Oxford, 1985.




                                        Course descriptions
208                       MSc program in mathematics: course descriptions


Title of the course:                  Fourier Integral

Number of contact hours per week:     2+1
Credit value:                         2+1
Course coordinator(s):                Gábor Halász
Department(s):                        Department of Analysis
Evaluation:                           oral examination
Prerequisites:                        Complex Functions (BSc),
                                      Analysis IV. (BSc),
                                      Probability 2. (BSc)

A short description of the course:
Fourier transform of functions in L_1. Riemann Lemma. Convolution in L_1. Inversion
formula. Wiener’s theorem on the closure of translates of L_1 functions. Applications to
Wiener’s general Tauberian theorem and special Tauberian theorems.
Fourier transform of complex measures. Characterizing continuous measures by its Fourier
transform. Construction of singular measures.
Fourier transform of functions in L_2. Parseval formula. Convolution in L_2. Inversion
formula. Application to non-parametric density estimation in statistics.
Young-Hausdorff inequality. Extension to L_p. Riesz-Thorin theorem. Marczinkiewicz
interpolation theorem.
Application to uniform distribution. Weyl criterion, its quantitative form by Erdős-Turán.
Lower estimation of the discrepancy for disks.
Characterization of the Fourier transform of functions with bounded support. Paley-Wiener
theorem.
Phragmén-Lindelöf type theorems.


Textbook:
Further reading:
E.C. Titchmarsh: Introduction to the Theory of Fourier Integrals, Clarendon Press, Oxford,
1937.
A. Zygmund: Trigonometric Series, University Press, Cambridge, 1968, 2 volumes
R. Paley and N. Wiener: Fourier Transforms in the Complex Domain, American
Mathematical Society, New York, 1934.
J. Beck and W.L. Chen: Irregularities of Distribution, University Press, Cambridge, 1987.




                                        Course descriptions
                          MSc program in mathematics: course descriptions               209


Title of the course:                  Function Series

Number of contact hours per week:     2+0
Credit value:                         2
Course coordinator(s):                János Kristóf
Department:                           Dept. of Appl. Analysis and Computational Math.
Evaluation:                           oral examination
Prerequisites:

A short description of the course:
Pointwise and L^2 norm convergence of orthogonal series. Rademacher-Menshoff theorem.
Weyl-sequence. Pointwise convergence of trigonometric Fourier-series. Dirichlet integral.
Riemann-Lebesgue lemma. Riemann’s localization theorem for Fourier-series. Local
convergence theorems. Kolmogorov’s counterexample. Fejér’s integral. Fejér’s theorem.
Carleson’s theorem.
Textbooks:
Bela Szokefalvi-Nagy: Introduction to real functions and orthogonal expansions,
Natanszon: Constructive function theory




                                        Course descriptions
210                       MSc program in mathematics: course descriptions


Title of the course:                  Functional analysis II

Number of contact hours per week:     1+2
Credit value:                         1+2
Course coordinator(s):                Sebestyén Zoltán
Department(s):                        Department of Appl. Analysis and Computational Math.
Evaluation:                           oral examination
Prerequisites:                        Algebra IV
                                      Analysis IV

A short description of the course:
Banach-Alaoglu Theorem. Daniel-Stone Theorem. Stone-Weierstrass Theorem. Gelfand
Theory, Representation Theory of Banach algebras.


Textbook:
Riesz–Szőkefalvi-Nagy: Functional analysis
Further reading:
W. Rudin: Functional analysis
F.F. Bonsall-J. Duncan: Complete normed algebras




                                        Course descriptions
                          MSc program in mathematics: course descriptions                     211


Title of the course:                  Game Theory

Number of contact hours per week:    2+0
Credit value:                         3
Course coordinator(s):                Tibor Illés
Department(s):                        Department of Operations Research
Evaluation:                           oral or written examination
Prerequisites:

A short description of the course:
Matrix games. Optimal strategies for matrix games with saddle point. Mixed strategies,
expected yield. Neumann minimax theorem. Solving matrix games with linear programming.
Nash equilibrium. Sperner lemma. The first and second Knaster-Kuratowski-Mazurkiewicz
theorems. The Brower and Kakutani fixed-point theorems. Shiffmann minimax theorem.
Arrow-Hurwitz and Arrow-Debreu theorems. The Arrow-Hurwitz-Uzawa condition. The
Arrow-Hurwitz and Uzawa algorithms. Applications of games in environment protection,
health sciences and psichology.


Textbook: none
Further reading:
Forgó F., Szép J., Szidarovszky F., Introduction to the theory of games: concepts, methods,
applications, Kluwer Academic Publishers, Dordrecht, 1999.
Osborne, M. J., Rubinstein A., A course in game theory, The MIT Press, Cambridge, 1994.
J. P. Aubin: Mathematical Methods of Game and Economic Theor. North-Holland,
Amsterdam, 1982.




                                        Course descriptions
212                       MSc program in mathematics: course descriptions


Title of the course:                  Geometric algorithms

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator(s):                Katalin Vesztergombi
Department(s):                        Department of Computer Science
Evaluation:                           oral or written examination
Prerequisites:

A short description of the course:
Convex hull algorithms in the plane and in higher dimensions.
Lower bounds: the Ben-Or theorem, moment curve, cyclic polyhedron. Decomposition of the
plane by lines. Search of convex hull in the plane (in higher dimensions), search of large
convex polygon (parabolic duality) . Point location queries in planar decomposition. Post
office problem. Voronoi diagrams and Delaunay triangulations and applications. Randomized
algorithms and estimations of running times.

Textbook: none
Further reading:
De Berg, Kreveld, Overmars, Schwartzkopf: Computational geometry. Algorithms and
applications, Berlin, Springer 2000.




                                        Course descriptions
                          MSc program in mathematics: course descriptions                 213


Title of the course:                  Geometric Foundations of 3D Graphics

Number of contact hours per week:    2+2
Credit value:                         3+3
Course coordinator(s):                György Kiss
Department(s):                        Department of Geometry
Evaluation:                           oral or written examination and tutorial mark
Prerequisites:

A short description of the course:
Planar representations of three-dimensional objects by methods of descriptive geometry
(parallel and perspective projections). Matrix representations of affine transformations in
Euclidean space. Homogeneous coordinates in projective space. Matrix representations of
collineations of projective space. Coordinate systems and transformations applied in computer
graphics. Position and orientation of a rigid body (in a fixed coordinate system).
Approximation of parameterized boundary surfaces by triangulated polyhedral surfaces.
Three primary colors, tristimulus coordinates of a light beam. RGB color model. HLS color
model. Geometric and photometric concepts of rendering. Radiance of a surface patch. Basic
equation of photometry. Phong interpolation for the radiance of a surface patch illuminated by
light sources. Digital description of a raster image. Representation of an object with
triangulated boundary surfaces, rendering image by the ray tracing method. Phong shading,
Gouraud shading.

Textbook: none
Further reading:
J. D. Foley, A. van Dam, S. K. Feiner, and J. F. Hughes: Computer Graphics, Principles and
Practice. Addison-Wesley, 1990.




                                        Course descriptions
214                       MSc program in mathematics: course descriptions


Title of the course:                  Geometric Measure Theory

Number of contact hours per week:     3+2
Credit value:                         4+3
Course coordinator(s):                Tamás Keleti
Department(s):                        Department of Analysis
Evaluation:                           oral or written examination and tutorial mark
Prerequisites:                        Topics in Analysis

A short description of the course:
Hausdorff measure, energy and capacity. Dimensions of product sets. Projection theorems.
Covering theorems of Vitali and Besicovitch. Differentiation of measures.
The Kakeya problem, Besicovitch set, Nikodym set.
Dini derivatives. Contingent. Denjoy-Young-Saks theorem.

Textbook: none
Further reading:
P. Mattila: Geometry of sets and measures in Euclidean spaces. Fractals and rectifiability.
Cambridge University Press, Cambridge, 1995.
K. Falconer: Geomerty of Fractal Sets, Cambridge University Press, Cambridge, 1986.
S. Saks: Theory of the Integral, Dover, 1964




                                        Course descriptions
                          MSc program in mathematics: course descriptions                 215


Title of the course:                  Geometric modeling

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator(s):                László Verhóczki
Department(s):                        Department of Geometry
Evaluation:                           oral or written examination
Prerequisites:

A short description of the course:
Solid modeling. Wire frames. Boundary representations. Implicit equations and
parameterizations of boundary surfaces. Constructive Solid Geometry, Boolean set
operations.
Representing curves and surfaces. Curve interpolation. Cubic Hermite polynomials. Fitting a
composite Hermite curve through a set of given points. Curve approximation. Control
polygon, blending functions. Bernstein polynomials. Bézier curves. De Casteljau algorithm.
B-spline functions, de Boor algorithm. Application of weights, rational B-spline curves.
Composite cubic B-spline curves, continuity conditions. Bicubic Hermite interpolation.
Fitting a composite Hermite surface through a set of given points. Surface design. Bézier
patches. Rational B-spline surfaces. Composite surfaces, continuity conditions.

Textbook: none
Further reading:
1. G. Farin: Curves and surfaces for computer aided geometric design. Academic Press,
   Boston, 1988.
2. I. D. Faux and M. J. Pratt: Computational geometry for design and manufacture. Ellis
   Horwood Limited, Chichester, 1979.




                                        Course descriptions
216                       MSc program in mathematics: course descriptions


Title of the course:                  Geometry III

Number of contact hours per week:     3+2
Credit value:                         3+2
Course coordinator(s):                Balázs Csikós
Department(s):                        Department of Geometry
Evaluation:                           oral or written examination and tutorial mark
Prerequisites:

A short description of the course:
Projective geometry: projective space over a field, projective subspaces, dual space,
collineations, the Fundamental Theorem of Projective Geometry. Cross ratio. The theorems of
Pappus and Desargues, and their rôle in the axiomatic foundations of projective geometry.
Quadrics: polarity, projective classification, conic sections.
Hyperbolic geometry: Minkowski spacetime, the hyperboloid model, the Cayley-Klein model,
the conformal models of Poincaré. The absolute notion of parallelism, cycles, hyperbolic
trigonometry.

Textbook:
M. Berger: Geometry I–II (Translated from the French by M. Cole and S. Levy).
Universitext, Springer–Verlag, Berlin, 1987.
Further reading:




                                        Course descriptions
                          MSc program in mathematics: course descriptions                   217


Title of the course:                  Graph theory

Number of contact hours per week:     2+0.
Credit value:                         3
Course coordinator(s):                András Frank and Zoltán Király
Department(s):                        Dept. of Operations Research
Evaluation:                           oral exam
Prerequisites:

Short description of the course:
Graph orientations, connectivity augmentation. Matchings in not necessarily bipartite graphs,
T-joins. Disjoint trees and arborescences. Disjoint paths problems. Colourings, perfect graphs.


Textbook:
András Frank: Connections in combinatorial optimization (electronic notes).

Further reading:
W.J. Cook, W.H. Cunningham, W.R. Pulleybank, and A. Schrijver, Combinatorial
Optimization, John Wiley and Sons, 1998.

R. Diestel, Graph Theory, Springer Verlag, 1996.

A. Schrijver, Combinatorial Optimization: Polyhedra and efficiency, Springer, 2003. Vol. 24
of the series Algorithms and Combinatorics.




                                        Course descriptions
218                       MSc program in mathematics: course descriptions


Title of the course:                  Graph theory seminar

Number of contact hours per week:     0+2.
Credit value:                         2
Course coordinator(s):                László Lovász
Department(s):                        Department of Computer Science
Evaluation:                           type C exam
Prerequisites:

A short description of the course:
Study and presentation of selected papers

Textbook: none
Further reading:




                                        Course descriptions
                          MSc program in mathematics: course descriptions                   219


Title of the course:                  Graph theory tutorial

Number of contact hours per week:     0+2
Credit value:                         3
Course coordinator(s):                András Frank and Zoltán Király
Department(s):                        Dept. of Operations Research
Evaluation:                           tutorial mark
Prerequisites:

A short description of the course:
Graph orientations, connectivity augmentation. Matchings in not necessarily bipartite graphs,
T-joins. Disjoint trees and arborescences. Disjoint paths problems. Colourings, perfect graphs.


Textbook:
András Frank: Connections in combinatorial optimization (electronic notes).

Further reading:
W.J. Cook, W.H. Cunningham, W.R. Pulleybank, and A. Schrijver, Combinatorial
Optimization, John Wiley and Sons, Icn., 1998.

R. Diestel, Graph Theory, Springer Verlag, 1996.

A. Schrijver, Combinatorial Optimization: Polyhedra and efficiency, Springer, 2003. Vol. 24
of the series Algorithms and Combinatorics.




                                        Course descriptions
220                       MSc program in mathematics: course descriptions


Title of the course:                  Groups and representations

Number of contact hours per week:     2+2
Credit value:                         2+3
Course coordinator(s):                Péter P. Pálfy
Department(s):                        Department of Algebra and Number Theory
Evaluation:                           oral or written examination and tutorial mark
Prerequisites:

A short description of the course:
Group actions, permutation groups, automorphism groups. Semidirect products. Sylow’s
Theorems.
Finite p-groups. Nilpotent groups. Solvable groups, Phillip Hall’s Theorems.
Free groups, presentations, group varieties. The Nielsen-Schreier Theorem.
Abelian groups. The Fundamental Theorem of finitely generated Abelian groups. Torsionfree
groups.
Linear groups and linear representations. Semisimple modules and algebras. Irreducible
representations. Characters, orthogonality relations. Induced representations, Frobenius
reciprocity, Clifford’s Theorems.

Textbook: none
Further reading:
     D.J.S. Robinson: A course in the theory of groups, Springer, 1993
     I.M. Isaacs: Character theory of finite groups, Academic Press, 1976




                                        Course descriptions
                          MSc program in mathematics: course descriptions                 221


Title of the course:                  Integer Programming I

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator(s):                Tamás Király
Department(s):                        Department of Operations Research
Evaluation:                           oral or written examination
Prerequisites:

A short description of the course:
Basic modeling techniques. Hilbert bases, unimodularity, total dual integrality. General
heuristic algorithms: Simulated annealing, Tabu search. Heuristic algorithms for the Traveling
Salesman Problem, approximation results. The Held-Karp bound. Gomory-Chvátal cuts.
Valid inequalities for mixed-integer sets. Superadditive duality, the group problem.
Enumeration algorithms.

Textbook: none
Further reading:
G.L. Nemhauser, L.A. Wolsey: Integer and Combinatorial Optimization, John Wiley and
Sons, New York, 1999.

D. Bertsimas, R. Weismantel: Optimization over Integers, Dynamic Ideas, Belmont, 2005.




                                        Course descriptions
222                       MSc program in mathematics: course descriptions




Title of the course:                  Integer Programming II

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator(s):                Tamás Király
Department(s):                        Department of Operations Research
Evaluation:                           oral or written examination
Prerequisites:

A short description of the course:
Sperner systems, binary sets defined by inequalities. Lattices, basis reduction. Integer
programming in fixed dimension. The ellipsoid method, equivalence of separation and
optimization. The Lift and Project method. Valid inequalities for the Traveling Salesman
Problem. LP-based approximation algorithms.

Textbook: none
Further reading:
G.L. Nemhauser, L.A. Wolsey: Integer and Combinatorial Optimization, John Wiley and
Sons, New York, 1999.

D. Bertsimas, R. Weismantel: Optimization over Integers, Dynamic Ideas, Belmont, 2005.




                                        Course descriptions
                          MSc program in mathematics: course descriptions               223


Title of the course:                  Introduction to information theory

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator(s):                István Szabó
Department(s):                        Department of Probability Theory and Statistics
Evaluation:                           oral or written examination
Prerequisites:                        Probability theory and Statistics

A short description of the course:
Source coding via variable length codes and block codes. Entropy and its formal properties.
Information divergence and its properties. Types and typical sequences. Concept of noisy
channel, channel coding theorems. Channel capacity and its computation. Source and channel
coding via linear codes. Multi-user communication systems: separate coding of correlated
sources, multiple access channels.


Textbook: none
Further reading:
Csiszár – Körner: Information Theory: Coding Theorems for Discrete Memoryless Systems.
Akadémiai Kiadó, 1981.
Cover – Thomas: Elements of Information Theory. Wiley, 1991.




                                        Course descriptions
224                       MSc program in mathematics: course descriptions


Title of the course:                  Introduction to Topology

Number of contact hours per week:     2+0
Credit value:                         2
Course coordinator(s):                András Szűcs
Department(s):                        Department of Analysis
Evaluation:                           written examination
Prerequisites:

A short description of the course:
Topological spaces and continuous maps. Constructions of spaces: subspaces, quotient spaces,
product spaces, functional spaces. Separation axioms, Urison’s lemma. Tietze
theorem.Countability axioms., Urison’s metrization theorem. Compactness,
compactifications, compact metric spaces. Connectivity, path-connectivity. Fundamental
group, covering maps.
The fundamental theorem of Algebra, The hairy ball theorem, Borsuk-Ulam theorem.


Textbook:

Further reading:
J. L. Kelley: General Topology, 1957, Princeton.




                                        Course descriptions
                        MSc program in mathematics: course descriptions                225


Title of the course:                Inventory Management

Number of contact hours per week:   2+0
Credit value:                        3
Course coordinator(s):               Gergely Mádi-Nagy
Department(s):                       Department of Operations Research
Evaluation:                          oral or written examination
Prerequisites:

A short description of the course: Harris formula (EOQ), Wagner-Whitin model, Silver-Meal
heuristics, (R,Q ) and (s,S) policy, The KANBAN system.
Textbook: none
Further reading:
Sven Axäter: Inventory Control, Kluwer, Boston, 2000, ISBN 0-7923-7758-3.




                                      Course descriptions
226                       MSc program in mathematics: course descriptions


Title of the course:                  Investments Analysis

Number of contact hours per week:     0+2
Credit value:                         3
Course coordinator(s):                Róbert Fullér
Department(s):                        Department of Operations Research
Evaluation:                           written examination
Prerequisites:                        none

A short description of the course:
Active portfolio management: The Treynor-Black model. Portfolio performance evaluation.
Pension fund performance evaluation. Active portfolio management. Forint-weighted versus
time-weighted returns.


Textbook:
Bodie/Kane/Marcus, Investments (Irwin, 1996)
Further reading:




                                        Course descriptions
                          MSc program in mathematics: course descriptions                      227


Title of the course:                  LEMON library: Solving optimization problems in C++

Number of contact hours per week:     0+2
Credit value:                         3
Course coordinator(s):                Alpár Jüttner
Department(s):                        Department of Operations Research
Evaluation:                           Implementing an optimization algorithm.
Prerequisites:

A short description of the course:
LEMON is an open source software library for solving graph and network optimization
related algorithmic problems in C++. The aim of this course is to get familiar with the
structure and usage of this tool, through solving optimization tasks. The audience also have
the opportunity to join to the development of the library itself.


Textbook: none
Further reading:
http://lemon.cs.elte.hu
Ravindra K. Ahuja, Thomas L. Magnanti, and James B. Orlin. Network Flows. Prentice Hall,
1993.
W.J. Cook, W.H. Cunningham, W. Puleyblank, and A. Schrijver. Combinatorial
Optimization. Series in Discrete Matehematics and Optimization. Wiley-Interscience, Dec
1997.
A. Schrijver. Combinatorial Optimization - Polyhedra and Efficiency. Springer-Verlag,
Berlin, Series: Algorithms and Combinatorics , Vol. 24, 2003




                                        Course descriptions
228                       MSc program in mathematics: course descriptions


Title of the course:                  Lie Groups and Symmetric Spaces

Number of contact hours per week:     4+2
Credit value:                         6+3
Course coordinator(s):                László Verhóczki
Department(s):                        Department of Geometry
Evaluation:                           oral or written examination and tutorial mark
Prerequisites:

A short description of the course:
Lie groups and their Lie algebras. Exponential mapping, adjoint representation, Hausdorff-
Baker-Campbell formula. Structure of Lie algebras; nilpotent, solvable, semisimple, and
reductive Lie algebras. Cartan subalgebras, classification of semisimple Lie algebras.

Differentiable structure on a coset space. Homogeneous Riemannian spaces. Connected
compact Lie groups as symmetric spaces. Lie group formed by isometries of a Riemannian
symmetric space. Riemannian symmetric spaces as coset spaces. Constructions from
symmetric triples. The exact description of the exponential mapping and the curvature tensor.
Totally geodesic submanifolds and Lie triple systems. Rank of a symmetric space.
Classification of semisimple Riemannian symmetric spaces. Irreducible symmetric spaces.

Textbook:
S. Helgason: Differential geometry, Lie groups, and symmetric spaces. Academic Press, New
York, 1978.
Further reading:
O. Loos: Symmetric spaces I–II. Benjamin, New York, 1969.




                                        Course descriptions
                          MSc program in mathematics: course descriptions                229


Title of the course:                  Linear Optimization

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator(s):                Tibor Illés
Department(s):                        Department of Operations Research
Evaluation:                           oral or written examination
Prerequisites:

A short description of the course:
Goldman-Tucker model. Self-dual linear programming problems, Interior point condition,
Goldman-Tucker theorem, Sonnevend theorem, Strong duality, Farkas lemma, Pivot
algorithms.


Textbook: none
Further reading:
Katta G. Murty: Linear Programming. John Wiley & Sons, New York, 1983.
Vašek Chvátal: Linear Programming. W. H. Freeman and Company, New York, 1983.
C. Roos, T. Terlaky and J.-Ph. Vial: Theory and Algorithms for Linear Optimization: An
Interior Point Approach. John Wiley & Sons, New York, 1997.




                                        Course descriptions
230                       MSc program in mathematics: course descriptions


Title of the course:                  Macroeconomics and the Theory of Economic
                                      Equilibrium

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator(s):                Mádi-Nagy Gergely
Department(s):                        Department of Operations Research
Evaluation:                           written examination
Prerequisites: none

A short description of the course:
GDP growth factors. Relation between fiscal and monetary policies. Inflation, taxes and
interes rates. Consumption versus savings. Money markets and stock markets. Employment
and labor market. Exports and imports. Analysis of macroeconomic models.

Textbook:
Paul A. Samuelson-William D. Nordhaus, Economics, Irwin Professiona Publishers, 2004.
Further reading:
McCuerty S.: Macroeconomic Theory, Harper & Row Publ. 1990.
Sargent Th. J.: Macroeconomic Theory, Academic Press, 1987.
Whiteman Ch. H.: Problems in Macroeconomic Theory, Academic Press, 1987.




                                        Course descriptions
                          MSc program in mathematics: course descriptions                  231


Title of the course:                  Manufacturing process management

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator(s):                Tamás Király
Department(s):                        Department of Operations Research
Evaluation:                           oral or written examination
Prerequisites:

A short description of the course:
Production as a physical and information process. Connections of production management
within an enterprise.
Harris formula, determination of optimal lot size: Wagner-Within model and generalizations,
balancing assembly lines, scheduling of flexible manufacturing systems, team technology,
MRP and JIT systems.


Textbook:

Ajánlott irodalom:




                                        Course descriptions
232                        MSc program in mathematics: course descriptions


Title of the course:                   Market analysis

Number of contact hours per week:      2+0
Credit value:                          3
Course coordinator(s):                 Róbert Fullér
Department(s):                         Department of Operations Research
Evaluation:                            oral or written examination
Prerequisites:

A short description of the course:
Description of the current state of some market (e.g. wholesale food markets, electric power
markets, the world market of wheat and maize); price elasticities, models using price
elasticities, determination of price elasticities from real life data; dynamic models, trajectories
in linear and non-linear models; attractor, Ljapunov exponent, fractals, measurement of
Ljapunov exponents and fractal dimension using computer.


Textbook:

Further reading:




                                         Course descriptions
                          MSc program in mathematics: course descriptions                    233


Title of the course:                  Markov chains in discrete and continuous time

Number of contact hours per week:     2+0
Credit value:                         2
Course coordinator(s):                Vilmos Prokaj
Department(s):                        Department of Probability Theory and Statistics
Evaluation:                           oral or written examination
Prerequisites:                        Probability theory and Statistics

A short description of the course:
Markov property and strong Markov property for stochastic processes. Discrete time Markov
chains with stationary transition probabilities: definitions, transition probability matrix.
Classification of states, periodicity, recurrence. The basic limit theorem for the transition
probabilities. Stationary probability distributions. Law of large numbers and central limit
theorem for the functionals of positive recurrent irreducible Markov chains. Transition
probabilities with taboo states. Regular measures and functions. Doeblin’s ratio limit theorem.
Reversed Markov chains.
Absorption probabilities. The algebraic approach to Markov chains with finite state space.
Perron-Frobenius theorems.

Textbook: none
Further reading:
Karlin – Taylor: A First Course in Stochastic Processes, Second Edition. Academic Press,
1975
Chung: Markov Chains With Stationary Transition Probabilities. Springer, 1967.
Isaacson – Madsen: Markov Chains: Theory and Applications. Wiley, 1976.




                                        Course descriptions
234                       MSc program in mathematics: course descriptions


Title of the course:                  Mathematical Logic

Number of contact hours per week:     2+0 (noncompulsory practice)
Credit value:                         2
Course coordinator(s):                Péter Komjáth
Department(s):                        Department of Computer Science
Evaluation:                           oral examination
Prerequisites:

A short description of the course:
Predicate calculus and first order languages. Truth and satisfiability. Completeness. Prenex
norm form. Modal logic, Kripke type models. Model theory: elementary equivalence,
elementary submodels. Tarski-Vaught criterion, Löwenheim-Skolem theorem. Ultraproducts.
Gödel’s compactness theorem. Preservation theorems. Beth’s interpolation theorem. Types
omitting theorem. Partial recursive and recursive functions. Gödel coding. Church thesis.
Theorems of Church and Gödel. Formula expressing the consistency of a formula set.
Gödel’s second incompleteness theorem. Axiom systems, completeness, categoricity, axioms
of set theory. Undecidable theories.


Textbook:
Further reading:




                                        Course descriptions
                          MSc program in mathematics: course descriptions                 235


Title of the course:                  Mathematics of networks and the WWW

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator:                   András Benczúr
Department:                           Department of Computer Science
Evaluation:                           oral or written examination and tutorial mark
Prerequisites:

A short description of the course:
Anatomy of search engines. Ranking in search engines. Markov chains and random walks in
graphs. The definition of PageRank and reformulation. Personalized PageRank, Simrank.
Kleinberg’s HITS algorithm. Singular value decomposition and spectral graph clustering.
Eigenvalues and expanders.
Models for social networks and the WWW link structure. The Barabási model and proof for
the degree distribution. Small world models.
Consistent hashing with applications for Web resource cacheing and Ad Hoc mobile routing.


Textbook: none
Further reading:
   Searching the Web. A Arasu, J Cho, H Garcia-Molina, A Paepcke, S Raghavan. ACM
   Transactions on Internet Technology, 2001
   Randomized Algorithms, R Motwani, P Raghavan, ACM Computing Surveys, 1996
   The PageRank Citation Ranking: Bringing Order to the Web, L. Page, S. Brin, R.
   Motwani, T. Winograd. Stanford Digital Libraries Working Paper, 1998.
   Authoritative sources in a hyperlinked environment, J. Kleinberg. SODA 1998.
   Clustering in large graphs and matrices, P Drineas, A Frieze, R Kannan, S Vempala, V
   Vinay
   Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms, 1999.
   David Karger, Alex Sherman, Andy Berkheimer, Bill Bogstad, Rizwan Dhanidina, Ken
   Iwamoto, Brian Kim, Luke Matkins, Yoav Yerushalmi: Web Caching and Consistent
   Hashing, in Proc. WWW8 conference Dept. of Appl. Analysis and Computational Math.




                                        Course descriptions
236                       MSc program in mathematics: course descriptions



Title of the course:                  Matroid theory

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator(s):                András Frank
Department(s):                        Department of Operations Research
Evaluation:                           oral examination
Prerequisites:

Short description of the course:
Matroids and submodular functions. Matroid constructions. Rado's theorem, Edmonds’
matroid intersection theorem, matroid union. Algorithms for intersection and union.
Applications in graph theory (disjoint trees, covering with trees, rooted edge-connectivity).

Textbook:
András Frank: Connections in combinatorial optimization (electronic notes).

Further reading:
W.J. Cook, W.H. Cunningham, W.R. Pulleybank, and A. Schrijver, Combinatorial
Optimization, John Wiley and Sons, 1998.

B. Korte and J. Vygen, Combinatorial Optimization: Theory and Algorithms, Springer, 2000.,

E. L. Lawler, Combinatorial Optimization: Networks and Matroids, Holt, Rinehart and
Winston, New York, 1976.

J. G. Oxley, Matroid Theory, Oxford Science Publication, 2004.,

Recski A., Matriod theory and its applications, Springer (1989).,

A. Schrijver, Combinatorial Optimization: Polyhedra and efficiency, Springer, 2003. Vol. 24
of the series Algorithms and Combinatorics.,

D. J.A. Welsh, Matroid Theory, Academic Press, 1976.




                                        Course descriptions
                          MSc program in mathematics: course descriptions                237


Title of the course:                  Microeconomy

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator(s):                Gergely Mádi-Nagy
Department(s):                        Department of Operations Research
Evaluation:                           written examination
Prerequisites:                        none


A short description of the course:
The production set, plan and function, The isoquant set, Cobb-Douglas and Leontief
technology, Hostelling lemma, The Le Chatelier principle, Cost minimization, The weak
axiom of cost minimization, Hicks and Marshall demand function, Hicks and Slutsky
compensation, Roy identity, Monetary utility, Engel curve, Giffen effect, Slutsky equation,
Properties of demand function, Axioms of observed preferences, Afriat theorem,
Approximation of preference relation in GARP model, Product aggregation, Hicks
separability, Functional separability, Consumer aggregation, Perfect competitive market,
Supply in competitive markets, Optimal production quantity, Inverse supply function, Pareto
optimality, Market entering, Representative manufacturer and consumer, Several
manufacturers and consumers, Oligopoly and monopoly markets, Welfare economics.



Textbook: Hal R. Varian, Microeconomic Analysis, Norton, New York, 1992.
Further reading:.




                                        Course descriptions
238                       MSc program in mathematics: course descriptions


Title of the course:                  Multiple Objective Optimization

Number of contact hours per week:     0+2
Credit value:                         3
Course coordinator(s):                Róbert Fullér
Department(s):                        Department of Operations Research
Evaluation:                           written examination
Prerequisites:                        none

A short description of the course:
Pareto optimality. The epsilon-constrained method. The value function. The problem of the
weighted objective functions. Lexicographical optimization. Trade-off methods.


Textbook: Kaisa Miettinen, Nonlinear Multiobjective Optimization, (Kluwer, 1999).
Further reading: Ralph L. Keeney and Howard Raiffa, Decisions with Multiple Objectives:
                 Preferences and Value Tradeoffs, (Cambridge University Press, 1993).




                                        Course descriptions
                          MSc program in mathematics: course descriptions                   239


Title of the course:                  Multiplicative Number Theory

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator:                   Mihály Szalay
Department:                           Department of Algebra and Number Theory
Evaluation:                           oral or written examination
Prerequisites:                        Number Theory 2.

A short description of the course:
Large sieve, applications to the distribution of prime numbers. Partitions, generating function.
Dirichlet's theorem concerning the prime numbers in arithmetic progressions. Introduction to
analytic number theory.


Textbook: none
Further reading:
     M. L. Montgomery, Topics in Multiplicative Number Theory, Springer, Berlin-
     Heidelberg-New York, 1971. (Lecture Notes in Mathematics 227)




                                        Course descriptions
240                       MSc program in mathematics: course descriptions


Title of the course:                  Multivariate statistical methods

Number of contact hours per week:     4+0
Credit value:                         4
Course coordinator(s):                György Michaletzky
Department(s):                        Department of Probability Theory and Statistics
Evaluation:                           oral or written examination
Prerequisites:                        Probability Theory and Statistics

A short description of the course:
Estimation of the parameters of multidimensional normal distribution. Matrix valued
distributions. Wishart distribution: density function, determinant, expected value of its
inverse.
Hypothesis testing for the parameters of multivariate normal distribution. Independence,
goodness-of-fit test for normality. Linear regression.
Correlation, maximal correlation, partial correlation, kanonical correlation.
Principal component analysis, factor analysis, analysis of variances.
Contingency tables, maximum likelihood estimation in loglinear models. Kullback–Leibler
divergence. Linear and exponential families of distributions. Numerical method for
determining the L-projection (Csiszár’s method, Darroch–Ratcliff method)


Textbook: none
Further reading:
J. D. Jobson, Applied Multivariate Data Analysis, Vol. I-II. Springer Verlag, 1991, 1992.
C. R. Rao: Linear statistical inference and its applications, Wiley and Sons, 1968,




                                        Course descriptions
                           MSc program in mathematics: course descriptions                  241


Title of the course:                   Nonlinear functional analysis and its applications

Number of contact hours per week:      3+2
Credit value:                          4+3
Course coordinator(s):                 János Karátson
Department(s):                         Dept. of Appl. Analysis and Computational Math.
Evaluation:                            oral examination and home exercises
Prerequisites:

A short description of the course:
Basic properties of nonlinear operators. Derivatives, potential operators, monotone operators,
duality.
Solvability of operator equations. Variational principle, minimization of functionals.
Fixed point theorems. Applications to nonlinear differential equations.
Approximation methods in Hilbert space. Gradient type and Newton-Kantorovich iterative
solution methods. Ritz–Galjorkin type projection methods.
Textbook: none


Further reading: Zeidler, E.: Nonlinear functional analysis and its applications I-III.
Kantorovich, L.V., Akilov, G.P.: Functional Analysis




                                         Course descriptions
242                      MSc program in mathematics: course descriptions


Title of the course:                 Nonlinear Optimization

Number of contact hours per week:   3+0
Credit value:                        4
Course coordinator(s):               Tibor Illés
Department(s):                       Department of Operations Research
Evaluation:                          oral or written examination
Prerequisites:

A short description of the course: Convex sets, convex functions, convex inequalities.
Extremal points, extremal sets. Krein-Milman theorem. Convex cones. Recession direction,
recession cones. Strictly-, strongly convex functions. Locally convex functions. Local minima
of the functions. Characterization of local minimas. Stationary points. Nonlinear
programming problem. Characterization of optimal solutions. Feasible, tangent and
decreasing directions and their forms for differentiable and subdifferentiable functions.
Convex optimization problems. Separation of convex sets. Separation theorems and their
consequences. Convex Farkas theorem and its consequences. Saddle-point, Lagrangean-
function, Lagrange multipliers. Theorem of Lagrange multipliers. Saddle-point theorem.
Necessary and sufficient optimality conditions for convex programming. Karush-Kuhn-
Tucker stationary problem. Karush-Kuhn-Tucker theorem. Lagrange-dual problem. Weak and
strong duality theorems. Theorem of Dubovickij and Miljutin. Specially structured convex
optimization problems: quadratic programming problem. Special, symmetric form of linearly
constrained, convex quadratic programming problem. Properties of the problem. Weak and
strong duality theorem. Equivalence between the linearly constrained, convex quadratic
programming problem and the bisymmetric, linear complementarity problem. Solution
algorithms: criss-cross algorithm, logarithmic barrier interior point method.


Textbook: none
Further reading:
Béla Martos: Nonlinear Programming: Theory and Methods. Akadémiai Kiadó, Budapest,
1975.
M. S. Bazaraa, H. D. Sherali and C. M. Shetty: Nonlinear Programming: Theory and
Algorithms. John Wiley & Sons, New York, 1993.
J.-B. Hiriart-Urruty and C. Lemaréchal: Convex Analysis and Minimization Algorithms I-II.
Springer-Verlag, Berlin, 1993.
J. P. Aubin: Mathematical Methods of Game and Economic Theor. North-Holland,
Amsterdam, 1982.
D. P. Bertsekas: Nonlinear Programming. Athena Scientific, 2004.




                                       Course descriptions
                          MSc program in mathematics: course descriptions               243


Title of the course:                  Number theory 2.

Number of contact hours per week:     2+0
Credit value:                         2
Course coordinator(s):                András Sárközy
Department(s):                        Department of Algebra and Number Theory
Evaluation:                           oral or written examination
Prerequisites:

A short description of the course:
Elements of multiplicative number theory. Dirichlet's theorem,special cases. Elements of
combinatorial number theory. Diophantine equations. The two square problem. Gaussian
integers, special quadraticextensions. Special cases of Fermat's last theorem. The four
squareproblem, Waring's problem. Pell equations. Diophantine approximation theory.
Algebraic and transcendent numbers. The circle problem, elements of the geometry of
numbers. The generating function method, applications. Estimates involving primes. Elements
of probabilistic number theory.

Textbook: none
Further reading:
     I. Niven, H.S. Zuckerman: An introduction to the theory of Numbers. Wiley, 1972.




                                        Course descriptions
244                       MSc program in mathematics: course descriptions


Title of the course:                  Operations Research Project

Number of contact hours per week:     0+2
Credit value:                         3
Course coordinator(s):                Róbert Fullér
Department(s):                        Department of Operations Research
Evaluation:                           written examination
Prerequisites:                        none

A short description of the course:
We model real life problems with operational research methods.
Topics: Portfolio optimization models, Decision support systems, Project management
models, Electronic commerce, Operations research models in telecommunication, Heuristic
yield management

Textbook: Paul A. Jensen and Jonathan F. Bard, Operations Research Models and Methods
(John
           Wiley and Sons, 2003)
Further reading: Mahmut Parlar, Interactive Operations Research with Maple: Methods and
               Models (Birkhauser, Boston, 2000)




                                        Course descriptions
                          MSc program in mathematics: course descriptions               245


Title of the course:                  Operator semigroups

Number of contact hours per week:     2+2
Credit value:                         3+3
Course coordinator(s):                András Bátkai
Department(s):                        Dept. of Appl. Analysis and Computational math.
Evaluation:                           oral or written examination and course work
Prerequisites:

A short description of the course:
Linear theory of operator semigroups. Abstract linear Cauchy problems, Hille-Yosida theory.
Bounded and unbounded perturbation of generators. Spectral theory for semigroups and
generators. Stability and hyperbolicity of semigroups. Further asymptotic properties.

Textbook: Engel, K.-J. and Nagel, R.: One-parameter Semigroups for Linear Evolution
Equations, Springer, 2000.
Further reading:




                                        Course descriptions
246                        MSc program in mathematics: course descriptions


Title of the course:                   Partial differential equations

Number of contact hours per week:      4+2
Credit value:                          6+3
Course coordinator(s):                 László Simon
Department(s):                         Dept. of Appl. Analysis and Computational math.
Evaluation:                            oral examination and tutorial mark
Prerequisites:

A short description of the course:
Fourier transform. Sobolev spaces. Weak, variational and classical solutions of boundary
value problems for linear elliptic equations (stationary heat equation, diffusion). Initial-
boundary value problems for linear equations (heat equation, wave equation): weak and
classical solutions by using Fourier method and Galerkin method.
Weak solutions of boundary value problems for quasilinear elliptic equations of divergence
form, by using the theory of monotone and pseudomonotone operators. Elliptic variational
inequalities. Quasilinear parabolic equations by using the theory of monotone type operators.
Qualitative properties of the solutions. Quasilinear hyperbolic equations.


Textbook: none
Further reading:
R.E. Showalter: Hilbert Space Method for Partial Differential Equations, Pitman, 1979;
E. Zeidler: Nonlinear Functional Analysis and its Applications II, III, Springer, 1990.




                                         Course descriptions
                          MSc program in mathematics: course descriptions              247


Title of the course:                  Polyhedral combinatorics

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator(s):                Tamás Király
Department(s):                        Department of Operations Research
Evaluation:                           oral examination and tutorial mark
Prerequisites:

A short description of the course:
Total dual integrality. Convex hull of matchings. Polymatroid intersection theorem,
submodular flows and their applications in graph optimization (Lucchesi-Younger theorem,
Nash-Williams’ oritentation theorem).


Textbook:

Further reading:

W.J. Cook, W.H. Cunningham, W.R. Pulleybank, and A. Schrijver, Combinatorial
Optimization, John Wiley and Sons, 1998.
B. Korte and J. Vygen, Combinatorial Optimization: Theory and Algorithms, Springer, 2000.
A. Schrijver, Combinatorial Optimization: Polyhedra and efficiency, Springer, 2003. Vol. 24
of the series Algorithms and Combinatorics.




                                        Course descriptions
248                       MSc program in mathematics: course descriptions


Title of the course:                  Probability and Statistics

Number of contact hours per week:     3+2
Credit value:                         3+3
Course coordinator(s):                Tamás F. Móri
Department(s):                        Department of Probability Theory and Statistics
Evaluation:                           oral or written examination and tutorial mark
Prerequisites: -

A short description of the course:
Probability space, random variables, distribution function, density function, expectation,
    variance, covariance, independence.
Types of convergence: a.s., in probability, in Lp, weak. Uniform integrability.
Characteristic function, central limit theorems.
Conditional expectation, conditional probability, regular version of conditional distribution,
    conditional density function.
Martingales, submartingales, limit theorem, regular martingales.
Strong law of large numbers, series of independent random variables, the 3 series theorem.
Statistical field, sufficiency, completeness.
Fisher information. Informational inequality. Blackwell-Rao theorem. Point estimation:
    method of moments, maximum likelihood, Bayes estimators.
Hypothesis testing, the likelihood ratio test, asymptotic properties.
The multivariate normal distribution, ML estimation of the parameters
Linear model, least squares estimator. Testing linear hypotheses in Gaussian linear models.

Textbook: none
Further reading:
J. Galambos: Advanced Probability Theory. Marcel Dekker, New York, 1995.
E. L. Lehmann: Theory of Point Estimation. Wiley, New York, 1983.
E. L. Lehmann: Testing Statistical Hypotheses, 2nd Ed., Wiley, New York, 1986.




                                        Course descriptions
                          MSc program in mathematics: course descriptions                  249


Title of the course:                  Reading course in Analysis

Number of contact hours per week:     0+2
Credit value:                         5
Course coordinator(s):                Tóth Árpád
Department(s):                        Department of Analysis
Evaluation:                           oral or written examination
Prerequisites:

A short description of the course:
Real functions. Functions of bounded variation. Riemann-Stieltjes integral, line integrals. The
inverse and implicit function theorems. Optimum problems with constraints. Measure theory.
The Lebesgue integral. Function spaces. Complex analysis. Cauchy's theorem and integral
formula. Power series expansion of analytic functions. Isolated singular points, the residue
theorem. Ordinary differential equations. Theorems on existence and uniqueness. Elementary
methods. Linear equations and systems. Hilbert spaces, orthonormal systems. Metric spaces,
basic topological concepts, sequences, limits and continuity of functions. Numerical methods.

Textbook: none
Further reading:
   W. Rudin: Principles of mathematical analyis,
   W. Rudin: Real and complex analyis,
   F. Riesz and B. Szokefalvi-Nagy: Functional analysis.
   G. Birkhoff and G-C. Rota: Ordinary Differential Equations,
   J. Munkres: Topology.




                                        Course descriptions
250                       MSc program in mathematics: course descriptions


Title of the course:                  Representations of Banach-*-algebras and Abstract
                                      Harmonic Analysis

Number of contact hours per week:     2+1
Credit value:                         2+2
Course coordinator(s):                János Kristóf
Department(s):                        Dept. of Appl. Analysis and Computational math.
Evaluation:                           oral and written examination
Prerequisites:

A short description of the course:
Representations of *-algebras. Positive functionals and GNS-construction. Representations of
Banach-*-algebras. Gelfand-Raikoff theorem. The second Gelfand-Naimark theorem.
Hilbert-integral of representations. Spectral theorems for C*-algebras and measurable
functional calculus. Basic properties of topological groups. Continuous topological and
unitary representations. Radon measures on locally compact spaces. Existence and uniqueness
of left Haar-measure on locally compact groups. The modular function of a locally compact
group. Regular representations. The group algebra of a locally compact group. The main
theorem of abstract harmonic analysis. Gelfand-Raikoff theorem. Unitary representations of
compact groups (Peter-Weyl theorems). Unitary representations of commutative locally
compact groups (Stone-theorems). Factorization of Radon measures. Induced unitary
representations (Mackey-theorems).
Textbook:

Further reading:
J. Dixmier: Les C*-algébres et leurs représentations, Gauthier-Villars Éd., Paris, 1969
E.Hewitt-K.Ross: Abstract Harmonic Analysis, Vols I-II, Springer-Verlag, 1963-1970




                                        Course descriptions
                          MSc program in mathematics: course descriptions             251


Title of the course:                  Riemann surfaces

Number of contact hours per week:     2+0,
Credit value:                         3
Course coordinator(s):                Róbert Szőke
Department(s):                        Department of Analysis
Evaluation:                           oral or written examination
Prerequisites:                        Complex analysis (Bsc),
                                      Algebraic topology (Bsc),
                                      Algebra IV (Bsc)

A short description of the course:
Abstract definition, coverings, analytic continuation, homotopy, theorem of monodromy,
universal covering, covering group, Dirichlet's problem, Perron's method, Green function,
homology, residue theorem, uniformization theorem for simply connected Riemann surfaces.
 Determining the Riemann surface from its covering group. Fundamental domain,
fundamental polygon. Riemann surface of an analytic function, compact Riemann surfaces
and complex algebraic curves.

Textbook:
Further reading:
O. Forster: Lectures on Riemann surfaces, GTM81, Springer-Verlag, 1981




                                        Course descriptions
252                       MSc program in mathematics: course descriptions


Title of the course:                  Riemannian Geometry

Number of contact hours per week:     4+2
Credit value:                         6+3
Course coordinator(s):                Balázs Csikós
Department(s):                        Department of Geometry
Evaluation:                           oral or written examination and tutorial mark
Prerequisites:

A short description of the course:
The exponential mapping of a Riemannian manifold. Variational formulae for the arc length.
Conjugate points. The index form assigned to a geodesic curve. Completeness of a
Riemannian manifold, the Hopf-Rinow theorem. Rauch comparison theorems. Non-positively
curved Riemannian manifolds, the Cartan-Hadamard theorem. Local isometries between
Riemannian manifolds, the Cartan-Ambrose-Hicks theorem. Locally symmetric Riemannian
spaces.
Submanifold theory: Connection induced on a submanifold. Second fundamental form, the
Weingarten equation. Totally geodesic submanifolds. Variation of the volume, minimal
submanifolds. Relations between the curvature tensors. Fermi coordinates around a
submanifold. Focal points of a submanifold.

Textbooks:
1. M. P. do Carmo: Riemannian geometry. Birkhäuser, Boston, 1992.
2. J. Cheeger, D. Ebin: Comparison theorems in Riemannian geometry. North-Holland,
   Amsterdam 1975.
Further reading:
S. Gallot, D. Hulin, J. Lafontaine: Riemannian geometry. Springer-Verlag, Berlin, 1987.




                                        Course descriptions
                          MSc program in mathematics: course descriptions                  253


Title of the course:                  Rings and algebras

Number of contact hours per week:     2+2
Credit value:                         2+3
Course coordinator(s):                István Ágoston
Department(s):                        Department of Algebra and Number Theory
Evaluation:                           oral or written examination and tutorial mark
Prerequisites:

A short description of the course:
Asociative rings and algebras. Constructions: polynomials, formal power series, linear
operators, group algebras, free algebras, tensor algebras, exterior algebras. Structure theory:
the radical, direct and semidirect decompositions. Chain conditions. The Hilbert Basis
Theorem, the Hopkins theorem.
Categories and functors. Algebraic and topological examples. Natural transformations. The
concept of categorical equivalence. Covariant and contravariant functors. Properties of the
Hom and tensor functors (for non-commutative rings). Adjoint functors. Additive categories,
exact functors. The exactness of certain functors: projective, injective and flat modules.
Homolgical algebra. Chain complexes, homology groups, chain homotopy. Examples from
algebra and topology. The long exact sequence of homologies.
Commutative rings. Ideal decompositions. Prime and primary ideals. The prime spectrum of a
ring. The Nullstellensatz of Hilbert.
Lie algebras. Basic notions, examples, linear Lie algebras. Solvable and nilpotent Lie
algebras. Engel’s theorem. Killing form. The Cartan subalgebra. Root systems and quadratic
forms. Dynkin diagrams, the classification of semisimple complex Lie algebras. Universal
enveloping algebra, the Poincaré–Birkhoff–Witt theorem.

Textbook: none
Further reading:
     Cohn, P.M.: Algebra I-III. Hermann, 1970, Wiley 1989, 1990.
     Jacobson, N.: Basic Algebra I-II. Freeman, 1985, 1989.
     Humphreys, J.E.: Introduction to Lie algebras and representation theory. Springer, 1980.




                                        Course descriptions
254                       MSc program in mathematics: course descriptions


Title of the course:                  Scheduling theory

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator(s):                Tibor Jordán
Department(s):                        Department of Operations Research
Evaluation:                           oral or written examination
Prerequisites:

A short description of the course:
 Classification of scheduling problems; one-machine scheduling, priority rules (SPT, EDD,
LCL), Hodgson algorithm, dynamic programming, approximation algorithms, LP relaxations.
Parallel machines, list scheduling, LPT rule, Hu's algorithm. Precedence constraints,
preemption. Application of network flows and matchings. Shop models, Johnson's algorithm,
timetables, branch and bound, bin packing.

Textbook: T. Jordán, Scheduling, lecture notes.
Further reading:




                                        Course descriptions
                          MSc program in mathematics: course descriptions               255


Title of the course:                  Selected topics in graph theory

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator(s):                László Lovász
Department(s):                        Department of Computer Science
Evaluation:                           oral or written examination
Prerequisites:

A short description of the course:
Selected topics in graph theory. Some topics: eigenvalues, automorphisms, graph polynomials
(e.g., Tutte polynomial), topological problems

Textbook: none
Further reading:
L. Lovász: Combinatorial Problems and Exercises, AMS, Providence, RI, 2007.




                                        Course descriptions
256                       MSc program in mathematics: course descriptions


Title of the course:                  Seminar in complex analysis

Number of contact hours per week:     0+2
Credit value:                         2
Course coordinator(s):                Róbert Szőke
Department(s):                        Department of Analysis
Evaluation:                           oral or written examination or lecture on a selected topic
Prerequisites:                        Topics in complex analysis (MSc)

A short description of the course:
There is no fixed syllabus. Covering topics (individual or several papers on a particular
subject) related to the first semester ―Topics in complex analysis‖
course, mostly by the lectures of the participating students.

Textbook: none

Further reading:




                                        Course descriptions
                          MSc program in mathematics: course descriptions                 257


Title of the course:                  Set Theory (introductory)

Number of contact hours per week:     2+0
Credit value:                         2
Course coordinator(s):                Péter Komjáth
Department(s):                        Department of Computer Science
Evaluation:                           oral examination
Prerequisites:

A short description of the course:
Naive and axiomatic set theory. Subset, union, intersection, power set. Pair, ordered pair,
Cartesian product, function. Cardinals, their comparison. Equivalence theorem. Operations
with sets and cardinals. Identities, monotonicity. Cantor’s theorem. Russell’s paradox.
Examples. Ordered sets, order types. Well ordered sets, ordinals. Examples. Segments.
Ordinal comparison. Axiom of replacement. Successor, limit ordinals. Theorems on
transfinite induction, recursion. Well ordering theorem. Trichotomy of cardinal comparison.
Hamel basis, applications. Zorn lemma, Kuratowski lemma, Teichmüller-Tukey lemma.
Alephs, collapse of cardinal arithmetic. Cofinality. Hausdorff’s theorem. Kőnig inequality.
Properties of the power function. Axiom of foundation, the cumulative hierarchy. Stationary
set, Fodor’s theorem. Ramsey’s theorem, generalizations. The theorem of de Bruijn and
Erdős. Delta systems.


Textbook:
A. Hajnal, P. Hamburger: Set Theory. Cambridge University Press, 1999.
Further reading:




                                        Course descriptions
258                       MSc program in mathematics: course descriptions


Title of the course:                  Set Theory I

Number of contact hours per week:     4+0
Credit value:                         6
Course coordinator(s):                Péter Komjáth
Department(s):                        Department of Computer Science
Evaluation:                           oral examination
Prerequisites:

A short description of the course:
Cofinality, Haussdorff’s theorem. Regular, singular cardinals. Stationary sets. Fodor’s
theorem. Ulam matrix. Partition relations. Theorems of Dushnik-Erdős-Miller, Erdős-Rado.
Delta systems. Set mappings. Theorems of Fodor and Hajnal. Todorcevic’s theorem. Borel,
analytic, coanalytic, projective sets. Regularity properties. Theorems on separation, reduction.
The hierarchy theorem. Mostowski collapse. Notions of forcing. Names. Dense sets. Generic
filter. The generic model. Forcing. Cohen’s result.


Textbook:
A. Hajnal, P. Hamburger: Set Theory. Cambridge University Press, 1999.
Further reading:




                                        Course descriptions
                          MSc program in mathematics: course descriptions                 259


Title of the course:                  Set Theory II

Number of contact hours per week:     4+0
Credit value:                         6
Course coordinator(s):                Péter Komjáth
Department(s):                        Department of Computer Science
Evaluation:                           oral examination
Prerequisites:

A short description of the course:
Constructibility. Product forcing. Iterated forcing. Lévy collapse. Kurepa tree. The
consistency of Martin’s axiom. Prikry forcing. Measurable, strongly compact, supercompact
cardinals. Laver diamond. Extenders. Strong, superstrong, Woodin cardinals. The singular
cardinals problem. Saturated ideals. Huge cardinals. Chang’s conjecture. Pcf theory. Shelah’s
theorem.


Textbook:
A. Hajnal, P. Hamburger: Set Theory. Cambridge University Press, 1999.
Further reading:
K. Kunen: Set Theory.
A. Kanamori: The Higher Infinite.




                                        Course descriptions
260                       MSc program in mathematics: course descriptions


Title of the course:                  Special Functions

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator(s):                Gábor Halász
Department(s):                        Department of Analysis
Evaluation:                           oral examination
Prerequisites:                        Complex Functions (BSc),
                                      Fourier Integral (BSc)

A short description of the course:
Gamma function. Stirling formula in the complex plane, saddle point method.
Zeta function. Functional equation, elementary facts about zeros. Prime number theorem.
Elliptic functions. Parametrization of elliptic curves, lattices. Fundamental domain for the
anharmonic and modular group.
Functional equation for the theta function. Holomorphic modular forms. Their application to
the four square theorem.
Textbook:
Further reading:
E.T. Whittaker and G.N. Watson: A Course of Modern Analysis, University Press,
Cambridge, 1927.
E.C. Titchmarsh (and D.R. Heath-Brown: The Theory of the Riemann Zeta-function, Oxford
University Press, 1986.
C.L. Siegel: Topics in Complex Function Theory, John Wiley & Sons, New York, 1988,
volume I.
R.C. Gunning: Lectures on Modular Forms, Princeton University Press, 1962, 96 pages




                                        Course descriptions
                          MSc program in mathematics: course descriptions                 261


Title of the course:                  Statistical computing 1

Number of contact hours per week:     0+2
Credit value:                         3
Course coordinator(s):                Zempléni András
Department(s):                        Department of Probability and Statistics
Evaluation:                           weekly homework or final practical and written
                                      examination, tutorial mark
Prerequisites:                        Probability and statistics

A short description of the course:
Statistical hypothesis testing and parameter estimation: algorithmic aspects and technical
instruments. Numerical-graphical methods of descriptive statistics. Estimation of the location
and scale parameters. Testing statistical hypotheses. Probability distributions.
Representation of distribution functions, random variate generation, estimation and fitting
probability distributions. The analysis of dependence. Analysis of variance. Linear regression
models. A short introduction to statistical programs of different category: instruments for
demonstration and education, office environments, limited tools of several problems, closed
programs, expert systems for users and specialists.

Computer practice (EXCEL, Statistica, SPSS, SAS, R-project).



Textbook:

Further reading:
http://office.microsoft.com/en-us/excel/HP100908421033.aspx
http://www.statsoft.com/textbook/stathome.html
http://www.spss.com/stores/1/Training_Guides_C10.cfm
http://support.sas.com/documentation/onlinedoc/91pdf/sasdoc_91/insight_ug_9984.pdf
http://www.r-project.org/doc/bib/R-books.html
http://www.mathworks.com/access/helpdesk/help/pdf_doc/stats/stats.pdf




                                        Course descriptions
262                       MSc program in mathematics: course descriptions


Title of the course:                  Statistical computing 2

Number of contact hours per week:     0+2
Credit value:                         3
Course coordinator(s):                Zempléni András
Department(s):                        Department of Probability and Statistics
Evaluation:                           weekly homework or final practical and written
                                      examination, tutorial mark
Prerequisites:                        Multidimensional statistics

A short description of the course:
Multidimensional statistics: review of methods and demonstration of computer instruments.
Dimension reduction. Principal components, factor analysis, canonical correlation.
Multivariate Analysis of Categorical Data. Modelling binary data, linear-logistic model.
Principle of multidimensional scaling, family of deduced methods. Correspondence analysis.
Grouping. Cluster analysis and classification. Statistical methods for survival data analysis.
Probit, logit and nonlinear regression. Life tables, Cox-regression.

Computer practice. Instruments: EXCEL, Statistica, SPSS, SAS, R-project.


Textbook:
Further reading:
http://www.statsoft.com/textbook/stathome.html
http://www.spss.com/stores/1/Training_Guides_C10.cfm
http://support.sas.com/documentation/onlinedoc/91pdf/sasdoc_91/stat_ug_7313.pdf
http://www.r-project.org/doc/bib/R-books.html
http://www.mathworks.com/access/helpdesk/help/pdf_doc/stats/stats.pdf




                                        Course descriptions
                          MSc program in mathematics: course descriptions                   263


Title of the course:                  Statistical hypothesis testing

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator(s):                Villő Csiszár
Department(s):                        Department of Probability Theory and Statistics
Evaluation:                           oral examination
Prerequisites:                        Probability and statistics

A short description of the course:
Monotone likelihood ratio, testing hypotheses with one-sided alternative. Testing with two-
sided alternatives in exponential families. Similar tests, Neyman structure. Hypothesis testing
in presence of nuisance parameters.
Optimality of classical parametric tests. Asymptotic tests. The generalized likelihood ratio
test. Chi-square tests.
Convergence of the empirical process to the Brownian bridge. Karhunen-Loève expansion of
Gaussian processes. Asymptotic analysis of classical nonparametric tests.
Invariant and Bayes tests.
Connection between confidence sets and hypothesis testing.

Textbook: none
Further reading:
E. L. Lehmann: Testing Statistical Hypotheses, 2nd Ed., Wiley, New York, 1986.




                                        Course descriptions
264                       MSc program in mathematics: course descriptions


Title of the course:                  Stochastic optimization

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator(s):                Csaba Fábián
Department(s):                        Department of Operations Research
Evaluation:                           oral or written examination
Prerequisites:

A short description of the course:
Static and dynamic models.
Mathematical characterization of stochastic programming problems. Solution methods.
Theory of logconcave measures. Logconcavity of probabilistic constraints. Estimation of
constraint functions through simulation.


Textbook:

Further reading:
Kall, P., Wallace, S.W., Stochastic Programming, Wiley, 1994.
Prékopa A., Stochastic Programming, Kluwer, 1995.
Birge, J.R., Louveaux, F.: Introduction to Stochastic Programming, Springer, 1997-1999.




                                        Course descriptions
                          MSc program in mathematics: course descriptions                 265


Title of the course:                  Stochastic optimization practice

Number of contact hours per week:     0+2
Credit value:                         3
Course coordinator(s):                Csaba Fábián
Department(s):                        Department of Operations Research
Evaluation:                           tutorial mark
Prerequisites:

A short description of the course:
Examples of stochastic models. Different formulations of aims and constraints: by
expectations or probabilities.
Building simple models, formulating and solving the deriving mathematical programming
problems. Applications.


Textbook:

Further reading:
Kall, P., Wallace, S.W., Stochastic Programming, Wiley, 1994.
Prékopa A., Stochastic Programming, Kluwer, 1995.
Birge, J.R., Louveaux, F.: Introduction to Stochastic Programming, Springer, 1997-1999.




                                        Course descriptions
266                       MSc program in mathematics: course descriptions


Title of the course:   Stochastic processes with independent increments, limit theorems

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator(s):                Vilmos Prokaj
Department(s):                        Department of Probability Theory and Statistics
Evaluation:                           oral or written examination
Prerequisites:                        Probability theory and Statistics

A short description of the course:
Infinitely divisible distributions, characteristic functions. Poisson process, compound Poisson-
process. Poisson point-process with general characteristic measure. Integrals of point-
processes. Lévy–Khinchin formula. Characteristic functions of non-negative infinitely
divisible distributions with finite second moments. Characteristic functions of stable
distributions.
Limit theorems of random variables in triangular arrays.


Textbook: none
Further reading:
Y. S. Chow – H. Teicher: Probability Theory: Independence, Interchangeability, Martingales.
Springer, New York, 1978.
W. Feller: An Introduction to Probability Theory and its Applications, vol. 2. Wiley, New
York, 1966.




                                        Course descriptions
                          MSc program in mathematics: course descriptions                267


Title of the course:                  Structures in combinatorial optimization

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator(s):                Tibor Jordán
Department(s):                        Department of Operations Research
Evaluation:                           oral or written examination
Prerequisites:

A short description of the course:
Chains and antichains in partially ordered sets, theorems of Greene and Kleitman.
Mader's edge splitting theorem. The strong orientation theorem of Nash-Williams.
The interval generator theorem of Győri.


Textbook:
A. Frank, Structures in combinatorial optimization, lecture notes
Further reading:
A. Schrijver, Combinatorial Optimization: Polyhedra and efficiency, Springer, 2003. Vol. 24
of the series Algorithms and Combinatorics.




                                        Course descriptions
268                       MSc program in mathematics: course descriptions


Title of the course:                  Supplementary chapters of topology I. – Topology of
                                      singularities. (special material)

Number of contact hours per week:     2+0
Credit value:                         3
Lecturer:                             András Némethi (scientific advisor, Rényi Institut)
Course coordinator(s):                András Szűcs (professor)
Department(s):                        Department of Analysis
Evaluation:                           oral examination
Prerequisites:                        BSc Algebraic Topology material

A short description of the course:
1)     Complex algebraic curves
2)     holomorphic functions of many variables
3)     implicit function theorem
4)     smooth and singular analytic varieties
5)     local singularities of plane curves
6)     Newton diagram, Puiseux theorem
7)     Resolution of plane curve singularities
8)     Resolution graphs
9)     topology of singularities, algebraic knots
10)    Milnor fibration
11)    Alexander polynomial, monodromy, Seifert matrix
12)    Projective plane curves
13)    Dual curve, Plucker formulae
14)    Genus, Hurwitz-, Clebsh, Noether formulae
15)    Holomorphic differential forms
16)    Abel theorem

Textbook:
Further reading:
C. T. C. Wall: singular points of plane curves, London Math. Soc. Student Texts 63.
F. Kirwan: Complex Algebraic Curves, London Math. Soc. Student Texts 23.
E. Brieskorn, H. Korner: Plane Algebraic Curves, Birkhauser




                                        Course descriptions
                          MSc program in mathematics: course descriptions                    269


Title of the course:                  Supplementary Chapters of Topology II Low
                                      dimensional manifolds

Number of contact hours per week:     2+0
Credit value:                         3
Lecturer:                             András Stipsicz (scientific advisor, Rényi Institut)
Course coordinator(s):                András Szűcs (professor)
Department(s):                        Department of Analysis
Evaluation:                           oral examination
Prerequisites:                        BSc Algebraic Topology

A short description of the course:
1) handle-body decomposition of manifolds
2) knots in 3-manfolds, their Alexander polynomials
3) Jones polynomial, applications
4) surfaces and mapping class groups
5) 3-manifolds, examples
6) Heegard decomposition and Heegard diagram
7) 4-manifolds, Freedman and Donaldson theorems (formulations)
8) Lefschetz fibrations
9) invariants (Seiberg-Witten and Heegard Floer invariants),
10) applications

Textbook:


Further reading:
J. Milnor: Morse theory
R.E. Gompf, A. I. Stipsicz: 4-manifolds and Kirby calculus, Graduate Studies in Mathematics,
Volume 20, Amer. Math. Soc. Providence, Rhode Island.




                                        Course descriptions
270                       MSc program in mathematics: course descriptions


Title of the course:                  Topics in Analysis

Number of contact hours per week:     2+1
Credit value:                         2+2
Course coordinator(s):                Tamás Keleti
Department(s):                        Department of Analysis
Evaluation:                           oral or written examination and tutorial mark
Prerequisites:                        Analysis IV

A short description of the course:
Hausdorff measure and Hausdorff dimension. The Hausdorff dimension of Rn and some
fractals, length and 1-dimensional measure.
Haar measure. Existence and uniqueness.
Approximation theory. Approximation with Fejér means, de la Vallée Poussin operator, Fejér-
Hermite interpolation, Bernstein polynom.
The order of approximation. Approximation with analytic functions.
Approximation with polynomials. Tschebishev polynomials.

Textbook: none
Further reading:
P. Halmos: Measure Theory, Van Nostrand, 1950
K.J. Falconer: The Geometry of Fractal Sets, CUP, 1985
D. Jackson: The theory of approximation, AMS, 1994.




                                        Course descriptions
                          MSc program in mathematics: course descriptions                271


Title of the course:                   Topics in Differential Geometry

Number of contact hours per week:      2+0
Credit value:                          2
Course coordinator:                    Balázs Csikós (associate professor)
Department:                            Department of Geometry
Evaluation:                            oral or written examination
Prerequisites:

A short description of the course:
Differential geometric characterization of convex surfaces. Steiner-Minkowski formula,
Herglotz integral formula, rigidity theorems for convex surfaces.
Ruled surfaces and line congruences.
Surfaces of constant curvature. Tchebycheff lattices, Sine-Gordon equation, Bäcklund
transformation, Hilbert’s theorem. Comparison theorems.
Variational problems in differential geometry. Euler-Lagrange equation, brachistochron
problem, geodesics, Jacobi fields, Lagrangian mechanics, symmetries and invariants, minimal
surfaces, conformal parameterization, harmonic mappings.


Textbook: none
Further reading:
1. W. Blaschke: Einführung in die Differentialgeometrie. Springer-Verlag, 1950.
2. J. A. Thorpe: Elementary Topics in Differential Geometry. Springer-Verlag, 1979.
3. J. J. Stoker: Differential Geometry. John Wiley & Sons Canada, Ltd.; 1989.
4. F. W. Warner: Foundations of Differentiable Manifolds and Lie Groups. Springer-Verlag,
   1983.




                                        Course descriptions
272                       MSc program in mathematics: course descriptions


Title of the course:                  Topics in group theory

Number of contact hours per week:     2+2
Credit value:                         3+3
Course coordinator(s):                Péter P. Pálfy
Department(s):                        Department of Algebra and Number Theory
Evaluation:                           oral or written examination and tutorial mark
Prerequisites:                        Groups and representations

A short description of the course:
Permutation groups. Multiply transitive groups, Mathieu groups. Primitive permutation
groups, the O’Nan-Scott Theorem.
Simple groups. Classical groups, groups of Lie type, sporadic groups.
Group extensions. Projective representations, the Schur multiplier.
p-groups. The Frattini subgroup. Special and extraspecial p-groups. Groups of maximal class.
Subgroup lattices. Theorems of Ore and Iwasawa.


Textbook: none
Further reading:
     D.J.S. Robinson: A course in the theory of groups, Springer, 1993
     P.J. Cameron: Permutation groups, Cambridge University Press, 1999
     B. Huppert, Endliche Gruppen I, Springer, 1967




                                        Course descriptions
                          MSc program in mathematics: course descriptions                     273


Title of the course:                  Topics in ring theory

Number of contact hours per week:     2+2
Credit value:                         3+3
Course coordinator(s):                István Ágoston
Department(s):                        Department of Algebra and Number Theory
Evaluation:                           oral or written examination and tutorial mark
Prerequisites:                        Rings and algebras

A short description of the course:
Structure theory: primitive rings, Jacobson’s Density Theorem, the Jacobson radical of a ring,
commutativity theorem. Central simple algebras: tensor product of algebras, the Noether–
Scolem Theorem, the Double Centralizer Therem, Brauer group, crossed product. Polynomial
identities: structure theorems, Kaplansky’s theorem, the Kurosh Problem, combinatorial
results, quantitative theory. Noetherian rings: Goldie’s theorems and generalizations,
dimension theory. Artinina rings and generalizations: Bass’s characterization of semiperfect
and perfect rings, coherent rings, von Neumann regular rings, homological properties. Morita
theory: Morita equivalence, Morita duality, Morita invariance. Quasi-Frobenius rings: group
algebras, symmetric algebras, homological properties. Representation theory: hereditary
algebras, Coxeter transformations and Coxeter functors, preprojective, regular and
preinjective representations, almost split sequences, the Baruer–Thrall Conjectures, finite
representation type.
The Hom and tensor functors: projective, imjective and flat modules. Derived functors:
projective and injective resolutions, the construction and basic properties of the Ext and Tor
functors. Exact seuqences and the Ext functor, the Yoneda composition, Ext algebras.
Homological dimensions: projective, injective and global dimension, The Hilbert Syzygy
Theorem, dominant dimension, finitistic dimension, the finitistic dimension conjecture.
Homological methods in representation theory: almost split sequences, Auslander–Reiten
quivers. Derived categories: triangulated categories, homotopy category of complexes,
localization of categories, the derived category of an algebra, the Morita theory of derived
categories by Rickard.

Textbook: none
Further reading:
     Anderson, F.–Fuller, K.: Rings and categories of modules, Springer, 1974, 1995
     Auslander, M.–Reiten, I.–Smalø: Representation theory of Artin algebras, Cambridge
     University Press, 1995
     Drozd, Yu. –Kirichenko, V.: Finite dimensional algebras, Springer, 1993
     Happel, D.: Triangulated categories in the representation theory of finite dimensional
     algebras, CUP, 1988
     Herstein, I.: Noncommutative rings. MAA, 1968.
     Rotman, J.: An introduction to homological algebra, AP, 1979




                                        Course descriptions
274                       MSc program in mathematics: course descriptions


Title of the course:                  Topological Vector Spaces and Banach-algebras

Number of contact hours per week:     2+2
Credit value:                         3+3
Course coordinator(s):                János Kristóf
Department:                           Dept. of Appl. Analysis and Computational Math.
Evaluation:                           oral and written examination
Prerequisites:

A short description of the course:
Basic properties of linear topologies. Initial linear topologies. Locally compact topological
vector spaces. Metrisable topological vector spaces. Locally convex and polinormed spaces.
Inductive limit of locally convex spaces. Krein-Milmans theorem. Geometric form of Hahn-
Banach theorem and separation theorems. Bounded sets in topological vector spaces. Locally
convex function spaces. Ascoli theorems. Alaoglu-Bourbaki theorem. Banach-Alaoglu
theorem. Banach-Steinhaus theorem. Elementary duality theory. Locally convex topologies
compatible with duality. Mackey-Arens theorem. Barrelled, bornologic, reflexive and Montel-
spaces. Spectrum in a Banach-algbera. Gelfand-representation of a commutative complex
Banach-algebra. Banach-*-algebras and C*-algebras. Commutative C*-algebras (I. Gelgand-
Naimark theorem). Continuous functional calculus. Universal covering C*-algebra and
abstract Stone’s theorem. Positive elements in C*-algebras. Baer C*-algebras.
Compulsory:

Further reading:
N. Bourbaki: Espaces vectoriels topologiques, Springer, Berlin-Heidelberg-New York, 2007
N. Bourbaki: Théories spectrales, Hermann, Paris, 1967
J. Dixmier: Les C*-algébres et leurs représentations, Gauthier-Villars Éd., Paris, 1969




                                        Course descriptions
                          MSc program in mathematics: course descriptions                   275


Title of the course:                  Unbounded operators of Hilbert spaces

Number of contact hours per week:     2+0
Credit value:                         3
Course coordinator(s):                Sebestyén Zoltán
Department:                           Dept. of Appl. Analysis and Computational Math.
Evaluation:                           oral examination
Prerequisites:                        Functional analysis (BSc)

A short description of the course:
Neumann’s theory of closed Hilbert space operators: existence of the second adjoint and the
product of the first two adjoints as a positive selfadjoint operator. Up to date theory of
positive selfadjoint extensions of not necessarily densely defined operators on Hilbert space:
Krein’s theory revisited. Extremal extensions are characterized including Friedrichs and
Krein-von Neumann extensions. Description of a general positive selfadjoint extension.

Textbook:
Further reading:




                                        Course descriptions
276                       MSc program in mathematics: course descriptions


Title of the course:                  Universal algebra and lattice theory

Number of contact hours per week:     2+2
Credit value:                         3+3
Course coordinator:                   Emil Kiss
Department:                           Department of Algebra and Number Theory
Evaluation:                           oral or written examination and tutorial mark
Prerequisites:

A short description of the course:
Similarity type, algebra, clones, terms, polynomials. Subalgebra, direct product,
homomorphism, identity, variety, free algebra, Birkhoff’s theorems. Subalgebra lattices,
congruence lattices, Grätzer-Schmidt theorem. Mal’tsev-lemma. Subdirect decomposition,
subdirectly irreducible algebras, Quackenbush-problem.
Mal’tsev-conditions, the characterization of congruence permutable, congruence distributive
and congruence modular varieties. Jónsson’s lemma, Fleischer-theorem. Congruences of
lattices, lattice varieties.
Partition lattices, every lattice is embeddable into a partition lattice. Free lattices, Whitman-
condition, canonical form, atoms, the free lattice is semidistributive, the operations are
continuous. There exists a fixed point free monotone map.
Closure systems. Complete, algebraic and geometric lattices. Modular lattices. The free
modular lattice generated by three elements. Jordan-Dedekind chain condition. Semimodular
lattices. Distributive lattices.
Lattices and geometry: subspace lattices of projective geometries. Desargues-identity,
geomodular lattices. Coordinatization. Complemented lattices. The congruences of relatively
complemented lattices.
The question of completeness, primal and functionally complete algebras, characterizations,
discriminator varieties. Directly representable varieties.
The Freese-Lampe-Taylor theorem about the congruence lattice of algebras with a few
operations. Abelian algebras, centrality, the properties of the commutator in modular varieties.
Difference term, the fundamental theorem of Abelian algebras. Generalized Jónsson-theorem.
The characterization of finitely generated, residually small varieties by Freese and McKenzie.
Congruence lattices of finite algebras: the results of McKenzie, Pálfy and Pudlak. Induced
algebra, their geometry, relationship with the congruence lattice of the entire algebra. The
structure of minimal algebras. Types, the labeling of the congruence lattice. Solvable
algebras.
The behavior of free spectrum. Abelian varieties. The distribution of subdirectly irreducible
algebras. Finite basis theorems. First order decidable varieties, undecidable problems.

Textbook: none
Further reading:
     Burris-Sankappanavar: A course in universal algebra. Springer, 1981.
     Freese-McKenzie: Commutator theory for congruence modular varieties. Cambridge
     University Press, 1987.
     Hobby-McKenzie: The structure of finite algebras. AMS Contemporary Math. 76, 1996




                                        Course descriptions
                            MSc program in mathematics: course list                        277



                       MSc in Mathematics: Course list
                                      English–Hungarian
      English                                         Hungarian

1.    Algebraic and differential topology             Algebrai és differenciáltopológia


2.    Algebraic Topology                              Algebrai topológia


3.    Algorithms I                                    Algoritmuselmélet I


4.    Analysis IV                                     Analízis IV.


5.    Analysis of time series                         Idősorok elemzése I.


6.    Applicatons of operations research              Az operációkutatás alkalmazásai

                                                      Alkalmazott diszkrét matematika
7.    Applied discrete mathematics seminar
                                                      szeminárium

8.    Approximation algorithms                        Approximációs algoritmusok


9.    Basic algebra                                   Az algebra alapjai


10.   Basic geometry                                  Geometriai alapozás


11.   Business economics                              Vállalatgazdaságtan


12.   Chapters of complex function theory             Fejezetek a komplex függvénytanból


13.   Codes and symmetric structures                  Kódok és szimmetrikus struktúrák


14.   Combinatorial algorithms I                      Kombinatorikus algoritmusok I.


15.   Combinatorial algorithms II                     Kombinatorikus algoritmusok II.




                                        Course list
278                            MSc program in mathematics: course list




16.   Combinatorial geometry                             Kombinatorikus geometria


17.   Combinatorial number theory                        Kombinatorikus számelmélet

                                                         Kombinatorikus struktúrák és
18.   Combinatorial structures and algorithms            algoritmusok feladatmegoldó
                                                         szeminárium

19.   Commutative algebra                                Kommutatív algebra


20.   Complex functions                                  Komplex függvénytan


21.   Complex manifolds                                  Komplex sokaságok


22.   Complexity theory                                  Bonyolultságelmélet


23.   Complexity theory seminar                          Bonyolultságelmélet szeminárium

      Computational methods in operations
24.                                                      Operációkutatás számítógépes módszerei
      research

25.   Continuous optimization                            Folytonos optimalizálás


26.   Convex geometry                                    Konvex geometria


27.   Cryptography                                       Kriptográfia


28.   Current topics in algebra                          Az algebra aktuális fejezetei


29.   Data mining                                        Adatbányászat


30.   Descriptive set theory                             Leíró halmazelmélet

      Design, analysis and implementation of             Algoritmusok és adatstruktúrák tervezése,
31.
      algorithms and data structures I                   elemzése és implementálása I.

      Design, analysis and implementation of             Algoritmusok és adatstruktúrák tervezése,
32.
      algorithms and data structures II                  elemzése és implementálása II.



                                           Course list
                              MSc program in mathematics: course list                       279




33.   Differential geometry I                           Differenciálgeometria


34.   Differential geometry II                          Differenciálgeometria II


35.   Differential Topology                             Differenciáltopológia


36.   Differential Topology Problem solving             Differenciáltopológia gyakorlat


37.   Discrete dynamical systems                        Diszkrét Dinamikus Rendszerek


38.   Discrete geometry                                 Diszkrét geometria


39.   Discrete mathematics                              Diszkrét matematika


40.   Discrete mathematics II                           Diszkrét matematika II


41.   Discrete optimization                             Diszkrét optimalizálás


42.   Discrete parameter martingales                    Diszkrét paraméterű martingálok


43.   Dynamical systems                                 Dinamikus rendszerek

      Dynamical systems and differential                Dinamikai rendszerek és
44.
      equations                                         differenciálegyenletek

45.   Dynamics in one complex variable                  Komplex dinamika


46.   Ergodic theory                                    Ergodelmélet


47.   Exponential sums in number theory                 Exponenciális összegek a számelméletben


48.   Finite geometries                                 Véges geometria


49.   Fourier integral                                  Fourier integrál



                                          Course list
280                            MSc program in mathematics: course list




50.   Function series                                    Függvénysorok


51.   Functional analysis II                             Funkcionálanalízis II


52.   Game theory                                        Játékelmélet


53.   Geometric algorithms                               Geometriai algoritmusok


54.   Geometric foundations of 3D graphics               A 3D grafika geometriai alapjai


55.   Geometric measure theory                           Geometriai mértékelmélet


56.   Geometric modelling                                Geometriai modellezés


57.   Geometry III                                       Geometria III


58.   Graph theory                                       Gráfelmélet


59.   Graph theory seminar                               Gráfelmélet szeminárium


60.   Graph theory tutorial                              Gráfelmélet gyakorlat


61.   Groups and representations                         Csoportok és reprezentációik


62.   Integer programming I                              Egészértékű Programozás I.


63.   Integer programming II                             Egészértékű Programozás II.


64.   Introduction to information theory                 Bevezetés az információelméletbe


65.   Introduction to Topology                           Bevezetés a topológiába


66.   Inventory management                               Készletgazdálkodás



                                           Course list
                             MSc program in mathematics: course list                          281




67.   Investments analysis                             Befektetések elemzése

      LEMON library: solving optimization              LEMON library: Optimalizációs
68.
      problems in C++                                  feladatok megoldása C++-ban

69.   Lie groups and symmetric spaces                  Lie-csoportok és szimmetrikus terek


70.   Linear optimization                              Lineáris optimalizálás

      Macroeconomics and the theory of
71.                                                    Makrogazdaságtan
      economic equilibrium

72.   Market analysis                                  Piacok elemzése

      Markov chains in discrete and continuous Diszkrét és folytonos paraméterű
73.
      time                                     Markov-láncok

74.   Mathematical logic                               Matematikai logika


75.   Mathematics of networks and the WWW WWW és hálózatok matematikája


76.   Matroid theory                                   Matroidelmélet


77.   Microeconomy                                     Mikrogazdaságtan


78.   Multiple objective optimization                  Többcélfüggvényű optimalizálás


79.   Multiplicative number theory                     Multiplikatív számelmélet


80.   Multivariate statistical methods                 Többdimenziós statisztikai eljárások

      Nonlinear functional analysis and its            Nemlineáris funkcionálanalízis és
81.
      applications                                     alkalmazásai

82.   Nonlinear optimization                           Nemlineáris optimalizálás


83.   Number theory 2.                                 Számelmélet 2.



                                         Course list
282                           MSc program in mathematics: course list




84.    Operations research project                      Operációkutatási projekt


85.    Operator semigroups                              Operátorfélcsoportok


86.    Partial differential equations                   Parciális differenciálegyenletek


87.    Polyhedral combinatorics                         Poliéderes kombinatorika


88.    Probability and statistics                       Valószínűségszámítás és statisztika


89.    Manufacturing process management                 Termelésirányítás


90.    Reading course in Analysis                       Analízis olvasókurzus matematikusoknak

       Representations of Banach-*-algebras and Banach*-algebrák ábrázolásai és
91.
       abstract haronic analysis                absztrakt harmonikus analízis

92.    Rieamnn surfaces                                 Riemann felületek


93.    Riemannian geometry                              Riemann-geometria


94.    Rings and algebras                               Gyűrűk és algebrák


95.    Scheduling theory                                Ütemezéselmélet


96.    Selected topics in graph theory                  Válogatott fejezetek a gráfelméletből


97.    Seminar in complex analysis                      Komplex függvénytani szeminárium


98.    Set theory (introductory)                        Halmazelmélet


99.    Set theory I                                     Halmazelmélet I.


100.   Set theory II                                    Halmazelmélet II



                                          Course list
                               MSc program in mathematics: course list                              283




101.   Special functions                                 Speciális függvények


102.   Statistical computing 1                           Statisztikai programcsomagok 1.


103.   Statistical computing 2                           Statisztikai programcsomagok 2


104.   Statistical hypothesis testing                    Statisztikai hipotézisvizsgálat


105.   Stochastic optimization                           Sztochasztikus optimalizálás


106.   Stochastic optimization practice                  Sztochasztikus optimalizálás gyakorlat

       Stochastic processes with independent             Független növekményű folyamatok,
107.
       increments, limit theorems                        határeloszlás-tételek

108.   Structures in combinatorial optimization          Kombinatorikus optimalizálási struktúrák

       Supplementary chapters of topology I. –           Kiegészítő fejezetek a topológiából I. –
109.
       Topology of singularities.                        Szingularitások topológiája

       Supplementary Chapters of Topology II             Kiegészítő fejezetek a topológiából II. –
110.
       Low dimensional manifolds                         Alacsony dimenziós sokaságok

111.   Topics in analysis                                Fejezetek az analízisből


112.   Topics in differential geometry                   Fejezetek a differenciálgeometriából


113.   Topics in group theory                            Fejezetek a csoportelméletből


114.   Topics in ring theory                             Fejezetek a gyűrűelméletből

       Topological vector spaces and Banach              Topologikus vektorterek és Banach-
115.
       algebras                                          algebrák

116.   Unbounded operators of Hilbert spaces             Nemkorlátos operátorok Hilbert téren


117.   Universal algebra and lattice theory              Univerzális algebra és hálóelmélet



                                           Course list
284                         MSc program in mathematics: course list



                       MSc in Mathematics: Course list
                                      Hungarian–English
      Hungarian                                       English
1.    A 3D grafika geometriai alapjai                 Geometric foundations of 3D graphics


2.    Adatbányászat                                   Data mining


3.    Algebrai és differenciáltopológia               Algebraic and differential topology


4.    Algebrai topológia                              Algebraic Topology


5.    Algoritmuselmélet I                             Algorithms I

      Algoritmusok és adatstruktúrák tervezése, Design, analysis and implementation of
6.
      elemzése és implementálása I.             algorithms and data structures I

      Algoritmusok és adatstruktúrák tervezése, Design, analysis and implementation of
7.
      elemzése és implementálása II.            algorithms and data structures II

      Alkalmazott diszkrét matematika
8.                                                    Applied discrete mathematics seminar
      szeminárium

9.    Analízis IV.                                    Analysis IV


10.   Analízis olvasókurzus matematikusoknak Reading course in Analysis


11.   Approximációs algoritmusok                      Approximation algorithms


12.   Az algebra aktuális fejezetei                   Current topics in algebra


13.   Az algebra alapjai                              Basic algebra


14.   Az operációkutatás alkalmazásai                 Applicatons of operations research

      Banach*-algebrák ábrázolásai és                 Representations of Banach-*-algebras and
15.
      absztrakt harmonikus analízis                   abstract haronic analysis




                                        Course list
                              MSc program in mathematics: course list                           285




16.   Befektetések elemzése                             Investments analysis


17.   Bevezetés a topológiába                           Introduction to Topology


18.   Bevezetés az információelméletbe                  Introduction to information theory


19.   Bonyolultságelmélet                               Complexity theory


20.   Bonyolultságelmélet szeminárium                   Complexity theory seminar


21.   Csoportok és reprezentációik                      Groups and representations


22.   Differenciálgeometria                             Differential geometry I


23.   Differenciálgeometria II                          Differential geometry II


24.   Differenciáltopológia                             Differential Topology


25.   Differenciáltopológia gyakorlat                   Differential Topology Problem solving

      Dinamikai rendszerek és                           Dynamical systems and differential
26.
      differenciálegyenletek                            equations

27.   Dinamikus rendszerek                              Dynamical systems


28.   Diszkrét Dinamikus Rendszerek                     Discrete dynamical systems

      Diszkrét és folytonos paraméterű                  Markov chains in discrete and continuous
29.
      Markov-láncok                                     time

30.   Diszkrét geometria                                Discrete geometry


31.   Diszkrét matematika                               Discrete mathematics


32.   Diszkrét matematika II                            Discrete mathematics II



                                          Course list
286                           MSc program in mathematics: course list




33.   Diszkrét optimalizálás                            Discrete optimization


34.   Diszkrét paraméterű martingálok                   Discrete parameter martingales


35.   Egészértékű Programozás I.                        Integer programming I


36.   Egészértékű Programozás II.                       Integer programming II


37.   Ergodelmélet                                      Ergodic theory


38.   Exponenciális összegek a számelméletben Exponential sums in number theory


39.   Fejezetek a csoportelméletből                     Topics in group theory


40.   Fejezetek a differenciálgeometriából              Topics in differential geometry


41.   Fejezetek a gyűrűelméletből                       Topics in ring theory


42.   Fejezetek a komplex függvénytanból                Chapters of complex function theory


43.   Fejezetek az analízisből                          Topics in analysis


44.   Folytonos optimalizálás                           Continuous optimization


45.   Fourier integrál                                  Fourier integral


46.   Funkcionálanalízis II                             Functional analysis II

      Független növekményű folyamatok,                  Stochastic processes with independent
47.
      határeloszlás-tételek                             increments, limit theorems

48.   Függvénysorok                                     Function series


49.   Geometria III                                     Geometry III



                                          Course list
                              MSc program in mathematics: course list                           287




50.   Geometriai alapozás                               Basic geometry


51.   Geometriai algoritmusok                           Geometric algorithms


52.   Geometriai mértékelmélet                          Geometric measure theory


53.   Geometriai modellezés                             Geometric modelling


54.   Gráfelmélet                                       Graph theory


55.   Gráfelmélet gyakorlat                             Graph theory tutorial


56.   Gráfelmélet szeminárium                           Graph theory seminar


57.   Gyűrűk és algebrák                                Rings and algebras


58.   Halmazelmélet                                     Set theory (introductory)


59.   Halmazelmélet I.                                  Set theory I


60.   Halmazelmélet II                                  Set theory II


61.   Idősorok elemzése I.                              Analysis of time series


62.   Játékelmélet                                      Game theory


63.   Készletgazdálkodás                                Inventory management

      Kiegészítő fejezetek a topológiából I. –          Supplementary chapters of topology I. –
64.
      Szingularitások topológiája                       Topology of singularities.

      Kiegészítő fejezetek a topológiából II. –         Supplementary Chapters of Topology II
65.
      Alacsony dimenziós sokaságok                      Low dimensional manifolds

66.   Kódok és szimmetrikus struktúrák                  Codes and symmetric structures



                                          Course list
288                            MSc program in mathematics: course list




67.   Kombinatorikus algoritmusok I.                     Combinatorial algorithms I


68.   Kombinatorikus algoritmusok II.                    Combinatorial algorithms II


69.   Kombinatorikus geometria                           Combinatorial geometry


70.   Kombinatorikus optimalizálási struktúrák Structures in combinatorial optimization

      Kombinatorikus struktúrák és
71.   algoritmusok feladatmegoldó                        Combinatorial structures and algorithms
      szeminárium

72.   Kombinatorikus számelmélet                         Combinatorial number theory


73.   Kommutatív algebra                                 Commutative algebra


74.   Komplex dinamika                                   Dynamics in one complex variable


75.   Komplex függvénytan                                Complex functions


76.   Komplex függvénytani szeminárium                   Seminar in complex analysis


77.   Komplex sokaságok                                  Complex manifolds


78.   Konvex geometria                                   Convex geometry


79.   Kriptográfia                                       Cryptography


80.   Leíró halmazelmélet                                Descriptive set theory

      LEMON library: Optimalizációs                      LEMON library: solving optimization
81.
      feladatok megoldása C++-ban                        problems in C++

82.   Lie-csoportok és szimmetrikus terek                Lie groups and symmetric spaces


83.   Lineáris optimalizálás                             Linear optimization



                                           Course list
                              MSc program in mathematics: course list                           289



                                                        Macroeconomics and the theory of
84.    Makrogazdaságtan
                                                        economic equilibrium

85.    Matematikai logika                               Mathematical logic


86.    Matroidelmélet                                   Matroid theory


87.    Mikrogazdaságtan                                 Microeconomy


88.    Multiplikatív számelmélet                        Multiplicative number theory


89.    Nemkorlátos operátorok Hilbert téren             Unbounded operators of Hilbert spaces

       Nemlineáris funkcionálanalízis és                Nonlinear functional analysis and its
90.
       alkalmazásai                                     applications

91.    Nemlineáris optimalizálás                        Nonlinear optimization

                                                        Computational methods in operations
92.    Operációkutatás számítógépes módszerei
                                                        research

93.    Operációkutatási projekt                         Operations research project


94.    Operátorfélcsoportok                             Operator semigroups


95.    Parciális differenciálegyenletek                 Partial differential equations


96.    Piacok elemzése                                  Market analysis


97.    Poliéderes kombinatorika                         Polyhedral combinatorics


98.    Riemann felületek                                Rieamnn surfaces


99.    Riemann-geometria                                Riemannian geometry


100.   Speciális függvények                             Special functions



                                          Course list
290                           MSc program in mathematics: course list




101.   Statisztikai hipotézisvizsgálat                  Statistical hypothesis testing


102.   Statisztikai programcsomagok 1.                  Statistical computing 1


103.   Statisztikai programcsomagok 2                   Statistical computing 2


104.   Számelmélet 2.                                   Number theory 2.


105.   Sztochasztikus optimalizálás                     Stochastic optimization


106.   Sztochasztikus optimalizálás gyakorlat           Stochastic optimization practice


107.   Termelésirányítás                                Manufacturing process management

       Topologikus vektorterek és Banach-               Topological vector spaces and Banach
108.
       algebrák                                         algebras

109.   Többcélfüggvényű optimalizálás                   Multiple objective optimization


110.   Többdimenziós statisztikai eljárások             Multivariate statistical methods


111.   Univerzális algebra és hálóelmélet               Universal algebra and lattice theory


112.   Ütemezéselmélet                                  Scheduling theory


113.   Vállalatgazdaságtan                              Business economics


114.   Válogatott fejezetek a gráfelméletből            Selected topics in graph theory


115.   Valószínűségszámítás és statisztika              Probability and statistics


116.   Véges geometria                                  Finite geometries


117.   WWW és hálózatok matematikája                    Mathematics of networks and the WWW



                                          Course list
MSc program in mathematics: course list   291




            Course list

				
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