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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 Personal data 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. Personal data 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 Personal data 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–; Personal data 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 Personal data 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. Personal data 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 Personal data 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. Personal data 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. Personal data 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. Personal data 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). Personal data 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. Personal data 128 MSc program in mathematics: personal data 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. Personal data 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 Personal data 132 MSc program in mathematics: personal data 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. Personal data 134 MSc program in mathematics: personal data 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. Personal data 136 MSc program in mathematics: personal data 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: Personal data 138 MSc program in mathematics: personal data 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 Personal data 140 MSc program in mathematics: personal data 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) Personal data 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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posted: | 11/11/2011 |

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