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					Undergraduate Calendar Content
2078-2008

MATHEMATICS
See also "Statistics".

Credit for MATH 1003

    1. Calculus Challenge Exam

         This examination which is held in early June is open to students registered in a calculus course
         at a high school that has made arrangements with the Department of Mathematics &
         Statistics. A fee will be charged.

         Students who qualify for credit will receive a certificate entitling them to credit for and
         therefore exemption from MATH 1003 when they register at UNB. Upon the student's
         acceptance of the credit (3ch), the letter grade of the exam will be recorded on their
         transcript.

         More information can be obtained from http://www.math.unb.ca or from the Department.

    2. Advanced Placement Test

         The Science Faculty offers Advanced Placement Tests for some first year science courses,
         including MATH 1003, during registration week (early September) each year.

         More information can be obtained by consulting the Science section of the calendar or by
         contacting the Science Faculty or the Department of Mathematics & Statistics.

Note: All prerequisite courses must be passed with a grade of C or better. See beginning of Section H
for abbreviations, course numbers, and coding.

MATH 1003
Introduction to Calculus I
3 ch (4C)
Functions and graphs, limits, derivatives of polynomial, log, exponential and trigonometric functions.
Curve sketching and extrema of functions. NOTE: Credit will not be given for both MATH 1003 and
1823. Prerequisite: A minimum grade of 60% in New Brunswick high school courses: Trigonometry
and 3-space, Advanced Math with an Introduction to Calculus, or equivalent courses; and a passing
score on the Department of Mathematics and Statistics placement test.

MATH 1013
Introduction to Calculus II
3 ch (4C)
Definition of the integral, fundamental theorem of Calculus, Techniques of integration, improper
integrals. Ordinary differential equations. Taylor polynomials and series. Prerequisite: A grade of C or
higher in MATH 1003.

MATH 1053
Enriched Introduction to Calculus
3 ch (4C)
The syllabus is similar to that for MATH 1003, with more emphasis placed both on the theory of
Calculus and interesting applications. The course will be of special interest to students with strong
Mathematical backgrounds. Any interested student (with or without High School Calculus) is
encouraged to consult with the Mathematics Department. Prerequisite: A grade of 85% or higher in a
Grade 12 Math course that contains some Calculus, or consent of the Mathematics Department.




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Undergraduate Calendar Content
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MATH 1063
Enriched Introduction to Calculus II
4 ch (4C)
The syllabus for this course is similar to that of MATH 1013. As with MATH 1053, more emphasis is
placed on theory, mathematical rigor and interesting applications. Prerequisite: A grade of B or higher
in MATH 1053.

MATH 1503
Introduction to Linear Algebra
3 ch (3C)
Lines and Planes, The Geometry and Algebra of vectors, Systems of linear equations, Matrix Algebra,
Linear Independance, Linear Transformations, Determinants, Complex numbers, Eigenvalues,
Eigenvectors, Diagonalization, Rotation matrices, Quadratic forms, Least squares. Prerequisite: A
minimum grade of 60% in New Brunswick Advanced Mathematics 120 or equivalent. Note: Credit will
not be given for both Math 1503 and Math 2213.

MATH 1823
Calculus for Management Sciences
3 ch (3C 1T)
Polynomial, logarithmic and exponential functions. Limits and derivatives. Extreme values and related
rates. Simple integration. Differential equations. Throughout stresses applications to business and
economics. NOTE: Credit will not be given for both MATH 1003 and 1823. Prerequisite: A minimum
grade of 60% in New Brunswick Advanced Mathematics (120), or equivalent.

MATH 1833
Finite Mathematics for Management Sciences
3 ch (3C)
Matrices and systems of linear equations. Linear programming concepts; graphical solution of two
variable problems. Permutations and combinations. Elementary probability. Mathematics of finance.
NOTE: Credit for MATH1833 will not be given if the student has previously taken either MATH 1503 or
MATH 2213. Prerequisite: New Brunswick Mathematics 112 GA (Geometry and Applications) and New
Brunswick Mathematics 112 FR (Functions and Relations), or equivalent.

MATH 2003
Intermediate Mathematics I
3 ch (3C 1T)
Analytic geometry and vectors. Parametric curves. Polar, cylindrical and spherical coordinates.
Functions of several variables, partial derivatives, applications to max-min. Double and triple integrals.
Prerequisite: A grade of C or higher in MATH 1013 or MATH 1063.

MATH 2013
Intermediate Mathematics II
3 ch (3C 1T)
Review of first order differential equations. Second order linear O.D.E.'s. Infinite series, including
power series solutions to O.D.E.'s. Line and surface integrals. Theorems of Green and Stokes.
Divergence Theorem. Prerequisite: A grade of C or higher in MATH 2003.

MATH 2203
Discrete Mathematics
3 ch (3C)
Logic, methods of proof, mathematical induction, elementary set theory, functions and relations.
NOTE: This course is designed for students desiring a good grounding in the foundations of
mathematics. Theorems and proofs are an important part of the course. Credit will not be given for
both MATH 2203 and CS 1303. Students majoring in Mathematics must take MATH 2203. Prerequisite:
MATH 1063 or MATH 1013 or permission of instructor. NOTE: It is strongly recommended that
students should have at least a grade of B in MATH 1013 to take this course.




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Undergraduate Calendar Content
2078-2008
MATH 2213
Linear Algebra I
3 ch (3C)
Linear equations, matrix algebra, determinants, vector spaces, basis, row and column spaces, linear
transformations and matrix representations, scalar products, orthogonal projection, least squares,
eigenvectors and diagonalization, quadratic forms, singular value decomposition. The course will
include use of mathematical software. Prerequisite: MATH 1013, or MATH 1053, or both MATH 1823
and 1833. This course may also be taken with the consent of the instructor. Interested first year
students are encouraged to enquire. Note: Credit will not be given for both Math 1503 and Math 2213.

MATH 2513
Multivariable Calculus for Engineers
4 ch (4C)
Functions of several variables, partial derivatives, multiple integrals, vector functions, Green's and
Stokes' Theorems. See the note following MATH 2003. Prerequisite: A grade of C or higher in both
MATH 1013 and MATH 1503.

MATH 2633
Fundamental Principles of Elementary School Mathematics
3 ch (3C 1L)
This course is intended for students who anticipate a career as an elementary teacher. The course
focuses on the mathematical content with topics taken from the K-6 Atlantic Canada Mathematics
Curriculum and extensions beyond the classroom to show the how and why behind school
mathematics. The major topics are problem solving, number concepts, number and relationship
operations, patterns and relations, shape and space, as well as data management and probability.
Intended for students registered in concurrent education or arts programs. Not available for credit to
students registered in the following programs: Mathematics (honours, major, or minor), Statistics
(honours, major, or minor), Computer Science, Engineering, Administration. Prerequisite: Successful
completion of at least one year of a university program, and consent of the undergraduate advisor for
mathematics.

MATH 3003
Applied Analysis
3 ch (3C)
Vector spaces of functions, convergence in normed linear spaces, orthogonal polynomials, Fourier
series, Fourier transform, Fast Fourier transform, introduction to wavelets, and selected applications.
Prerequisites: MATH 2013 or MATH 3503, and MATH 2213 or MATH 1503 (MATH 3213 recommended).

MATH 3033
Group Theory
3 ch (3C)
Groups are the mathematical objects used to describe symmetries. This course covers the
fundamentals of group theory, together with applications selected from chemistry, geometry and
advanced algebra. Prerequisites: Either MATH 2203 or CS 2303, and MATH 2213 or MATH 1503 (MATH
3213 recommended).

MATH 3043
Nonlinear Differential Equations, Stability and Chaos
3 ch (3C)
Many of the processes studied in science, engineering and economics are nonlinear. This course covers
geometrical, analytical and numerical methods for systems of nonlinear ordinary differential equations
as an introduction to nonlinear phenomena: stability, attractors, bifurcation and chaos. Also covered
are the basic local existence and uniqueness theorem and its applications, as well as linear systems
and nonlinear difference systems to the extent necessary to understand approximations to nonlinear
differential equations. An introduction to the use of mathematical software to illustrate regular and
chaotic behaviour is included. Prerequisite: MATH 2013 or both MATH 2513 and 3503.




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MATH 3063
Geometry
3 ch (3C)
Axiomatic systems, non-Euclidian geometry, transformations in geometries, topological properties of
figures. Recommended for Education students or prospective Mathematics teachers. Prerequisite: 9 ch
in Math and/or Stat.

MATH 3073
Partial Differential Equations
3 ch (3C)
Methods of solution for first order equations. Classification of second order equations. Characteristics.
Analytic and numerical methods of solution for hyperbolic, elliptic and parabolic equations.
Prerequisite: MATH 2013 or both MATH 2513 and 3503.

MATH 3093
Elementary Number Theory
3 ch (3C)
Primes, unique factorization, congruences, Diophantine equations, basic number theoretic functions.
Recommended for Education students or prospective Mathematics teachers.

MATH 3103
Analysis I
3 ch (3C)
The real number system. Elementary set theory. Metric spaces. Sequences and series. Continuity.
Prerequisites: MATH 2013, 2203, and MATH 2213 or 1503.

MATH 3113
Analysis II
3 ch (3C)
Differential calculus, integration, sequences and series of functions, completeness of basis,
convergence of Fourier Series, Fourier Transforms, wavelets and wavelet transforms. Prerequisite:
MATH 3103.

MATH 3213
Linear Algebra II
3 ch (3C)
Possible topics: Vector spaces and subspaces, independent and spanning sets, dimension, linear
operators, determinants, inner product spaces, canonical forms. Prerequisite: MATH 2213 or MATH
1503 or consent of the instructor.

MATH 3243
Complex Analysis
3 ch (3C)
Complex analytic functions, contour integrals and Cauchy's theorems; Taylor's, Laurent's and
Liouville's theorems; residue calculus. Prerequisites: MATH 2003, MATH 2013 or equivalent.

MATH 3333
Combinatorial Theory
3 ch (3C)
Topics selected from: Principle of inclusion and exclusion, Mobius inversion, generating functions;
systems of distinct representatives, Ramsey's Theorem; duality in external problems, duality in
programing; dynamic programing; block designs; introduction to matroid theory; signal-flow graphs.
(The course is also of interest to students in Computer Science and Engineering.) Prerequisite: MATH
1003, 1823 or 1833.




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Undergraduate Calendar Content
2078-2008
MATH 3343
Networks and Graphs
3 ch (3C)
Graphs, Euler paths, tournaments, factors, spanning trees, applications; electric networks and
Kirchhoff's laws, matroids; kernels, Grundy function and application to game theory; Menger's
theorem, flows in networks, flow algorithms. Prerequisite: MATH 1003, 1823 or 1833.

MATH 3353
Computational Algebra
3 ch (3C)
Topics in abstract algebra are approached from the perspective of what can be computed using such
software packages as Maple, Macaulay and GAP. The topics covered will be selected from: Grobner
bases, resultants, solving polynomial equations, invariant theory of finite groups, and the exact
solution of differential equations. The course work will include a mixture of problem sets emphasizing
theory and pratical lab assignments. Prerequisites: one of MATH 1013 or MATH 1063, and one of
MATH 1503 or MATH 2213.

MATH 3363
Finite Mathematics (A)
3 ch (3C)
Applications of algebraic and combinatorial methods to a selection of problems from coding theory,
computability, information theory, formal languages, cybernetics and the social and physical sciences.
Prerequisite: 12 ch in Math and/or Stat.

MATH 3413
Introduction to Numerical Methods
4 ch (3C)
Error analysis, convergence and stability. Approximation of functions by polynomials. Numerical
quadrature and differentiation. The solution of linear and nonlinear equations and the solution of
ordinary differential equations. This course will emphasize the development of computer algorithms
and stress applications in the applied sciences. Note: This course is also listed as CS 3113. Credit will
not be given for both MATH 3413 and CS 3113. Prerequisites: CS 1003 or CS 1073, and MATH 2213 or
MATH 1503.

MATH 3473
Mathematical Models (A)
3 ch (3C)
Overview of the field of mathematical biology. Development, simulation and analysis of simple
mathematical models describing biological systems. Equal emphasis is placed on developing simple
models and case studies of successful models. The principle mathematical tools are differential and
difference equations, finite mathematics, probability and statistics. Note: This course is also listed as
BIOL 4563. Projects and assignments for MATH 3473 will place more emphasis on model development
and analysis. Students cannot receive credit for both BIOL 4563 and MATH 3473. Prerequisite: a
statistics course, MATH2013 or MATH2513 or permission of the instructor.

MATH 3503
Differential Equations for Engineers
3 ch (3C 1T)
Nonhomogeneous differential equations, undetermined coefficients, variation of parameters, systems
of 1st and 2nd order ordinary differential equations, Laplace transforms, Fourier series, partial
differential equations with constant coefficients, boundary value problems. Prerequisite: MATH 1503 or
2213 (C grade minimum). Co-requisite MATH 2513 or MATH 2003.

MATH 3543
Differential Geometry for Geomatics Engineers
4 ch (4L 1T)
Basic analytic geometry, spherical trigonometry, geometry of curves in space, measurements on
surfaces, Gaussian surface geometry. Prerequisites: MATH 2513.



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Undergraduate Calendar Content
2078-2008
MATH 3623
History of Mathematics (A)
3 ch (3C) [W]
A non-technical survey of the development of mathematics from primitive peoples through Indian,
Oriental, Babylonian, Egyptian and Greek cultures. More emphasis will be placed on Western European
and post-Renaissance mathematics, and recent (post-1940) history. An attempt is made to discuss
each new mathematical contribution in light of both past mathematics and social scientific forces of
the day. Some background in Mathematics necessary. Prerequisite: 12 ch in Math and/or Stat.

MATH 3633
Fundamental Principles of School Mathematics I.
3 ch (3C)
A course for undergraduate students who anticipate a career as teachers. Topics build around the K-
12 syllabus, with extensions beyond the classroom, to show the 'how' and 'why' behind school
mathematics. Mathematical language; real numbers and other mathematical structures; Euclidean
geometry; functions; mathematical connections; problem solving. Intended for students registered in
concurrent B.Ed. programs, but may be taken by others with the approval of the student's
departmental Chair or Dean. Prerequisite: 6 ch of university mathematics.

MATH 3803
Introduction to the Mathematics of Finance
3 ch (3C)
Measurement of interest, compound interest, annuities, amortization schedules and sinking funds.
Bonds. Prerequisite: MATH1013 or a grade of B or better in MATH 1823.

MATH 3813
Mathematics of Finance II (0)
3 ch (3C)
A more advanced study of the topics in MATH3803 including varying and continuous annuities and
yield rates. Prerequisite: MATH3803 with a grade of B or better.

MATH 3843
Introduction to Life Contingencies
3 ch (3C)
Survival distributions, general life insurances and life annuities, reserves. Joint annuities and last
survivor annuities. Prerequisite: One term of statistics and MATH3803.

MATH 4023
Functional Analysis
3 ch (3C)
Normed spaces, the Hahn-Banach theorem, uniform boundedness theorem. Wavelets. The contraction
mapping theorem. Existence and uniqueness for nonlinear differental equations. Prerequisite: Any two
of MATH 3003, 3103, 3113, or permission of the instructor.

MATH 4043
Advanced Algebra (A)
3 ch (3C)
Prime fields and characteristic, extension fields, algebraic extensions, theory of finite fields, Galois
theory, and topics which may include some of: rings, topological algebra, multilinear and exterior
algebra, quadratic forms. Prerequisites: MATH 3033.

MATH 4063
Advanced Geometry (Exotic Spaces) (O)
3 ch (3C)
A deeper investigation of Euclidean and Non-Euclidean spaces of any dimension. Topics selected from:
axiom systems, linear and affine transformations, conformal and linear models for Euclidean and
hyperbolic spaces and their isometry groups, basic theory of convexity, combinatorial properties of
polytopes. Prerequisites: At least one of MATH 2213 or MATH 2003 or MATH 2513 or MATH 3063.



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Undergraduate Calendar Content
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MATH 4100
Honours Project
6 ch [W]
Mathematics Honours students must complete a project under the supervision of a faculty member.
The project is to include a written report and an oral presentation. Prior to being admitted into MATH
4100, the student must have been admitted to the Honours Program and have submitted an
acceptable project proposal to the department. Normally students would begin preparation and
research for the project during their third year of study, submit the proposal by October of their fourth
(final) year of study, and complete the written and oral presentation by the end of the winter term, to
graduate in May of that year.

MATH 4123
Advanced Linear Algebra (O)
3 ch (3C)
The theory of vector spaces and linear transformations, dual spaces, multilinear maps (including
tensors and determinants); further topics chosen from canonical forms, metric vector spaces,
algebras, etc. Prerequisites: MATH 3213.

MATH 4153
Topology (A)
3 ch (3C)
A continuation of the topological concepts introduced in MATH 3103. Basic results in point-set
topology. Prerequisites: MATH 3103.

MATH 4413
Fluid Mechanics (A)
3 ch (3C)
Derivation of the Equations of Motion: Euler's equations, rotation and vorticity, Navier-Stokes
equations. Potential Flow: complex potentials, harmonic functions, conformal mapping, potential flow
in three dimensions. Slightly Viscous Flow: boundary layers and Prandtl boundary layer equations. Gas
Flow in one dimension: characteristics and shocks. Prerequisite: MATH 2003-2013 or equivalent.

MATH 4423
Mathematical Theory of Control (A)
3 ch (3C)
Topics selected according to the interests of students and faculty which may include the following:
optimal control of linear systems, Pontryagin's maximum principle, controlability, observability,
distributed parameter systems, differential games, stochastic systems. Prerequisite: MATH 2003-2013
or equivalent.

MATH 4433
Calculus of Variations (A)
3 ch (3C)
Introduction to functionals and function spaces. Variation of a functional. Euler's equations, necessary
condition for an extremum, case of several variables, invariance of Euler's equation, fixed end point
problem for unknown functions, variational problems in parametric form, functionals depending on
high order derivatives. Prerequisite: MATH 2003-2013 or equivalent.

MATH 4443
Introduction to Quantum Field Theory
3 ch (3C)
Relativistic quantum mechanics. The negative energy problem. Classical field theory, symmetries and
Noether's theorem. Free field theory and Fock space quantization. The interacting field: LSZ reduction
formula, Wick's theorem, Green's functions, and Feynman diagrams. Introduction to Quantum
electrodynamics and renormalization. This course is crosslisted as PHYS 5153. Prerequisites: MATH
3003, PHYS 3051, and one of MATH 3043, 3503, PHYS 3011, 3031, or permission of instructor.




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Undergraduate Calendar Content
2078-2008
MATH 4453
Special Functions (A)
3 ch (3C)
Covers in depth those functions which commonly occur in Physics and Engineering, namely, the
Gamma, Beta, Bessel, Legendre, hypergeometric, Hermite and Laguerre functions. Additional or
alternative special functions may be included. Applications to Physics and Engineering will be
discussed. Prerequisite: MATH 3043 or 3503 or equivalent.

MATH 4473
Introduction to Differential Geometry (A)
3 ch (3C)
Geometry of embedded curves and surfaces, n-dimensional manifolds, tensors, Riemannian geometry.
Prerequisites: MATH 2003-2013 or equivalent.

MATH 4483
Introduction to General Relativity (A)
3 ch (3C)
Special relativity, foundations of general relativity, solutions of Einstein's equations, classical tests,
cosmology, additional topics. Prerequisites: MATH 4473 or consent of instructor.

MATH 4503
Numerical Methods for Differential Equations
3 ch (3C)
The numerical solution of ordinary differential equations, and partial differential equations of elliptic,
hyperbolic and parabolic type. The course is a basic introduction to finite difference methods, including
the associated theory of stability, accuracy and convergence. Students will gain practical experience
using state-of-the-art numerical solvers and visualization tools, while solving problems from the
physical and biological sciences. Prerequisites: One of: MATH 3043, 3073, 3503, CS 3113, CHE 3418,
or ME 3522.

MATH 4633
Calculus Revisited
3 ch (3C)
A course for high school mathematics teachers. The course is built around a set of optimization
problems, whose solution requires review of topics in first and second year calculus and linear algebra.
Connections are made with topics in the Common Atlantic High School Mathematics Curriculum.
Prerequisite: Permission of Instructor. Students should be near completion of requirements for a
major or minor in mathematics.

MATH 4643
Formal Languages
3 ch (3C)
Brief history of structural linguistics. Introduction to mathematical methods of linguistics. Finite state
automata, regular languages. Computability. Chomsky hierarchy. Phrase-structure grammars. Artificial
intelligence problem. Critiques of structural linguistics. Prerequisite: Consent of the instructor. MATH
2203 or CS2303 recommended.

MATH 4853
Mathematics of Financial Derivatives (A)
3 ch (3C)
Basics of options, futures, and other derivative securities. Introduction to Arbitrage. Brief introduction
to partial differential equations. Stochastic calculus and Ito's Lemma. Option pricing using the Black-
Scholes model. Put-call parity and Hedging. Pricing of European and American call and put options.
Numerical methods for the Black-Scholes model: binary trees, moving boundary problems, and linear
complementarity. The barrier, and other exotic options. Prerequisites: (MATH 3503 and STAT 2593) or
(MATH 2013, 2213 and STAT 3083), and CS1073 or experience with a computer programming
language.




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Undergraduate Calendar Content
2078-2008
MATH 4903
Independent Study in Mathematics
3 ch
Topics to be chosen jointly by student, advisor, and Department Chair. May be taken for credit more
than once. Title of topic chosen will appear on transcript. Prerequisite: Permission of Department.




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