Course Descriptions

Numerical methods in linear algebra. Topics covered include approximation theory, least squares, direct methods for linear equations, iterative methods in matrix algebra, eigenvalues, systems of non-linear equations.

Weekly hours: 3 Lecture hours
Prerequisite(s): MATH 164 or MATH 266; and MATH 211.

Numerical differentiation and integration, initial-value, and boundary-value problems for ordinary differential equations, introduction to numerical solutions to partial-differential equations.

Weekly hours: 3 Lecture hours
Prerequisite(s): MATH 211.3 and MATH 238.3

Graph Theory and its contemporary applications including the nomenclature, special types of paths, matchings and coverings, and optimization problems soluble with graphs.

Weekly hours: 3 Lecture hours
Prerequisite(s): MATH 164.3 or MATH 266.3; and CMPT 260.3 or 6 credit units 200-level MATH.

The theory of Combinatorics and Enumeration and its contemporary applications, including generating functions and recurrence relations, and the Polya and Ramsey Theories. A wide variety of practical applications will be presented.

Weekly hours: 3 Lecture hours
Prerequisite(s): ): MATH 164.3 or MATH 266.3; and CMPT 260.3 or 6 credit units 200-level MATH.

General theory of ordinary differential equations with constant coefficients, series solutions of ordinary differential equations, special functions, Fourier series, introduction to Sturm-Liouville theory, physical origin of heat, wave and Laplace equations, solution by separation of variables.

Weekly hours: 3 Lecture hours and 1.5 Practicum/Lab hours
Prerequisite(s): MATH 224.3 or MATH 226.3 or MATH 238.3 (or approval of instructor)
Note: Students with credit for MATH 338 may not take this course for credit.

The course is designed to teach students how to apply Mathematics by formulating, analyzing and criticizing models arising in real-world situations. An important aspect in modelling a problem is to choose an appropriate set of mathematical methods - 'tools' - in which to formulate the problem mathematically. In most cases a problem can be categorized into one of three types, namely: continuous, discrete, and probabilistic. The course will consist of an introduction to mathematical modelling through examples of these three basic modelling types.

Weekly hours: 3 Lecture hours
Prerequisite(s): MATH 164.3 or MATH 266.3; and MATH 211.3, and STAT 241.3, and (MATH 224.3) or (MATH 225.3 and MATH 226.3) or (MATH 277.3).

Basic Sturm-Liouville theory, Green's functions, hypergeometric equation, special functions of Mathematical Physics, Fourier transform, introduction to distributions/generalized functions, applications to linear differential equations.

Weekly hours: 3 Lecture hours and 1.5 Practicum/Lab hours
Prerequisite(s): MATH 223 and MATH 224; or MATH 225 and MATH 226; or MATH 238 and MATH 276; or approval of the instructor.
Note: Students with credit for MATH 338 may not take this course for credit.

Introduction to differential geometry of curves, surfaces, hypersurfaces, curvature and geodesics.

Weekly hours: 3 Lecture hours
Prerequisite(s): MATH 266; and (MATH 238 and MATH 277) or (MATH 223 and MATH 224) or (MATH 225 and MATH 226 - with grades of at least 80% and permission of the instructor).
Note: Students may receive credit for only one of MATH 350 or MATH 352.

Introduction to group theory, including: cyclic groups, symmetric groups, subgroups and normal subgroups, Lagrange's theorem, quotient groups and homomorphisms, isomorphism theorems, group actions, Sylow's theorem, simple groups, direct and semidirect products, fundamental theorem on finitely generated Abelian groups.

Weekly hours: 3 Lecture hours and 1 Practicum/Lab hours
Prerequisite(s): MATH 163 and MATH 164; or MATH 266

Introduction to ring and field theory, including: polynomial rings, matrix rings, ideals and homomorphisms, quotient rings, Chinese remainder theorem, Euclidean domains, principal ideal domains, unique factorization domains, introduction to module theory, basic theory of field extensions, splitting fields and algebraic closures, finite fields, introduction to Galois theory.

Weekly hours: 3 Lecture hours and 1 Practicum/Lab hours
Prerequisite(s): MATH 163 and MATH 164; or MATH 266

A course in elementary number theory with emphasis upon the interrelation of number theory and algebraic structures: review of unique factorization and congruences, the ring of integers modulo n and its units, Fermat's little theorem, Euler's function, Wilson's theorem, Chinese remainder theorem, and quadratic reciprocity.

Weekly hours: 3 Lecture hours
Prerequisite(s): MATH 163

An introduction to concepts and principles of mathematical analysis in Rn, including Cauchy sequences, compactness, the theory of continuous functions, and uniform convergence.

Weekly hours: 3 Lecture hours
Prerequisite(s): MATH 163 and MATH 277; or MATH 277 and permission of the instructor.
Note: Students majoring in Applied Mathematics who have completed MATH 223 and 224; or MATH 225 and 226 will be granted a prerequisite waiver to register in MATH 371.

A continuation of MATH 371, centering around Lebesgue integration theory, Lp spaces, and applications.

Weekly hours: 3 Lecture hours
Prerequisite(s): MATH 371.

Fundamental concepts, analytic functions, infinite series, integral theorems, calculus of residues, conformal mappings and applications.

Weekly hours: 3 Lecture hours
Prerequisite(s): MATH 225 and 226; or MATH 238 and 277.

Offered occasionally by visiting faculty and in other special situations to cover, in depth, topics that are not thoroughly covered in regularly offered courses.

Weekly hours: 3 Seminar/Discussion hours

Offered occasionally by visiting faculty and in other special situations to cover, in depth, topics that are not thoroughly covered in regularly offered courses.

Weekly hours: 3 Seminar/Discussion hours