MATH 313.3
Numerical Analysis II
1(3L)
Prerequisite(s): MATH 211, and either 266 or an equivalent course in linear algebra.

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.

MATH 314.3
Numerical Analysis III
2(3L)
Prerequisite(s): MATH 211 and 238.

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

MATH 327.3
Graph Theory
1(3L)
Prerequisite(s): MATH 264 or 266, and either CMPT 260 or 6 credit units of 200-level mathematics.

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

MATH 328.3
Combinatorics and Enumeration
2(3L)
Prerequisite(s): MATH 264 or 266, and either CMPT 260 or 6 credit units of second year mathematics.

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.

MATH 338.6
Differential Equations II
1&2(3L)
Prerequisite(s): MATH 238 or 226.

Use of Laplace transforms, theory of infinite series, solution of ordinary linear equations in series, Sturm-Liouville problems, Fourier series, Bessel and Legendre functions, the Fourier integral, the Laplace, diffusion, and wave equations, calculus of variations, matrices, quadratic forms, oscillations of conservative systems.

MATH 350.6
Differential Geometry
1&2(3L)
Prerequisite(s): MATH 276 or 225, and 277.

Curves in 3-space, Euclidean motions, surface theory, introduction to differentiable manifolds, Gaussian and mean curvature, imbedding conditions, geodesics, parallel transport, Gauss-Bonnet theorem.

MATH 358.6
Projective Geometry and Linear Algebra
1&2(3L)
Prerequisite(s): MATH 110 and 112 or 116.

Provides an introduction to the projective line and plane, determinants, vector spaces, linear equations, linear transformations, and eigenvalues.

Note: Particularly recommended for teachers of mathematics. May not be included in the courses making up an Honours program in mathematics or statistics.

Students are not permitted to take more than one of MATH 264, 266 or 358. Students who have credit for a course or half-course in linear algebra are not permitted to take this course for credit.

MATH 360.6
Algebra I
1&2(3L)
Prerequisite(s): MATH 264, 266 or 358.

Groups, rings, unique factorization domains, modules over principal ideal domains, vector spaces, linear transformations and canonical forms.

Note: Students may not obtain credit for both MATH 363 and 360.

MATH 363.3
Abstract Algebra
2(3L)
Prerequisite(s): One of MATH 100, 101, (or 102), 110 or STATS 103.

Introduction to algebraic structures, notably groups and rings. Topics include binary operations, groups, subgroups, homomorphisms, cosets, Lagrange's theorem, permutation groups, the general linear group; rings, polynomial rings, Euclidean rings.

Note: Recommended for teachers of mathematics. May not be included in the courses making up an Honours program in either Mathematics or Statistics.

Students having credit for MATH 360 may not take this course for credit.

MATH 364.3
Number Theory
1(3L)
Prerequisite(s): One of MATH 100, 101, (or 102), 110 or STATS 103.

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, finite fields, quadratic reciprocity, Gaussian integers, and the Fermat theorem on primes congruent to one modulo four.

Note: Recommended for teachers of mathematics. May not be included in the courses making up an Honours program in either Mathematics or Statistics.