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4.9.3 Mathematics Course Descriptions4000 Level
Course Code 
MATH 4240 
Credits 
3 


Title 
Advanced Group Theory 
Description 
Representation theory of finite groups, presentations of finite and infinite groups, or other topics. Prerequisite: MATH 3322 (C) or the former MATH 3350 (C) or consent of instructor.

Course Code 
MATH 4260 
Credits 
3 


Title 
Abstract Measure Theory 
Description 
Lebesgue and abstract measures, measurable functions, convergence theorems, absolutely continuous functions, measure spaces, the RadonNikodym theorem, Fubini's and Tonnelli's theorems. Not to be held with the former MATH 4750. Prerequisite: MATH 3472 (C) or the former MATH 3740 (B+) or the former MATH 3760 (C).

Course Code 
MATH 4270 
Credits 
3 


Title 
Algebraic Topology 
Description 
This course will serve as an introduction to elements of homotopy or homology theory. Not to be held with the former MATH 4230. Prerequisites: [MATH 3320 (C) or the former MATH 3300 (C)] and [MATH 3390 (C) or the former MATH 3240 (C)], or consent of instructor.

Course Code 
MATH 4280 
Credits 
3 


Title 
Basic Functional Analysis 
Description 
Banach spaces, HahnBanach, open mapping and closed graph theorems, principle of uniform boundedness, linear operators and functionals, dual space, Lp and Lq spaces, weak and weak* topologies, Hilbert spaces and compact operators on a Hilbert space. Not to be held with the former MATH 4750. Prerequisites: [MATH 3472 (C) or the former MATH 3740 (B+) or the former MATH 3760 (C)] and [MATH 3390 (C) or the former MATH 3240 (C)], or consent of instructor.

Course Code 
MATH 4290 
Credits 
3 


Title 
Complex Analysis 2 
Description 
Conformal mappings, normal families, harmonic and subharmonic functions, Perron's family, Dirichlet problem and Green's function. Not to be held with the former MATH 4710. Prerequisites: [MATH 3340 (C) or the former MATH 3700 (B+) or the former MATH 3710 (C)] and [MATH 3390 (C) or the former MATH 3240 (C)].

Course Code 
MATH 4300 
Credits 
3 


Title 
Combinatorial Geometry 
Description 
Topics in combinatorial geometry, including arrangements of convex bodies, introduction to polytopes, problems in discrete geometry, repeated distances, and geometric graphs. Prerequisite: MATH 3360 (C) or the former MATH 3400 (C) or consent of instructor.

Course Code 
MATH 4320 
Credits 
3 


Title 
Dynamical Systems 
Description 
Techniques for the qualitative analysis of nonlinear systems of ordinary differential equations and discretetime systems. Not to be held with the former MATH 4800. Prerequisite: MATH 3440 (C) or the former MATH 3800 (C).

Course Code 
MATH 4330 
Credits 
3 


Title 
Fundamentals of Approximation Theory 
Description 
Theoretical aspects of approximation theory: density, existence, uniqueness; direct and inverse theorems for polynomial approximation. Prerequisites: [MATH 2080 (C) or MATH 2081 (C) or the former MATH 2202 (C)] and [MATH 2160 (C) or MATH 2161 (C) or the former MATH 2600 (C) or the former MATH 2601 (C)], or consent of instructor.

Course Code 
MATH 4340 
Credits 
3 


Title 
Introduction to Algebraic Geometry 
Description 
This course will introduce students to the basics of affine and projective varieties through a combination of basic theoretical tools and elementary examples. Prerequisite: MATH 3322 (C) or the former MATH 3350 (C) or consent of instructor.

Course Code 
MATH 4360 
Credits 
3 


Title 
Introduction to Differential Geometry 
Description 
Manifolds and submanifolds; vector and tensor fields, Lie brackets and derivatives. Also at least one of the following: exterior differential calculus and Stokes' theorem, introduction to Riemannian geometry, symplectic geometry and hamiltonian mechanics. Not to be held with the former MATH 4730. Prerequisites: [MATH 3472 (C) or the former MATH 3740 (B) or the former MATH 3760 (C)] and [MATH 3390 (C) or the former MATH 3240 (C)].

Course Code 
MATH 4370 
Credits 
3 


Title 
Linear Algebra and Matrix Analysis 
Description 
Vector and matrix norms, matrix factorizations, eigenvalues and eigenvectors, theory of nonnegative matrices. Applications to differential equations, math biology, numerical analysis, digital image processing, data mining, GPS, Markov chains, graph theory, etc will be given in this course. Not to be held with the former MATH 4310. Prerequisite: MATH 2090 (C) or MATH 2091 (C) or the former MATH 2300 (B) or the former MATH 2301 (B) or the former MATH 2350 (C) or the former MATH 2352 (C).

Course Code 
MATH 4380 
Credits 
3 


Title 
Mathematical Biology 
Description 
Formulation, analysis and simulation of suitable models in mathematical biology. Applications will be chosen from fields such as population dynamics, epidemiology, ecology, immunology and cellular dynamics. Not to be held with the former MATH 3530. Prerequisite: MATH 4320 (C) or the former MATH 3800 (C) or consent of instructor.

Course Code 
MATH 4390 
Credits 
3 


Title 
Numerical Approximation Theory 
Description 
Computational aspects of approximation by interpolatory polynomials, convolutions, artificial neural networks, splines and wavelets. Prerequisites: [MATH 2150 (C) or MATH 2151 (C) or MATH 2720 (B) or MATH 2721 (B) or the former MATH 2750 (C)] and [MATH 2160 (C) or MATH 2161 (C) or the former MATH 2600 (C) or the former MATH 2601 (C)], or consent of instructor.

Course Code 
MATH 4440 
Credits 
3 


Title 
Numerical Analysis of Partial Differential Equations 
Description 
Finite difference method, mathematical theory of Elliptic PDEs, finite element method, iterative solution of linear systems. Emphasis will be on the error analysis (stability, consistency and convergence) of the various methods. Prerequisites: [MATH 3420 (C) or the former MATH 3600 (C) or the former MATH 3601 (C)] and [MATH 3460 (C) or the former MATH 3810 (C)] and [MATH 3470 (C) or the former MATH 3740 (B) or the former MATH 3760 (C)], or consent of instructor. It is recommended that MATH 4370 be taken prior to or at the same time.

Course Code 
MATH 4450 
Credits 
3 


Title 
Number Theory 2 
Description 
Algebraic number theory, arithmetic geometry and analytic number theory, Diophantine equations, examples such as arithmetic of elliptic curves and Dirichlet Lfunctions. Not to be held with the former MATH 3450. Prerequisites: [MATH 2020 (C) or MATH 2021 (C)) and MATH 2170 (C)] or [(the former MATH 2500 (C) or the former MATH 2501 (C)) and the former MATH 2202 (C) and the former MATH 2750 (C)], or consent of instructor.

Course Code 
MATH 4460 
Credits 
3 


Title 
Partial Differential Equations 2 
Description 
Green's function, Poisson, heat, Schrodinger and wave equations in two and three spatial dimensions, variational characterization of eigenvalues, Fourier and Laplace transforms, introduction to functional analytic techniques in PDEs. Not to be held with the former MATH 4810. Prerequisites: [MATH 3460 (C) or the former MATH 3810] and [MATH 3470 (C) or the former MATH 3740 (B) or the former MATH 3760 (C)], or consent of instructor.

Course Code 
MATH 4470 
Credits 
3 


Title 
Rings and Modules 
Description 
The general theory of (noncommutative) rings, modules and algebras. Prerequisite: MATH 3322 (C) or the former MATH 3350 or consent of instructor.

Course Code 
MATH 4910 
Credits 
3 


Title 
Project Course in Mathematics 
Description 
A research project by the student in consultation with the department head and an appropriate supervising Faculty member. A written report will be required to be submitted by the end of the term. An oral examination may be required. This course is restricted to students in the fourth year of the Honours or Major program in Mathematics and is not available to Graduate Students.
This course may not be held for credit with MATH 4900. Prerequisite: Consent of
Department. 
Course Code 
MATH 4920 
Credits 
3 


Title 
Topics in Mathematics 
Description 
Topics of current interest in Mathematics or Applied Mathematics upon the interests and requirements of students and faculty, and will include specialized topics not available in regular course offerings. Prerequisite: consent of department. 
