4.9.3 Mathematics Course Descriptions-4000 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 Radon-Nikodym 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, Hahn-Banach, 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 discrete-time 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 non-negative 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 L-functions. 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 (non-commutative) 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.