4.9.3 Mathematics Course Descriptions-3000 Level

Course Code	MATH 3120  Credits 3
Title	Applied Discrete Mathematics
Description	(Lab Required) Sets, groups, graphs, and Boolean algebra. For Engineering students only. May not be held with COMP 2130. Prerequisites: ECE 2220 (C) and MATH 2130 (C).

Course Code	MATH 3132  Credits 3
Title	Engineering Mathematical Analysis 3
Description	(Lab required) Vector integral calculus; series of Ordinary differential equations; Fourier series and Partial differential equations. For Engineering and Geophysics students only. May not be held with the former MATH 3740, the former MATH 3800, or the former MATH 3100. Prerequisites: MATH 2130 and MATH 2132.

Course Code	MATH 3142  Credits 3
Title	Engineering Mathematical Analysis 4
Description	Introduction to discrete mathematics; systems of linear differential equations; complex function theory and applications. For Engineering and Geophysics students only. May not be held with MATH 3110, MATH 3700, MATH 3710, or MATH 3800. Prerequisites: MATH 2130 (C); and MATH 2132 or the former MATH 2110 (C). NOTE: MATH 3132 is highly recommended.

Course Code	MATH 3320  Credits 3
Title	Algebra 2
Description	Basic structure theory of groups, integral domains and field extensions. Not to be held with the former MATH 3350. Prerequisite: MATH 2020 (C) or MATH 2021 (C) or [the former MATH 3300 (C) and consent of instructor].

Course Code	MATH 3322  Credits 3
Title	Algebra 3
Description	A continuation of topics in Algebra 1 and Algebra 2. More structure theory of groups, general ring theory, fields and field extensions, Galois theory. Prerequisite: MATH 3320 (C) or [the former MATH 3350 (C) and consent of instructor].

Course Code	MATH 3330  Credits 3
Title	Computational Algebra
Description	An introduction to the use of computers for symbolic mathematical computation, involving solving nonlinear systems and differential equations. A suitable software package will be used to explore applications. Prerequisite: MATH 2090 (C) or MATH 2091 (C) or the former MATH 2300 (C) or the former MATH 2301 (C) or the former MATH 2350 (C) or the former MATH 2352 (C) or consent of instructor.

Course Code	MATH 3340  Credits 3
Title	Complex Analysis 1
Description	Analytic functions, Cauchy's theorem and integral formula, series representation of analytic functions, calculus of residues, Rouche's theorem and the principle of the argument. May not be held with the former MATH 3710. Prerequisites: [MATH 2180 (C) or the former MATH 3230 (C)] and [MATH 2150 (C) or MATH 2151 (C) or MATH 2720 (B) or MATH 2721 (B) or the former MATH 2750 (C)].

Course Code	MATH 3360  Credits 3
Title	Combinatorics 2
Description	Advanced topics in combinatorics, including generating functions, elementary design theory, recurrences, chains and antichains, Polya counting. The course is challenging and is intended for students in mathematically rich disciplines. May not be held with the former MATH 4400. Prerequisite: MATH 2030 (C) or MATH 2031 (C) or the former MATH 3400 (C).

Course Code	MATH 3370  Credits 3
Title	Graph Theory 2
Description	Advanced topics in graph theory, including matchings and coverings, optimization, factors, flows, extremal graph theory, basic Ramsey theory, connectivity, and spectral graph theory. Selected applications in science and operations research are studied. The course is challenging and is intended for students in mathematically rich disciplines. May not be held with COMP 4340. Prerequisite: MATH 2070 (C) or MATH 2071 (C) or the former MATH 2400 (B) or permission of instructor.

Course Code	MATH 3380  Credits 3
Title	Introduction to Projective Planes
Description	Affine planes and projective planes, cross ratio, complex projective plane (the great unifier), Desargues' theorem, projective planes over division rings, Pappus' theorem and commutativity, the fundamental theorem for projectivities on a line, introduction of coordinates in a projective plane. May not be held with the former MATH 2552 or the former MATH 3430. Prerequisite: MATH 2020 (C) or MATH 2021 (C) or the former MATH 3300 (C) or the former MATH 3350 (C) or consent of instructor.

Course Code	MATH 3390  Credits 3
Title	Introduction to Topology
Description	Topological spaces, continuity, connectedness, compactness, separation properties. May not be held with the former MATH 3240. Prerequisite: MATH 2180 (C) or the former MATH 3230 (C) or consent of instructor.

Course Code	MATH 3410  Credits 3
Title	Introduction to Mathematical Logic
Description	Propositional and first-order logic. Recursion theory. May not be held with the former MATH 4250. Prerequisite: MATH 2020 (C) or MATH 2021 (C) or the former MATH 2202 (C) or the former MATH 2352 (C) or consent of instructor.

Course Code	MATH 3420  Credits 3
Title	Numerical Analysis 2
Description	Numerical methods for eigenvalue problems, nonlinear systems, initial-value problems, boundary-value problems; finite difference methods for ordinary and partial differential equations; error analysis. Not to be held with the former MATH 3600 or the former MATH 3601. Prerequisites: [MATH 2090 (C) or MATH 2091 (C) or the former MATH 2300 (B) or the former MATH 2301 (B) or the former MATH 2352 (C)] and [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)]. Pre- or corequisite: MATH 3440 or the former MATH 2800 or the former MATH 2801.

Course Code	MATH 3440  Credits 3
Title	Ordinary Differential Equations
Description	Theory and applications of ordinary differential equations; existence and uniqueness of solutions, linear systems, simple nonlinear systems. This course is theory-based and is intended for students in mathematically rich disciplines. Not to be held with the former MATH 3800. Prerequisite: MATH 2180 (C) or [(MATH 1300 (B) or MATH 1301 (B)) and (the former MATH 2730 (B) or the former MATH 2731 (B) or the former MATH 2750 (C))].

Course Code	MATH 3460  Credits 3
Title	Partial Differential Equations
Description	Method of characteristics for first order PDEs, wave, beam, heat and Laplace equations, derivation of PDEs, existence and uniqueness, energy estimates, well-posedness, maximum principles, separation of variables. Not to be held with the former MATH 3810. Prerequisites: [MATH 2150 (C) or MATH 2151 (C) (the former MATH 2750 (C)) or ((MATH 2720 (B) or MATH 2721 (B)) and (the former MATH 2730 (B) or the former MATH 2731 (B)))] and [MATH 3440 (C) or the former MATH 3800 (C)].

Course Code	MATH 3470  Credits 3
Title	Real Analysis 2
Description	Functions of bounded variation, Riemann-Stietjes integration and Lebesgue integration. Not to be held with the former MATH 3740 or the former MATH 3760. Prerequisites: [MATH 2150 (C) or MATH 2151 (C) or MATH 2720 (B) or MATH 2721 (B) or the former MATH 2750 (C)] and [MATH 2180 (C) or the former MATH 3230 (C)].

Course Code	MATH 3472  Credits 3
Title	Real Analysis 3
Description	Fourier series and Fourier transforms; orthogonal systems and L2 theory, convergence and approximation. Multivariable calculus of maps from Rn to Rm, general chain rule and general notion of derivative, implicit function and inverse function theorems. Not to be held with the former MATH 3740 or the former MATH 3760. Prerequisite: MATH 3470 (C).

Course Code	MATH 3480  Credits 3
Title	Set Theory
Description	Axiomatic set theory. Cardinality, well-ordered sets, ordinal numbers, cardinal numbers. Axiom of Choice. Ordinal and cardinal arithmetic. Transfinite induction and recursion. May not be held with the former MATH 3220. Prerequisite: MATH 2020 (C) or MATH 2021 (C) or the former MATH 2202 (C) or consent of instructor.

Course Code	MATH 3490  Credits 3
Title	Optimization
Description	(Lab required) This course introduces the theory and practice of optimization. Both unconstrained and constrained problems are considered, as well as continuous and discrete optimization. Topics include linear programming, unconstrained optimization, constrained nonlinear optimization and integer programming. Applications to Statistics and Data Science will be explored. Prerequisites: [one of MATH 2090, MATH 2091, MATH 2740, the former MATH 2300, the former MATH 2301, the former MATH 2350, or the former MATH 2352] and [one of MATH 2150, MATH 2151, MATH 2720, MATH 2721, or the former MATH 2750].

Course Code	MATH 3610  Credits 3
Title	Introduction to Mathematical Modelling
Description	An introduction to the principles and techniques involved in the design, development, solution, testing and revision of mathematical models of real world phenomena illustrated through the discussion of case studies. May not be held with the former MATH 3820 or the former MATH 3821. Prerequisite: MATH 2150 (C) or MATH 2151 (C) or MATH 2720 (B) or MATH 2721 (B) or MATH 2130 (B) or consent of Instructor.