## Course Descriptions

You are reading the 2022/23 Academic Calendar. The 2021/22 version remains in effect until 31 August 2022 and is available here

## Mathematics, Faculty of Science

### MATH: Mathematics

MATH 100 (3) Differential Calculus with Applications to Physical Sciences and Engineering
Derivatives of elementary functions, limits. Covers applications and modelling: graphing and optimization. Credit will be granted for only one of MATH 100 or MATH 116. [3-1-0]
Prerequisite: Either (a) a score of 67% or higher in one of MATH 12, PREC 12 or (b) a score of 60% or higher in one of MATH 125, MATH 126.
Equivalency: MATH 116.
MATH 101 (3) Integral Calculus with Applications to Physical Sciences and Engineering
Definite integral, integration techniques, applications, modelling, linear ODE's. Credit will be granted for only one of MATH 101 or MATH 142. [3-1-0]
Prerequisite: One of MATH 100, MATH 116.
MATH 103 (3) Integral Calculus with Applications to Life Sciences
Antiderivatives, the definite integral, integration techniques, numerical integration, infinite series, applications of integration to differential equations and probability, linear algebra. Credit will be granted for only one of MATH 101, MATH 103, or MATH 142. [3-1-0]
Prerequisite: One of MATH 100, MATH 116.
MATH 111 (3) Finite Mathematics
Intended for students not majoring in Mathematics or the Sciences who want some exposure to mathematical thinking. Logic, set theory, combinatorics, probability theory, matrix algebra, linear programming, graphs, and networks. This course cannot be taken for credit toward a B.Sc. degree. [3-0-1]
Prerequisite: Foundations of Mathematics 11.
MATH 116 (3) Calculus I for Management and Economics
The derivative; limits; rate of change; derivatives of algebraic, logarithmic, trigonometric and exponential functions; applications to marginal analysis; elasticity of demand; optimization and curve-sketching, Newtons Method and Taylor polynomials. Credit will be granted for only one of MATH 116 or MATH 100. [3-0-1]
Prerequisite: Either (a) a score of 67% or higher in one of MATH 12, PREC 12 or (b) a score of 60% or higher in one of MATH 125, MATH 126.
Equivalency: MATH 100.
MATH 125 (3) Pre-Calculus
Prepares students for a calculus course. Functions and their graphs; inverse functions; algebraic, exponential, logarithmic, trigonometric functions; trigonometric identities. Cannot be counted for credit toward the B.Sc. or B.M.S. degree. Credit will be granted for only one of MATH 125 or MATH 126. Students with credit for MATH 100 or 116 may not take MATH 125 for further credit. [3-0-1]
Prerequisite: One of Principles of Mathematics 11, Pre-Calculus 11, Foundations of Mathematics 12.
MATH 126 (3) Basic Mathematics: An Indigenous Perspective
Prepares students for calculus. Functions; graphs; inverse, algebraic, exponential, logarithmic, trigonometric functions; trigonometric identities. Uses cyclical analysis common in some Indigenous cultures. Cannot be counted for credit toward the B.Sc. or B.M.S. degree. Credit will be granted for only one of MATH 126 or 125. Students with credit for MATH 100 or 116 may not take MATH 126 for credit. [3-0-1]
Prerequisite: One of Principles of Mathematics 11, Pre-Calculus 11, Foundations of Mathematics 12, or permission of the Department.
MATH 142 (3) Calculus II for Management and Economics
Continuation of MATH 116. Antiderivatives, the definite integral, integration techniques, numerical integration, double integrals, applications of integration including application to probability, elementary differential equations, functions of several variables; partial derivatives; Lagrange multipliers. Credit will be granted for only one of MATH 142 or MATH 101. [3-0-0]
Prerequisite: One of MATH 100, MATH 116.
MATH 160 (3) Mathematical Reasoning for Arts and Education
For Arts and prospective Education students who wish to gain a deeper understanding of mathematics. Using the approach of problem solving and logical reasoning throughout, topics are chosen from discrete mathematics, elementary number theory, probability and statistics, measurement and geometry, linear algebra, and applications. Credit will only be granted for one of MATH 160 or EDUC 160. Cannot be used for credit toward a B.Sc. or B.M.S. degree, or for the B.A. Major in Mathematics program. [3-0-0]
Prerequisite: Prerequisite: Foundations of Mathematics 11 or Pre-calculus 11
Equivalency: EDUC 160.
MATH 200 (3) Calculus III
Analytic geometry in two and three dimensions, partial and directional derivatives, chain rule, maxima and minima, second derivative test, Lagrange multipliers, multiple integrals with applications. [3-1-0]
Prerequisite: Either (a) MATH 101 or (b) a score of 65% or higher in MATH 103.
MATH 220 (3) Mathematical Proof
Sets and functions; induction; cardinality; properties of the real numbers; sequences, series, and limits. Logic, structure, style, and clarity of proofs emphasized throughout. [3-0-1]
Prerequisite: Either (a) MATH 101 or (b) a score of 65% or higher in MATH 103.
MATH 221 (3) Matrix Algebra
Systems of linear equations, operations on matrices, determinants, eigenvalues and eigenvectors, diagonalization of symmetric matrices. [3-1-0]
Prerequisite: One of MATH 100, MATH 116.
Corequisite: One of MATH 101, MATH 103, MATH 142.
MATH 225 (3) Introduction to Differential Equations
First-order equations, initial value problems, existence and uniqueness theorems, second-order linear equations, superposition of solutions, independence, general solutions, non-homogeneous equations, phaseplane analysis, numerical methods, matrix methods for linear systems, and applications of differential equations to the physical, biological, and social sciences. [3-0-1]
Prerequisite: Either (a) MATH 101 or (b) a score of 65% or higher in MATH 103.
Corequisite: MATH 221 is recommended.
MATH 302 (3) Introduction to Probability
Basic notions of probability, random variables, expectation and conditional expectation, limit theorems. [3-0-0]
Prerequisite: MATH 200.
Equivalency: STAT 303.
MATH 303 (3) Numerical Analysis
Numerical techniques for basic mathematical processes and their analysis. Taylor polynomials, root-finding, linear systems, eigenvalues, approximating derivatives, locating minimizers, approximating integrals, solving differential equations. Credit will be granted for only one of MATH 303 or COSC 303. [3-1-0]
Prerequisite: All of MATH 200, MATH 221 and either (a) COSC 111 or (b) DATA 301.
Equivalency: COSC 303.
MATH 307 (3) Applied Linear Algebra
Dependence/independence, bases and orthogonality; linear transformations from Rn to Rm; change of basis; triangularization; quadratic forms in variables. [3-0-0]
Prerequisite: MATH 221.
MATH 308 (3) Euclidean Geometry
Classical plane geometry, solid geometry, spherical trigonometry, polyhedra, and linear and affine transformations. Linear algebra proofs are used. [3-0-0]
Prerequisite: MATH 221.
Corequisite: MATH 307 is recommended.
MATH 311 (3) Abstract Algebra I
Properties of integers, the integers modulo n, groups, subgroups, cyclic groups, permutation groups, linear groups, quotient groups and homomorphisms, isomorphism theorems, direct products, and an introduction to rings and fields. [3-0-0]
Prerequisite: MATH 220.
MATH 312 (3) Introduction to Number Theory
Euclidean algorithm, congruences, Fermat's theorem, applications, diophantine equations. Distribution of the prime numbers. [3-0-0]
Prerequisite: 12 credits of MATH.
MATH 313 (3) Topics in Number Theory
Topics chosen by the instructor. These might include: division algorithms, group theory, continued fractions, primality testing, factoring. [3-0-0]
Prerequisite: MATH 312.
MATH 317 (3) Calculus IV
Parametrizations, inverse and implicit functions, integrals with respect to length and area; grad, div, and curl, and theorems of Green, Gauss, and Stokes. [3-0-0]
Prerequisite: MATH 200.
MATH 319 (3) Introduction to Partial Differential Equations
Methods of separation of variable, Fourier series, heat, wave and Laplace's equations, boundary value problems, eigenfunction expansions, and Sturm-Liouville problems. [3-0-1]
Prerequisite: All of MATH 200, MATH 225.
MATH 323 (3) Applied Abstract Algebra
Congruences and groups, introduction to rings and fields, and topics chosen from: lattices, Boolean algebra and applications, balanced incomplete block designs, introduction to cryptography, applications to group theory. [3-0-0]
Prerequisite: MATH 221.
Corequisite: MATH 311.
MATH 327 (3) Analysis I
Provides a rigorous foundation of calculus. Real numbers; limits and continuous functions; differentiation; elementary functions; the elementary real integral; normed vector spaces. [3-0-0]
Prerequisite: MATH 220.
MATH 328 (3) Analysis II
Continuation of MATH 327. Limits in normed vector spaces; compactness, series; the integral in one variable and approximation with convolutions. [3-0-0]
Prerequisite: MATH 327.
MATH 330 (3) Abstract Algebra II
Covers properties of rings and fields, factorization, polynomials over a field, field extensions, field isomorphisms and automorphism, group of automorphisms, and Galois theory of unsolvability. [3-0-0]
Prerequisite: MATH 311.
MATH 339 (3) Introduction to Dynamical Systems
Non-linear systems and iteration of functions; flows, phase portraits, periodic orbits, chaotic attractors, fractals, and invariant sets. [3-0-0]
Prerequisite: All of MATH 200, MATH 225.
MATH 340 (3) Introduction to Linear Programming
Linear programming problems, dual problems, the simplex algorithm, solution of primal and dual problems, sensitivity analysis. Additional topics chosen from: Karmarkar's algorithm, non-linear programming, game theory, applications. [3-0-0]
Prerequisite: MATH 221.
MATH 350 (3) Complex Variables and Applications
Covers analytic functions, Cauchy-Riemann equations, power series, Laurent series, elementary functions, contour integrals, and poles and residues. Introduction to conformal mapping and applications of analysis to problems in physics and engineering. [3-0-0]
Prerequisite: MATH 200.
MATH 408 (3) Differential Geometry
Local theory of curves, Frenet-Serret apparatus, fundamentals of the Gaussian theory of surface, normal curvature, geodesics, Gaussian and mean curvatures, theorema egregium, an introduction to Riemannian geometry, Gauss-Bonnet Theorem, and applications. [3-0-0]
Prerequisite: All of MATH 200, MATH 221 and 9 credits of 300-level MATH.
MATH 409 (3) Mathematics of Financial Derivatives
Pricing theory of financial derivative securities. Options and markets, present and future values, price movement modeled by Brownian motion, Ito's formula, parbolic partial differential equations, Black-Scholes model. Prices of European options as solutions of initial/boundary value problems for heat equations, American options, free boundary problems. [3-0-0]
Prerequisite: All of MATH 221, MATH 319 and one of MATH 302, STAT 303.
MATH 410 (3) Introduction to General Topology
General (point-set) topology. Naive set theory, relations and functions, order relations, cardinality, Axiom of Choice, well-ordering, topological spaces, bases, subspaces, product spaces, limit points, continuous functions, homeomorphisms, metric spaces, connectedness, compactness, countability axioms, separation axioms, Urysohn lemma, Tietze extension theorem, Urysohn metrization theorem, Tychonoff theorem. [3-0-0]
Prerequisite: MATH 327.
MATH 429 (3) Analysis III
Continuation of MATH 328. Fourier series, improper integrals, the Fourier integral, calculus in vector spaces. Credit will be granted for only one of MATH 429 or MATH 329. [3-0-0]
Prerequisite: MATH 328.
MATH 430 (3/12) d Special Topics in Optimization and Analysis
Students should consult the department for the particular topics offered in a given year. [3-0-0]
Prerequisite: Third-year standing and permission of the department head.
MATH 432 (3/12) d Special Topics in Algebra and Number Theory
Students should consult the department for the particular topics offered in a given year. [3-0-0]
Prerequisite: Third-year standing and permission of the department head.
MATH 441 (3) Modelling of Discrete Optimization Problems
Formulation of real-world optimization problems using techniques such as linear programming, network flows, integer programming, and dynamic programming. Solution by appropriate software. [3-0-0]
Prerequisite: MATH 340.
MATH 442 (3) Optimization in Graphs and Networks
Basic graph theory, emphasizing trees, tree growing algorithms, and proof techniques. Problems chosen from: shortest paths, maximum flows, minimum cost flows, matchings, graph colouring. Linear programming duality will be an important tool. [3-0-0]
Prerequisite: MATH 340.
MATH 443 (3) Graph Theory
Introductory course in mostly non-algorithmic topics. Planarity and Kuratowski's theorem, graph colouring, graph minors, random graphs, cycles in graphs, Ramsey theory, extremal graph theory. Proofs emphasized. [3-0-0]
Prerequisite: At least 12 credits of 300-level MATH.
MATH 448 (3/6) d Directed Studies in Mathematics
Investigation of a specific topic as agreed upon by the student and the faculty supervisor. Students will be expected to complete a project and make an oral presentation.
Prerequisite: 15 credits of 300- or 400-level MATH and STAT courses and permission of the department head and faculty supervisor.
MATH 459 (3) Mathematical Biology
Mathematical modelling in biological disciplines such as population dynamics, ecology, pattern formation, tumour growth, immune response, biomechanics, and epidemiology. Theory of such models formulated as difference equations, ordinary differential equations, and partial differential equations. [3-0-0]
Prerequisite: MATH 225. MATH 319 is recommended.
MATH 460 (3/12) d Special Topics in Mathematics
Students should consult the department for the particular topics offered in a given year. [3-0-0]
Prerequisite: Third-year standing and permission of the department head.
MATH 461 (3) Continuous Optimization
Convex analysis, non-smooth optimization, Karush-Kuhn-Tucker theorem, iterative methods. [3-0-0]
Prerequisite: MATH 327.
MATH 462 (3) Derivative-Free Optimization
Mathematical analysis and development of derivative-free optimization methods. Heuristic methods, direct search methods, model-based methods, convergence analysis, topics in implementation and testing. Credit will be granted for only one of MATH 462 or MATH 562. [3-0-0]
Prerequisite: All of MATH 200, MATH 220, MATH 221. MATH 303 or COSC 303 is recommended.
MATH 510 (3) General Topology
Topological spaces, interior, closure, and boundary of a set, creating new topological spaces, quotient spaces: examples and applications, continuous functions and homeomorphism, metric spaces & metrizability, connectedness, compactness, countability and separation axioms, applications chosen from the above topics. [3-0-0]
Prerequisite: MATH 327.
MATH 523 (3) Combinatorial Optimization
Theory of the nature of problems from combinatorial optimization; solution techniques and theory; topics from integer programming, network flows, and matroids. [3-0-0]
MATH 538 (3) Algebraic Number Theory
Ring localizations, integral elements, prime and maximal ideals, Dedekind domains, unique factorization of ideals, algebraic number fields, integral bases, discriminants, norms, class number. [3-0-0]
MATH 549 (12) Thesis for Master's Degree
Pass/Fail.
MATH 559 (3) Mathematical Biology
Mathematical methods in modelling biological processes at levels from cell biochemistry to community ecology. [3-0-0]
MATH 562 (3) Derivative-Free Optimization
Mathematical analysis and development of derivative-free optimization methods. Heuristic methods, direct search methods, model-based methods, convergence analysis, topics in implementation and testing. Credit will be granted for only one of MATH 562 or MATH 462. [3-0-0]
MATH 563 (3) Convex Optimization and Non-smooth Analysis
Separation and support properties of convex sets; polar, tangent, and normal cones; Fenchel conjugation; subgradient calculus for convex functions; Fenchel duality for convex optimization problems; algorithms for non-differentiable optimization; non-smooth analysis and optimization for non-convex objects. [3-0-0]
MATH 570 (1-3) c Optimization and Analysis I
Topics from optimization and analysis that are particularly relevant for beginning graduate students at the master's level. [0-0-3]
MATH 590 (1-3) c Graduate Seminar
Presentation and discussion of recent results in the mathematical, statistical, or related literature. Credit may be obtained more than once. Pass/Fail. [0-0-1]
MATH 600 (2-15) c Topics in Algebra
Topics chosen from group theory, rings and modules, Galois theory, commutative rings, categorical algebra, representations of finite groups, and other topics.
MATH 601 (2-15) c Topics in Analysis
Topics, which depend on the students' background and requirements and on the instructor, are drawn from functional analysis, measure and integration theory, non-smooth analysis, and variational analysis. [3-0-0]
MATH 604 (2-15) c Topics in Optimization
Advanced theoretical, algorithmic, or computational topics in optimization. Non-smooth optimization and analysis in infinite-dimensional spaces; monotone operators; subgradient calculus for non-convex functions; semidefinite programming. Interior point methods, projection, and other non-differentiable algorithms. Complexity of optimization algorithms; practical overview of optimization solvers for continuous and discrete problems; numerical and symbolic computation of Fenchel conjugates. [3-0-0]
MATH 605 (2-15) c Topics in Applied Mathematics
Topics will be chosen from different areas of applied mathematics. Content will be determined so as to complement course offerings and meet the needs of the students. Credit for this course may be obtained more than once.
MATH 610 (2-15) c Topics in Pure Mathematics
Topics chosen will depend on the instructor. These may include algebraic number theory, group representation theory, analytic number theory, category theory, combinatorics or algebraic topology.
MATH 620 (2-15) c Directed Studies in Mathematics
Advanced study under the direction of a faculty member may be arranged in special situations.
MATH 649 (0) d Ph.D. Thesis
Pass/Fail.

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