Program Requirement:
This Minor concentration is open only to students registered in the Major Concentration Mathematics. Taken together, these two concentrations constitute a program equivalent to the Major in Mathematics offered by the Faculty of Science.
No course overlap between the Major Concentration Mathematics and the Supplementary Minor Concentration in Mathematics is permitted.
Note that according to the Faculty of Arts Multitrack System degree requirements, option C, students registered in the Supplementary Minor Concentration in Mathematics must also complete another minor concentration in a discipline other than Mathematics.
For more information about the Multitrack System options please refer to the Faculty of Arts regulations under "Faculty Degree Requirements", "About Program Requirements", and "Departmental Programs".
Required Course (3 credits)
* Note: If Math 315 has already been taken as part of the Major Concentration Mathematics, an additional 3credit complementary course must be taken to replace it.

MATH 315
Ordinary Differential Eqns
3 Credits*
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions.
Offered by: Mathematics and Statistics
 Terms
 This course is not scheduled for the 20242025 academic year
 Instructors
 There are no professors associated with this course for the 20242025 academic year
Complementary Courses (15 credits)
15 credits selected as follows:
3 credits from:
* Note: If either of MATH 249 or MATH 316 has been taken as part of the Major Concentration Mathematics, another 3credit complementary course must be taken.

MATH 249
Honours Complex Variables
3 Credits*
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Functions of a complex variable; CauchyRiemann equations; Cauchy's theorem and consequences. Taylor and Laurent expansions. Residue calculus; evaluation of real integrals; integral representation of special functions; the complex inversion integral. Conformal mapping; SchwarzChristoffel transformation; Poisson's integral formulas; applications.
Offered by: Mathematics and Statistics
 Winter
 Prerequisite(s): MATH 248 or MATH 358 or equivalent.
 Restriction: Intended for Honours Physics and Engineering students
 Restriction: Not open to students who have taken or are taking MATH 316
 Terms
 This course is not scheduled for the 20242025 academic year
 Instructors
 There are no professors associated with this course for the 20242025 academic year

MATH 316
Complex Variables
3 Credits*
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Algebra of complex numbers, CauchyRiemann equations, complex integral, Cauchy's theorems. Taylor and Laurent series, residue theory and applications.
Offered by: Mathematics and Statistics
 Terms
 This course is not scheduled for the 20242025 academic year
 Instructors
 There are no professors associated with this course for the 20242025 academic year
12 credits from:

MATH 204
Principles of Statistics 2
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): The concept of degrees of freedom and the analysis of variability. Planning of experiments. Experimental designs. Polynomial and multiple regressions. Statistical computer packages (no previous computing experience is needed). General statistical procedures requiring few assumptions about the probability model.
Offered by: Mathematics and Statistics
 Winter
 Prerequisite: MATH 203 or equivalent. No calculus prerequisites
 Restriction: This course is intended for students in all disciplines. For extensive course restrictions covering statistics courses see Section 3.6.1 of the Arts and of the Science sections of the calendar regarding course overlaps.
 You may not be able to receive credit for this course and other statistic courses. Be sure to check the Course Overlap section under Faculty Degree Requirements in the Arts or Science section of the Calendar.
 Terms
 This course is not scheduled for the 20242025 academic year
 Instructors
 There are no professors associated with this course for the 20242025 academic year

MATH 308
Fundls of Statistical Learning
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Theory and application of various techniques for the exploration and analysis of multivariate data: principal component analysis, correspondence analysis, and other visualization and dimensionality reduction techniques; supervised and unsupervised learning; linear discriminant analysis, and clustering techniques. Data applications using appropriate software.
Offered by: Mathematics and Statistics
 Terms
 This course is not scheduled for the 20242025 academic year
 Instructors
 There are no professors associated with this course for the 20242025 academic year

MATH 317
Numerical Analysis
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations.
Offered by: Mathematics and Statistics
 Terms
 This course is not scheduled for the 20242025 academic year
 Instructors
 There are no professors associated with this course for the 20242025 academic year

MATH 318
Mathematical Logic
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Propositional logic: truthtables, formal proof systems, completeness and compactness theorems, Boolean algebras; firstorder logic: formal proofs, Gödel's completeness theorem; axiomatic theories; set theory; Cantor's theorem, axiom of choice and Zorn's lemma, Peano arithmetic; Gödel's incompleteness theorem.
Offered by: Mathematics and Statistics
 Terms
 This course is not scheduled for the 20242025 academic year
 Instructors
 There are no professors associated with this course for the 20242025 academic year

MATH 319
Partial Differential Equations
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): First order equations, geometric theory; second order equations, classification; Laplace, wave and heat equations, SturmLiouville theory, Fourier series, boundary and initial value problems.
Offered by: Mathematics and Statistics
 Terms
 This course is not scheduled for the 20242025 academic year
 Instructors
 There are no professors associated with this course for the 20242025 academic year

MATH 324
Statistics
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference.
Offered by: Mathematics and Statistics
 Fall and Winter
 Prerequisite: MATH 323 or equivalent
 Restriction: Not open to students who have taken or are taking MATH 357
 You may not be able to receive credit for this course and other statistic courses. Be sure to check the Course Overlap section under Faculty Degree Requirements in the Arts or Science section of the Calendar.
 Terms
 This course is not scheduled for the 20242025 academic year
 Instructors
 There are no professors associated with this course for the 20242025 academic year

MATH 326
Nonlinear Dynamics and Chaos
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Linear systems of differential equations, linear stability theory. Nonlinear systems: existence and uniqueness, numerical methods, one and two dimensional flows, phase space, limit cycles, PoincareBendixson theorem, bifurcations, Hopf bifurcation, the Lorenz equations and chaos.
Offered by: Mathematics and Statistics
 Terms
 This course is not scheduled for the 20242025 academic year
 Instructors
 There are no professors associated with this course for the 20242025 academic year

MATH 327
Matrix Numerical Analysis
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): An overview of numerical methods for linear algebra applications and their analysis. Problem classes include linear systems, least squares problems and eigenvalue problems.
Offered by: Mathematics and Statistics
 Terms
 This course is not scheduled for the 20242025 academic year
 Instructors
 There are no professors associated with this course for the 20242025 academic year

MATH 329
Theory of Interest
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Simple and compound interest, annuities certain, amortization schedules, bonds, depreciation.
Offered by: Mathematics and Statistics
 Terms
 This course is not scheduled for the 20242025 academic year
 Instructors
 There are no professors associated with this course for the 20242025 academic year

MATH 335
Groups, Tilings and Algorithms
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Transformation groups of the plane. Inversions and Moebius transformations. The hyperbolic plane. Tilings in dimension 2 and 3. Group presentations and Cayley graphs. Free groups and Schreier's theorem. Coxeter groups. Dehn's Word and Conjugacy Problems. Undecidability of the Word Problem for semigroups. Regular
languages and automatic groups. Automaticity of Coxeter groups.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 235
 Note: This course is intended primarily for students in the Major Program in Mathematics and the Joint Major Program in Mathematics and Computer Science.
 Terms
 This course is not scheduled for the 20242025 academic year
 Instructors
 There are no professors associated with this course for the 20242025 academic year

MATH 338
History & Philosophy of Math
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Egyptian, Babylonian, Greek, Indian and Arab contributions to mathematics are studied together with some modern developments they give rise to, for example, the problem of trisecting the angle. European mathematics from the Renaissance to the 18th century is discussed, culminating in the discovery of the infinitesimal and integral calculus by Newton and Leibnitz. Demonstration of how mathematics was done in past centuries, and involves the practice of mathematics, including detailed calculations, arguments based on geometric reasoning, and proofs.
Offered by: Mathematics and Statistics
 Terms
 This course is not scheduled for the 20242025 academic year
 Instructors
 There are no professors associated with this course for the 20242025 academic year

MATH 340
Discrete Mathematics
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Discrete Mathematics and applications. Graph Theory: matchings, planarity, and colouring. Discrete probability. Combinatorics: enumeration, combinatorial techniques and proofs.
Offered by: Mathematics and Statistics
 Terms
 This course is not scheduled for the 20242025 academic year
 Instructors
 There are no professors associated with this course for the 20242025 academic year

MATH 346
Number Theory
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Divisibility. Congruences. Quadratic reciprocity. Diophantine equations. Arithmetical functions.
Offered by: Mathematics and Statistics
 Winter
 Prerequisite: MATH 235 or consent of instructor
 Restriction: Not open to students who have taken or are taking MATH 377.
 Terms
 This course is not scheduled for the 20242025 academic year
 Instructors
 There are no professors associated with this course for the 20242025 academic year

MATH 348
Euclidean Geometry
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Points and lines in a triangle. Quadrilaterals. Angles in a circle. Circumscribed and inscribed circles. Congruent and similar triangles. Area. Power of a point with respect to a circle. Ceva’s theorem. Isometries. Homothety. Inversion.
Offered by: Mathematics and Statistics
 Prerequisite: MATH 133 or equivalent or permission of instructor.
 Restriction: Not open to students who have taken MATH 398.
 Terms
 This course is not scheduled for the 20242025 academic year
 Instructors
 There are no professors associated with this course for the 20242025 academic year

MATH 352
Problem Seminar
1 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Seminar in Mathematical Problem Solving. The problems considered will be of the type that occur in the Putnam competition and in other similar mathematical competitions.
Offered by: Mathematics and Statistics
 Prerequisite: Enrolment in a math related program or permission of the instructor. Requires departmental approval.
 Prerequisite: Enrolment in a math related program or permission of the instructor.
 Terms
 This course is not scheduled for the 20242025 academic year
 Instructors
 There are no professors associated with this course for the 20242025 academic year

MATH 378
Nonlinear Optimization
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Optimization terminology. Convexity. First and secondorder optimality conditions for unconstrained problems. Numerical methods for unconstrained optimization:
Gradient methods, Newtontype methods, conjugate gradient methods, trustregion methods. Least squares problems (linear + nonlinear). Optimality conditions for smooth constrained optimization problems (KKT theory). Lagrangian duality. Augmented Lagrangian methods. Activeset method for quadratic programming. SQP methods.
Offered by: Mathematics and Statistics
 Terms
 This course is not scheduled for the 20242025 academic year
 Instructors
 There are no professors associated with this course for the 20242025 academic year

MATH 410
Majors Project
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): A supervised project.
Offered by: Mathematics and Statistics
 Prerequisite: Students must have 21 completed credits of the required mathematics courses in their program, including all required 200 level mathematics courses.
 Requires departmental approval.
 Terms
 This course is not scheduled for the 20242025 academic year
 Instructors
 There are no professors associated with this course for the 20242025 academic year

MATH 417
Linear Optimization
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): An introduction to linear optimization and its applications: Duality theory, fundamental theorem, sensitivity analysis, convexity, simplex algorithm, interiorpoint methods, quadratic optimization, applications in game theory.
Offered by: Mathematics and Statistics
 Terms
 This course is not scheduled for the 20242025 academic year
 Instructors
 There are no professors associated with this course for the 20242025 academic year

MATH 423
Applied Regression
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Multiple regression estimators and their properties. Hypothesis tests and confidence
intervals. Analysis of variance. Prediction and prediction intervals. Model diagnostics. Model selection. Introduction to weighted least squares. Basic contingency table analysis. Introduction to logistic and Poisson regression. Applications to experimental and observational data.
Offered by: Mathematics and Statistics
 Terms
 This course is not scheduled for the 20242025 academic year
 Instructors
 There are no professors associated with this course for the 20242025 academic year

MATH 430
Mathematical Finance
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Introduction to concepts of price and hedge derivative securities. The following concepts will be studied in both concrete and continuous time: filtrations, martingales, the change of measure technique, hedging, pricing, absence of arbitrage opportunities and the Fundamental Theorem of Asset Pricing.
Offered by: Mathematics and Statistics
 Terms
 This course is not scheduled for the 20242025 academic year
 Instructors
 There are no professors associated with this course for the 20242025 academic year

MATH 447
Intro. to Stochastic Processes
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Conditional probability and conditional expectation, generating functions. Branching processes and random walk. Markov chains, transition matrices, classification of states, ergodic theorem, examples. Birth and death processes, queueing theory.
Offered by: Mathematics and Statistics
 Winter
 Prerequisite: MATH 323
 Restriction: Not open to students who have taken or are taking MATH 547.
 Terms
 This course is not scheduled for the 20242025 academic year
 Instructors
 There are no professors associated with this course for the 20242025 academic year

MATH 463
Convex Optimization
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Introduction to convex analysis and convex optimization: Convex sets and functions, subdifferential calculus, conjugate functions, Fenchel duality, proximal calculus.
Subgradient methods, proximalbased methods. Conditional gradient method, ADMM. Applications including data classification, networkflow problems, image processing, convex feasibility problems, DC optimization, sparse optimization, and compressed
sensing.
Offered by: Mathematics and Statistics
 Terms
 This course is not scheduled for the 20242025 academic year
 Instructors
 There are no professors associated with this course for the 20242025 academic year

MATH 523
Generalized Linear Models
4 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Exponential families, link functions. Inference and parameter estimation for generalized linear models; model selection using analysis of deviance. Residuals. Contingency table analysis, logistic regression, multinomial regression, Poisson regression, loglinear models. Multinomial models. Overdispersion and Quasilikelihood.
Applications to experimental and observational data.
Offered by: Mathematics and Statistics
 Terms
 This course is not scheduled for the 20242025 academic year
 Instructors
 There are no professors associated with this course for the 20242025 academic year

MATH 524
Nonparametric Statistics
4 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Distribution free procedures for 2sample problem: Wilcoxon rank sum, SiegelTukey, Smirnov tests. Shift model: power and estimation. Single sample procedures: Sign, Wilcoxon signed rank tests. Nonparametric ANOVA: KruskalWallis, Friedman tests. Association: Spearman's rank correlation, Kendall's tau. Goodness of fit: Pearson's chisquare, likelihood ratio, KolmogorovSmirnov tests. Statistical software packages used.
Offered by: Mathematics and Statistics
 Fall
 Prerequisite: MATH 324 or equivalent
 Restriction: Not open to students who have taken MATH 424
 Terms
 This course is not scheduled for the 20242025 academic year
 Instructors
 There are no professors associated with this course for the 20242025 academic year

MATH 525
Sampling Theory & Applications
4 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Simple random sampling, domains, ratio and regression estimators, superpopulation models, stratified sampling, optimal stratification, cluster sampling, sampling with unequal probabilities, multistage sampling, complex surveys, nonresponse.
Offered by: Mathematics and Statistics
 Prerequisite: MATH 324 or equivalent
 Restriction: Not open to students who have taken MATH 425
 Terms
 This course is not scheduled for the 20242025 academic year
 Instructors
 There are no professors associated with this course for the 20242025 academic year