Supplementary Minor Conc. Mathematics (B. A.)

Please note: Due to the ongoing transition to the new course catalogue, the program and course information displayed below may be temporarily unavailable or outdated. In particular, details about whether a course will be offered in an upcoming term may be inaccurate. Official course scheduling information for Fall 2025 will be available on Minerva during the first week of May. We appreciate your patience and understanding during this transition.


Mathematics Concentration (Supplementary Minor) (18 credits)

Offered by: Mathematics and Statistics (Faculty of Science)
Degree: Bachelor of Arts
Program credit weight: 18

Program Description

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 Multi-track 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 Multi-track System options please refer to the Faculty of Arts regulations under "Faculty Degree Requirements", "About Program Requirements", and "Departmental Programs".

Required Course (3 credits)

Course Title Credits
MATH 315Ordinary Differential Equations. 13

Ordinary Differential Equations.

Terms offered: Fall 2025, Winter 2026

First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions.

See course page for more information

1

Note: If MATH 315 Ordinary Differential Equations. has already been taken as part of the Major Concentration Mathematics, an additional 3-credit complementary course must be taken to replace it.

Complementary Courses (15 credits)

15 credits selected as follows:

3 credits from:

Course Title Credits
MATH 249Honours Complex Variables. 13

Honours Complex Variables.

Terms offered: Winter 2026

Functions of a complex variable; Cauchy-Riemann 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; Schwarz-Christoffel transformation; Poisson's integral formulas; applications. Additional topics if time permits: homotopy of paths and simple connectivity, Riemann sphere, rudiments of analytic continuation.

See course page for more information

MATH 316Complex Variables. 13

Complex Variables.

Terms offered: Fall 2025

Algebra of complex numbers, Cauchy-Riemann equations, complex integral, Cauchy's theorems. Taylor and Laurent series, residue theory and applications.

See course page for more information

1

Note: If either of MATH 249 Honours Complex Variables. or MATH 316 Complex Variables. has been taken as part of the Major Concentration Mathematics, another 3-credit complementary course must be taken.

12 credits from:

Course Title Credits
MATH 204Principles of Statistics 2.3

Principles of Statistics 2.

Terms offered: Winter 2026

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.

See course page for more information

MATH 308Fundamentals of Statistical Learning.3

Fundamentals of Statistical Learning.

Terms offered: Winter 2026

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.

See course page for more information

MATH 317Numerical Analysis.3

Numerical Analysis.

Terms offered: Fall 2025

Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations.

See course page for more information

MATH 318Mathematical Logic.3

Mathematical Logic.

Terms offered: Fall 2025

Propositional logic: truth-tables, formal proof systems, completeness and compactness theorems, Boolean algebras; first-order 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.

See course page for more information

MATH 319Partial Differential Equations .3

Partial Differential Equations .

Terms offered: Winter 2026

First order equations, geometric theory; second order equations, classification; Laplace, wave and heat equations, Sturm-Liouville theory, Fourier series, boundary and initial value problems.

See course page for more information

MATH 324Statistics.3

Statistics.

Terms offered: Fall 2025, Winter 2026

Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference.

See course page for more information

MATH 326Nonlinear Dynamics and Chaos.3

Nonlinear Dynamics and Chaos.

Terms offered: Fall 2025

Linear systems of differential equations, linear stability theory. Nonlinear systems: existence and uniqueness, numerical methods, one and two dimensional flows, phase space, limit cycles, Poincare-Bendixson theorem, bifurcations, Hopf bifurcation, the Lorenz equations and chaos.

See course page for more information

MATH 327Matrix Numerical Analysis.3

Matrix Numerical Analysis.

Terms offered: this course is not currently offered.

An overview of numerical methods for linear algebra applications and their analysis. Problem classes include linear systems, least squares problems and eigenvalue problems.

See course page for more information

MATH 329Theory of Interest.3

Theory of Interest.

Terms offered: Winter 2026

Simple and compound interest, annuities certain, amortization schedules, bonds, depreciation.

See course page for more information

MATH 335Groups, Tilings and Algorithms.3

Groups, Tilings and Algorithms.

Terms offered: Winter 2026

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.

See course page for more information

MATH 338History and Philosophy of Mathematics.3

History and Philosophy of Mathematics.

Terms offered: Fall 2025

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.

See course page for more information

MATH 340Discrete Mathematics.3

Discrete Mathematics.

Terms offered: Winter 2026

Discrete Mathematics and applications. Graph Theory: matchings, planarity, and colouring. Discrete probability. Combinatorics: enumeration, combinatorial techniques and proofs.

See course page for more information

MATH 346Number Theory.3

Number Theory.

Terms offered: this course is not currently offered.

Divisibility. Congruences. Quadratic reciprocity. Diophantine equations. Arithmetical functions.

See course page for more information

MATH 348Euclidean Geometry.3

Euclidean Geometry.

Terms offered: Fall 2025

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.

See course page for more information

MATH 352Problem Seminar.1

Problem Seminar.

Terms offered: this course is not currently offered.

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.

See course page for more information

MATH 378Nonlinear Optimization .3

Nonlinear Optimization .

Terms offered: Fall 2025

Optimization terminology. Convexity. First- and second-order optimality conditions for unconstrained problems. Numerical methods for unconstrained optimization: Gradient methods, Newton-type methods, conjugate gradient methods, trust-region methods. Least squares problems (linear + nonlinear). Optimality conditions for smooth constrained optimization problems (KKT theory). Lagrangian duality. Augmented Lagrangian methods. Active-set method for quadratic programming. SQP methods.

See course page for more information

MATH 410Majors Project.3

Majors Project.

Terms offered: Summer 2025, Fall 2025, Winter 2026

A supervised project.

See course page for more information

MATH 417Linear Optimization.3

Linear Optimization.

Terms offered: this course is not currently offered.

An introduction to linear optimization and its applications: Duality theory, fundamental theorem, sensitivity analysis, convexity, simplex algorithm, interior-point methods, quadratic optimization, applications in game theory.

See course page for more information

MATH 423Applied Regression.3

Applied Regression.

Terms offered: Fall 2025

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.

See course page for more information

MATH 430Mathematical Finance.3

Mathematical Finance.

Terms offered: this course is not currently offered.

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.

See course page for more information

MATH 447Introduction to Stochastic Processes.3

Introduction to Stochastic Processes.

Terms offered: Winter 2026

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.

See course page for more information

MATH 463Convex Optimization.3

Convex Optimization.

Terms offered: Winter 2026

Introduction to convex analysis and convex optimization: Convex sets and functions, subdifferential calculus, conjugate functions, Fenchel duality, proximal calculus. Subgradient methods, proximal-based methods. Conditional gradient method, ADMM. Applications including data classification, network-flow problems, image processing, convex feasibility problems, DC optimization, sparse optimization, and compressed sensing.

See course page for more information

MATH 523Generalized Linear Models.4

Generalized Linear Models.

Terms offered: Winter 2026

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, log-linear models. Multinomial models. Overdispersion and Quasilikelihood. Applications to experimental and observational data.

See course page for more information

MATH 524Nonparametric Statistics.4

Nonparametric Statistics.

Terms offered: Fall 2025

Distribution free procedures for 2-sample problem: Wilcoxon rank sum, Siegel-Tukey, Smirnov tests. Shift model: power and estimation. Single sample procedures: Sign, Wilcoxon signed rank tests. Nonparametric ANOVA: Kruskal-Wallis, Friedman tests. Association: Spearman's rank correlation, Kendall's tau. Goodness of fit: Pearson's chi-square, likelihood ratio, Kolmogorov-Smirnov tests. Statistical software packages used.

See course page for more information

MATH 525Sampling Theory and Applications.4

Sampling Theory and Applications.

Terms offered: Winter 2026

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.

See course page for more information

Follow us on

Back to top