Â鶹AV

Program Requirements

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)

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

• MATH 315 Ordinary Differential Equations (3 credits) *

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions.

  Terms: Fall 2022, Winter 2023, Summer 2023

  Instructors: Berk, Aaron (Fall) Bélanger-Rioux, Rosalie (Winter) Roth, Charles (Summer)

  • Prerequisite: MATH 222.

  • Corequisite: MATH 133.

  • Restriction: Not open to students who have taken or are taking MATH 325.

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 3-credit complementary course must be taken.

• MATH 249 Honours Complex Variables (3 credits) *

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : 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.

  Terms: Winter 2023

  Instructors: Guan, Pengfei (Winter)

  • 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

• MATH 316 Complex Variables (3 credits) *

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Algebra of complex numbers, Cauchy-Riemann equations, complex integral, Cauchy's theorems. Taylor and Laurent series, residue theory and applications.

  Terms: Fall 2022

  Instructors: Pym, Brent (Fall)

  • Fall

  • Prerequisites: MATH 314 or equivalent and MATH 243.

  • Restriction: Not open to students who have taken or are taking MATH 249, MATH 366, MATH 381 or MATH 466.

12 credits from:

• MATH 204 Principles of Statistics 2 (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  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.

  Terms: Winter 2023

  Instructors: Correa, Jose Andres (Winter)

  • 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.

• MATH 308 Fundamentals of Statistical Learning (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  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.

  Terms: Winter 2023

  Instructors: Alam, Shomoita (Winter)

  • Prerequisite(s): MATH 208, one of MATH 223, MATH 236, MATH 247, MATH 251; MATH 323 or MATH 356.

• MATH 317 Numerical Analysis (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations.

  Terms: Fall 2022

  Instructors: Lessard, Jean-Philippe (Fall)

  • Fall

  • Prerequisites: MATH 315 or MATH 325 or MATH 263, and COMP 202 or permission of instructor.

  • Restrictions: Not open to students who have taken COMP 350

• MATH 318 Mathematical Logic (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : 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.

  Terms: Fall 2022

  Instructors: Sabok, Marcin (Fall)

  • Fall

  • Prerequisite(s): MATH 235 or MATH 240 or MATH 242.

• MATH 319 Partial Differential Equations (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : First order equations, geometric theory; second order equations, classification; Laplace, wave and heat equations, Sturm-Liouville theory, Fourier series, boundary and initial value problems.

  Terms: Winter 2023

  Instructors: Bélanger-Rioux, Rosalie (Winter)

  • Winter

  • Prerequisites: MATH 223 or MATH 236, MATH 314 or equivalent, MATH 315

  • Not open to students who have taken or are taking MATH 475.

• MATH 324 Statistics (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference.

  Terms: Fall 2022, Winter 2023

  Instructors: Nadarajah, Tharshanna (Fall) Nadarajah, Tharshanna (Winter)

  • 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.

• MATH 326 Nonlinear Dynamics and Chaos (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  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, Poincare-Bendixson theorem, bifurcations, Hopf bifurcation, the Lorenz equations and chaos.

  Terms: Fall 2022

  Instructors: Nave, Jean-Christophe (Fall)

  • Fall

  • Prerequisites: MATH 222, MATH 223

  • Restriction: Not open to students who have taken or are taking MATH 376

• MATH 327 Matrix Numerical Analysis (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  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.

  Terms: Winter 2023

  Instructors: Panayotov, Ivo (Winter)

  • Winter

  • Prerequisites: MATH 223 or MATH 236 or MATH 247 or MATH 251, COMP 202 or consent of instructor.

• MATH 329 Theory of Interest (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Simple and compound interest, annuities certain, amortization schedules, bonds, depreciation.

  Terms: Winter 2023

  Instructors: Kelome, Djivede (Winter)

  • Winter

  • Prerequisite: MATH 141

• MATH 335 Computational Algebra (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Computational aspects of modern algebra. Computing in groups: algorithms, algorithmic problems in groups, finitely generated abelian groups, free groups and automata, finitely presented groups. Computing in rings: elementary notions of ring theory, ideals of polynomial rings in several variables, Groebner bases, elements of field theory.

  Terms: This course is not scheduled for the 2022-2023 academic year.

  Instructors: There are no professors associated with this course for the 2022-2023 academic year.

  • Prerequisites: MATH 235 and MATH 236.

  • Note: This course is intended primarily for students in the Major Program in Mathematics and the Joint Major Program in Mathematics and Computer Science.

• MATH 338 History and Philosophy of Mathematics (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  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.

  Terms: Fall 2022

  Instructors: Fortier, Jérôme (Fall)

  • Fall

  • Prerequisites: MATH 133, MATH 141.

• MATH 340 Discrete Mathematics (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Discrete Mathematics and applications. Graph Theory: matchings, planarity, and colouring. Discrete probability. Combinatorics: enumeration, combinatorial techniques and proofs.

  Terms: Winter 2023

  Instructors: Norin, Sergey (Winter)

  • Winter

  • Prerequisites: MATH 235 or MATH 240 or MATH 242.

  • Corequisites: MATH 223 or MATH 236.

  • Restriction: Restriction: Not open to students who have taken or are taking MATH 350.

• MATH 346 Number Theory (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Divisibility. Congruences. Quadratic reciprocity. Diophantine equations. Arithmetical functions.

  Terms: Winter 2023

  Instructors: Love, Jonathan (Winter)

  • Winter

  • Prerequisite: MATH 235 or consent of instructor

  • Restriction: Not open to students who have taken or are taking MATH 377.

• MATH 348 Euclidean Geometry (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  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.

  Terms: Fall 2022

  Instructors: Przytycki, Piotr (Fall)

  • Prerequisite: MATH 133 or equivalent or permission of instructor.

  • Restriction: Not open to students who have taken MATH 398.

• MATH 352 Problem Seminar (1 credit)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  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.

  Terms: Fall 2022

  Instructors: Norin, Sergey (Fall)

  • 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.

• MATH 378 Nonlinear Optimization (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : 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.

  Terms: This course is not scheduled for the 2022-2023 academic year.

  Instructors: There are no professors associated with this course for the 2022-2023 academic year.

  • Prerequisites: MATH 223 or MATH 247 or MATH 236 or MATH 251. MATH 248 or MATH 314 or MATH 358. MATH 243 or MATH 255.

  • Not open to students who have taken MATH 560.

• MATH 410 Majors Project (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : A supervised project.

  Terms: Fall 2022, Winter 2023, Summer 2023

  Instructors: Kelome, Djivede; Khadra, Anmar; Stephens, David; Nave, Jean-Christophe; Tan, Hongping; Yang, Archer Yi; Kolaczyk, Eric; Steele, Russell; Asgharian, Masoud; Ding, Yichuan Daniel (Fall) Kelome, Djivede; Steele, Russell; Yang, Archer Yi; Neslehova, Johanna; Macdonald, Jeremy; Sabok, Marcin; Tan, Hongping; Kolaczyk, Eric (Winter) Yang, Archer Yi; Kelome, Djivede; Nadarajah, Tharshanna; Sajjad, Alia; Khadra, Anmar; Jakobson, Dmitry (Summer)

  • 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.

• MATH 417 Linear Optimization (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : 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.

  Terms: Fall 2022

  Instructors: Paquette, Courtney (Fall)

  • Prerequisites: COMP 202, and MATH 223 or MATH 236, and MATH 314 or equivalent

  • Restriction: Not open to students who have taken or are taking MATH 487 or MATH 517.

• MATH 423 Applied Regression (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  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.

  Terms: Fall 2022

  Instructors: Nadarajah, Tharshanna (Fall)

  • Fall

  • Prerequisites: MATH 324, and MATH 223 or MATH 236

• MATH 430 Mathematical Finance (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  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.

  Terms: This course is not scheduled for the 2022-2023 academic year.

  Instructors: There are no professors associated with this course for the 2022-2023 academic year.

  • Prerequisite(s): MATH 243 or MATH 255, and MATH 323 or MATH 356, and MATH 133 or equivalent.

• MATH 447 Introduction to Stochastic Processes (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  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.

  Terms: Winter 2023

  Instructors: Addario-Berry, Louigi Dana (Winter)

  • Winter

  • Prerequisite: MATH 323

  • Restriction: Not open to students who have taken or are taking MATH 547.

• MATH 463 Convex Optimization (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : 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.

  Terms: Winter 2023

  Instructors: Paquette, Courtney (Winter)

  • Prerequisites: MATH 223 or MATH 247 or MATH 236 or MATH 251. MATH 248 or MATH 314 or MATH 358. MATH 243 or MATH 255. COMP 202 or COMP 204 or COMP 208 or equivalent.

  • Restriction: Not open to students who have taken or are taking MATH 563.

• MATH 523 Generalized Linear Models (4 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

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

  Terms: Winter 2023

  Instructors: Chatelain, Simon (Winter)

  • Winter

  • Prerequisite: MATH 423 or MATH 533 or EPIB 697.

• MATH 524 Nonparametric Statistics (4 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : 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.

  Terms: Fall 2022

  Instructors: Neslehova, Johanna (Fall)

  • Fall

  • Prerequisite: MATH 324 or equivalent

  • Restriction: Not open to students who have taken MATH 424

• MATH 525 Sampling Theory and Applications (4 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  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.

  Terms: Winter 2023

  Instructors: Yang, Archer Yi (Winter)

  • Prerequisite: MATH 324 or equivalent

  • Restriction: Not open to students who have taken MATH 425