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 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 Equations (3 credits) *
Overview
Mathematics & Statistics (Sci) : First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions.
Terms: Fall 2020, Winter 2021
Instructors: Paquette, Courtney (Fall)
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) *
Overview
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.
Terms: Winter 2021
Instructors: Harrison, Sarah (Winter)

MATH 316 Complex Variables (3 credits) *
Overview
Mathematics & Statistics (Sci) : Algebra of complex numbers, CauchyRiemann equations, complex integral, Cauchy's theorems. Taylor and Laurent series, residue theory and applications.
Terms: Fall 2020
Instructors: Pym, Brent (Fall)
12 credits from:

MATH 204 Principles of Statistics 2 (3 credits)
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 2021
Instructors: Genest, Christian (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)
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 2021
Instructors: Genest, Christian (Winter)

MATH 317 Numerical Analysis (3 credits)
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 2020
Instructors: Bartello, Peter (Fall)

MATH 318 Mathematical Logic (3 credits)
Overview
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.
Terms: Fall 2020
Instructors: Tserunyan, Anush (Fall)

MATH 319 Introduction to Partial Differential Equations (3 credits)
Overview
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.
Terms: Winter 2021
Instructors: Bartello, Peter (Winter)

MATH 320 Differential Geometry (3 credits)
Overview
Mathematics & Statistics (Sci) : Review of Euclidean geometry. Local theory of plane and space curves: the Frenet formulas. Local theory of surfaces: the first and second fundamental forms, the shape operator, the mean and Gaussian curvatures, surfaces of revolution with prescribed curvature, ruled and developable surfaces. Geodesic curves on surfaces of revolution. The GaussCodazzi equations, rigidity.
Terms: This course is not scheduled for the 20202021 academic year.
Instructors: There are no professors associated with this course for the 20202021 academic year.

MATH 324 Statistics (3 credits)
Overview
Mathematics & Statistics (Sci) : Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference.
Terms: Fall 2020, Winter 2021
Instructors: AsgharianDastenaei, Masoud (Fall) Yang, Yi (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)
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, PoincareBendixson theorem, bifurcations, Hopf bifurcation, the Lorenz equations and chaos.
Terms: Fall 2020
Instructors: Nave, JeanChristophe (Fall)

MATH 327 Matrix Numerical Analysis (3 credits)
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 2021
Instructors: Oberman, Adam (Winter)

MATH 329 Theory of Interest (3 credits)
Overview
Mathematics & Statistics (Sci) : Simple and compound interest, annuities certain, amortization schedules, bonds, depreciation.
Terms: Winter 2021
Instructors: Kelome, Djivede (Winter)
Winter
Prerequisite: MATH 141

MATH 335 Computational Algebra (3 credits)
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 20202021 academic year.
Instructors: There are no professors associated with this course for the 20202021 academic year.

MATH 338 History and Philosophy of Mathematics (3 credits)
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 in some detail.
Terms: Fall 2020
Instructors: Fox, Thomas F (Fall)
Fall

MATH 340 Discrete
Mathematics (3 credits)
Overview
Mathematics & Statistics (Sci) : Discrete Mathematics and applications. Graph Theory: matchings, planarity, and colouring. Discrete probability. Combinatorics: enumeration, combinatorial techniques and proofs.
Terms: Winter 2021
Instructors: Fortier, Jérôme (Winter)

MATH 346 Number Theory (3 credits)
Overview
Mathematics & Statistics (Sci) : Divisibility. Congruences. Quadratic reciprocity. Diophantine equations. Arithmetical functions.
Terms: Winter 2021
Instructors: Goren, Eyal Z (Winter)

MATH 348 Euclidean Geometry (3 credits)
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 2020
Instructors: Kamran, Niky (Fall)

MATH 352 Problem Seminar (1 credit)
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 2020
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 407 Dynamic Programming (3 credits)
Overview
Mathematics & Statistics (Sci) : Sequential decision problems, resource allocation, transportation problems, equipment replacement, integer programming, network analysis, inventory systems, project scheduling, queuing theory calculus of variations, markovian decision processes, stochastic path problems, reliability, discrete and continuous control processes.
Terms: This course is not scheduled for the 20202021 academic year.
Instructors: There are no professors associated with this course for the 20202021 academic year.

MATH 410 Majors Project (3 credits)
Overview
Mathematics & Statistics (Sci) : A supervised project.
Terms: Fall 2020
Instructors: Kelome, Djivede; Khadra, Anmar; Choksi, Rustum; Steele, Russell (Fall)
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)
Overview
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.
Terms: Fall 2020
Instructors: Hoheisel, Tim (Fall)

MATH 423 Applied Regression (3 credits)
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 2020
Instructors: Yang, Yi (Fall)

MATH 430 Mathematical Finance (3 credits)
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 20202021 academic year.
Instructors: There are no professors associated with this course for the 20202021 academic year.

MATH 447 Introduction to Stochastic Processes (3 credits)
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 2021
Instructors: Paquette, Elliot (Winter)

MATH 523 Generalized Linear Models (4 credits)
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, loglinear models. Multinomial models. Overdispersion and Quasilikelihood. Applications to experimental and observational data.
Terms: Winter 2021
Instructors: Neslehova, Johanna (Winter)

MATH 524 Nonparametric Statistics (4 credits)
Overview
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.
Terms: Fall 2020
Instructors: Wolfson, David B (Fall)

MATH 525 Sampling Theory and Applications (4 credits)
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 2021
Instructors: Steele, Russell (Winter)