Program Requirements
Program Prerequisites
Students entering the Major program are normally expected to have completed the courses below or their equivalents. Otherwise, they will be required to make up any deficiencies in these courses over and above the 54 credits of required courses.

MATH 133 Linear Algebra and Geometry (3 credits)
Overview
Mathematics & Statistics (Sci) : Systems of linear equations, matrices, inverses, determinants; geometric vectors in three dimensions, dot product, cross product, lines and planes; introduction to vector spaces, linear dependence and independence, bases; quadratic loci in two and three dimensions.
Terms: Fall 2018, Winter 2019, Summer 2019
Instructors: Jerome Fortier, Liangming Shen, Yann Batiste Pequignot, Damian Osajda (Fall) Jerome Fortier (Winter) Rebecca Patrias (Summer)
3 hours lecture, 1 hour tutorial
Prerequisite: a course in functions
Restriction A: Not open to students who have taken MATH 221 or CEGEP objective 00UQ or equivalent.
Restriction B: Not open to students who have taken or are taking MATH 123, MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics.
Restriction C: Not open to students who are taking or have taken MATH 134.

MATH 140 Calculus 1 (3 credits)
Overview
Mathematics & Statistics (Sci) : Review of functions and graphs. Limits, continuity, derivative. Differentiation of elementary functions. Antidifferentiation. Applications.
Terms: Fall 2018, Winter 2019, Summer 2019
Instructors: Sidney Trudeau, Jerome Fortier, Rebecca Patrias (Fall) Alexander Garver (Winter) Peter Zenz (Summer)
3 hours lecture, 1 hour tutorial
Prerequisite: High School Calculus
Restriction: Not open to students who have taken MATH 120, MATH 139 or CEGEP objective 00UN or equivalent
Restriction: Not open to students who have taken or are taking MATH 122 or MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics
Each Tutorial section is enrolment limited

MATH 141 Calculus 2 (4 credits)
Overview
Mathematics & Statistics (Sci) : The definite integral. Techniques of integration. Applications. Introduction to sequences and series.
Terms: Fall 2018, Winter 2019, Summer 2019
Instructors: Corentin PerretGentilditMaillard, Jonah Gaster (Fall) Sidney Trudeau, Jerome Fortier, Thomas F Fox (Winter) Bogdan Nica (Summer)
Restriction: Not open to students who have taken MATH 121 or CEGEP objective 00UP or equivalent
Restriction Note B: Not open to students who have taken or are taking MATH 122 or MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics.
Each Tutorial section is enrolment limited
Guidelines for Selection of Courses in the Major Program
The following informal guidelines should be discussed with the student's adviser. Where appropriate, Honours courses may be substituted for equivalent Major courses. Students planning to pursue graduate studies are encouraged to make such substitutions.
Students interested in computer science are advised to choose courses from the following: MATH 317, MATH 318, MATH 327, MATH 335, MATH 340, MATH 407, MATH 417 and to complete the Computer Science Minor.
Students interested in probability and statistics are advised to take MATH 204, MATH 324, MATH 407, MATH 423, MATH 447, MATH 523, MATH 525.
Students interested in applied mathematics should take MATH 317, MATH 319, MATH 324, MATH 326, MATH 327, MATH 407, MATH 417.
Students considering a career in secondary school teaching are advised to take MATH 318, MATH 338, MATH 346, MATH 348.
Students interested in careers in business, industry or government are advised to select courses from the following list:
MATH 317, MATH 319, MATH 327, MATH 329, MATH 407, MATH 417, MATH 423, MATH 430, MATH 447, MATH 523, MATH 525.
Required Courses (27 credits)
Note: Students who have done well in MATH 235 and MATH 242 should consider entering the Honours stream by registering in MATH 251 and MATH 255 instead of MATH 236 and MATH 243.
* Students may select either MATH 249 or MATH 316 but not both.
** Students who have successfully completed a course equivalent to MATH 222 with a grade of C or better may omit MATH 222, but must replace it with 3 credits of elective courses.

MATH 222 Calculus 3 (3 credits) **
Overview
Mathematics & Statistics (Sci) : Taylor series, Taylor's theorem in one and several variables. Review of vector geometry. Partial differentiation, directional derivative. Extreme of functions of 2 or 3 variables. Parametric curves and arc length. Polar and spherical coordinates. Multiple integrals.
Terms: Fall 2018, Winter 2019, Summer 2019
Instructors: Jeremy Macdonald, Dmitry Faifman (Fall) Lars Sektnan (Winter) Yann Batiste Pequignot (Summer)

MATH 235 Algebra 1 (3 credits)
Overview
Mathematics & Statistics (Sci) : Sets, functions and relations. Methods of proof. Complex numbers. Divisibility theory for integers and modular arithmetic. Divisibility theory for polynomials. Rings, ideals and quotient rings. Fields and construction of fields from polynomial rings. Groups, subgroups and cosets; group actions on sets.
Terms: Fall 2018
Instructors: Daniel Wise (Fall)
Fall
3 hours lecture; 1 hour tutorial
Prerequisite: MATH 133 or equivalent

MATH 236 Algebra 2 (3 credits)
Overview
Mathematics & Statistics (Sci) : Linear equations over a field. Introduction to vector spaces. Linear mappings. Matrix representation of linear mappings. Determinants. Eigenvectors and eigenvalues. Diagonalizable operators. CayleyHamilton theorem. Bilinear and quadratic forms. Inner product spaces, orthogonal diagonalization of symmetric matrices. Canonical forms.
Terms: Winter 2019
Instructors: Bogdan Nica (Winter)
Winter
Prerequisite: MATH 235

MATH 242 Analysis 1 (3 credits)
Overview
Mathematics & Statistics (Sci) : A rigorous presentation of sequences and of real numbers and basic properties of continuous and differentiable functions on the real line.
Terms: Fall 2018
Instructors: Jerome Vetois (Fall)

MATH 243 Analysis 2 (3 credits)
Overview
Mathematics & Statistics (Sci) : Definition and properties of Riemann integral, Fundamental Theorem of Calculus, Taylor's theorem. Infinite series: alternating, telescoping series, rearrangements, conditional and absolute convergence, convergence tests. Power series and Taylor series. Elementary functions. Introduction to metric spaces.
Terms: Winter 2019
Instructors: Axel W Hundemer (Winter)

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 2019
Instructors: Charles Roth (Winter)

MATH 314 Advanced Calculus (3 credits)
Overview
Mathematics & Statistics (Sci) : Derivative as a matrix. Chain rule. Implicit functions. Constrained maxima and minima. Jacobians. Multiple integration. Line and surface integrals. Theorems of Green, Stokes and Gauss. Fourier series with applications.
Terms: Fall 2018, Winter 2019
Instructors: Charles Roth (Fall) Stephen W Drury (Winter)

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 2018, Winter 2019, Summer 2019
Instructors: JeanChristophe Nave (Fall) Antony Raymond Humphries (Winter) Charles Roth (Summer)

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 2018
Instructors: Bogdan Nica (Fall)

MATH 323 Probability (3 credits)
Overview
Mathematics & Statistics (Sci) : Sample space, events, conditional probability, independence of events, Bayes' Theorem. Basic combinatorial probability, random variables, discrete and continuous univariate and multivariate distributions. Independence of random variables. Inequalities, weak law of large numbers, central limit theorem.
Terms: Fall 2018, Winter 2019, Summer 2019
Instructors: David Stephens (Fall) David B Wolfson (Winter) Djivede Kelome (Summer)
Complementary Courses (27 credits)
27 credits selected as follows:
612 credits selected from the following:

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 2018
Instructors: Peter Bartello (Fall)

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 2018, Winter 2019
Instructors: Abbas Khalili Mahmoudabadi (Fall) Masoud AsgharianDastenaei (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 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 20182019 academic year.
Instructors: There are no professors associated with this course for the 20182019 academic year.

MATH 340 Discrete Structures 2 (3 credits)
Overview
Mathematics & Statistics (Sci) : Review of mathematical writing, proof techniques, graph theory and counting. Mathematical logic. Graph connectivity, planar graphs and colouring. Probability and graphs. Introductory group theory, isomorphisms and automorphisms of graphs. Enumeration and listing.
Terms: Winter 2019
Instructors: Jerome Fortier (Winter)
1521 credits selected from the following: at least 6 credits must be at the 400 or 500 level.

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 2019
Instructors: Christian Genest (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 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 2018
Instructors: Marcin Sabok (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 2019
Instructors: Jessica Lin (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 20182019 academic year.
Instructors: There are no professors associated with this course for the 20182019 academic year.

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 2018
Instructors: JeanPhilippe Lessard (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 2019
Instructors: Ivo Panayotov (Winter)

MATH 329 Theory of Interest (3 credits)
Overview
Mathematics & Statistics (Sci) : Simple and compound interest, annuities certain, amortization schedules, bonds, depreciation.
Terms: Winter 2019
Instructors: Djivede Kelome (Winter)
Winter
Prerequisite: MATH 141

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 2018
Instructors: Thomas F Fox (Fall)
Fall

MATH 346 Number Theory (3 credits)
Overview
Mathematics & Statistics (Sci) : Divisibility. Congruences. Quadratic reciprocity. Diophantine equations. Arithmetical functions.
Terms: Winter 2019
Instructors: Michael Lipnowski (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 2018
Instructors: Piotr Przytycki (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 2018
Instructors: Jacques Claude Hurtubise (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 20182019 academic year.
Instructors: There are no professors associated with this course for the 20182019 academic year.

MATH 410 Majors Project (3 credits)
Overview
Mathematics & Statistics (Sci) : A supervised project.
Terms: Fall 2018, Winter 2019, Summer 2019
Instructors: Djivede Kelome, Johanna Neslehova, JeanPhilippe Lessard, David Stephens, Russell Steele, Gantumur Tsogtgerel (Fall) Djivede Kelome, David Stephens, Dmitry Jakobson, Christian Genest, Russell Steele, Gantumur Tsogtgerel, Masoud AsgharianDastenaei, Niky Kamran (Winter) Djivede Kelome, Russell Steele (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)
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 2018
Instructors: Van Quang Nguyen (Fall)

MATH 423 Regression and Analysis of Variance (3 credits)
Overview
Mathematics & Statistics (Sci) : Leastsquares estimators and their properties. Analysis of variance. Linear models with general covariance. Multivariate normal and chisquared distributions; quadratic forms. General linear hypothesis: Ftest and ttest. Prediction and confidence intervals. Transformations and residual plot. Balanced designs.
Terms: Fall 2018
Instructors: Yi Yang (Fall)

MATH 427 Statistical Quality Control (3 credits)
Overview
Mathematics & Statistics (Sci) : Introduction to quality management; variability and productivity. Quality measurement: capability analysis, gauge capability studies. Process control: control charts for variables and attributes. Process improvement: factorial designs, fractional replications, response surface methodology, Taguchi methods. Acceptance sampling: operating characteristic curves; single, multiple and sequential acceptance sampling plans for variables and attributes.
Terms: This course is not scheduled for the 20182019 academic year.
Instructors: There are no professors associated with this course for the 20182019 academic year.

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: Winter 2019
Instructors: Djivede Kelome (Winter)

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 2019
Instructors: Russell Steele (Winter)

MATH 478 Computational Methods in Applied Mathematics
(3 credits)
Overview
Mathematics & Statistics (Sci) : Solution to initial value problems: Linear, Nonlinear Finite Difference Methods: accuracy and stability, Lax equivalence theorem, CFL and von Neumann conditions, Fourier analysis: diffusion, dissipation, dispersion, and spectral methods. Solution of large sparse linear systems: iterative methods, preconditioning, incomplete LU, multigrid, Krylov subspaces, conjugate gradient method. Applications to, e.g., weighted least squares, duality, constrained minimization, calculus of variation, inverse problems, regularization, level set methods, NavierStokes equations
Terms: Winter 2019
Instructors: JeanChristophe Nave (Winter)

MATH 523 Generalized Linear Models (4 credits)
Overview
Mathematics & Statistics (Sci) : Modern discrete data analysis. Exponential families, orthogonality, link functions. Inference and model selection using analysis of deviance. Shrinkage (Bayesian, frequentist viewpoints). Smoothing. Residuals. Quasilikelihood. Contingency tables: logistic regression, loglinear models. Censored data. Applications to current problems in medicine, biological and physical sciences. R software.
Terms: Winter 2019
Instructors: Johanna Neslehova (Winter)

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 2019
Instructors: Russell Steele (Winter)

MATH 545 Introduction to Time Series Analysis (4 credits)
Overview
Mathematics & Statistics (Sci) : Stationary processes; estimation and forecasting of ARMA models; nonstationary and seasonal models; statespace models; financial time series models; multivariate time series models; introduction to spectral analysis; long memory models.
Terms: Fall 2018
Instructors: Russell Steele (Fall)
If necessary, 6 additional credits in Mathematics or related disciplines selected in consultation with the Adviser.