Offered by:Mathematics and Statistics
Degree:Bachelor of Science
Program Requirement:
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
Offered in the:
 Fall
 Winter
 Summer
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. Linear transformations. Eigenvalues and diagonalization.
Offered by: Mathematics and Statistics
 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, except by permission of the Department of Mathematics and Statistics.
 Restriction C: Not open to students who are taking or have taken MATH 134.
 Terms
 Instructors
 Rosalie BélangerRioux, Jake Chinis, Sean Bibby, Wanlin Li, Antonio Alfieri
 Jérôme Fortier

MATH 140
Calculus 1
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Review of functions and graphs. Limits, continuity, derivative. Differentiation of elementary functions. Antidifferentiation. Applications.
Offered by: Mathematics and Statistics
 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, except by permission of the Department of Mathematics and Statistics
 Each Tutorial section is enrolment limited
 Terms
 Instructors
 Sidney Trudeau, Magid Sabbagh, Erfan Nazari Zahraei Motlagh
 Djivede A Kelome

MATH 141
Calculus 2
4 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): The definite integral. Techniques of integration. Applications. Introduction to sequences and series.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 139 or MATH 140 or MATH 150.
 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, except by permission of the Department of Mathematics and Statistics.
 Each Tutorial section is enrolment limited
 Terms
 Instructors
 Jeremy Macdonald, Michael Albanese
 Jérôme Fortier
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 complementary courses.

MATH 222
Calculus 3
3 Credits**
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 Terms
 Instructors
 Patrick Allen, Allysa Lumley
 Sidney Trudeau

MATH 235
Algebra 1
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 Fall
 3 hours lecture; 1 hour tutorial
 Prerequisite: MATH 133 or equivalent

MATH 236
Algebra 2
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics

MATH 242
Analysis 1
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): A rigorous presentation of sequences and of real numbers and basic properties of continuous and differentiable functions on the real line.
Offered by: Mathematics and Statistics
 Fall
 Prerequisite: MATH 141
 Restriction(s): Not open to students who are taking or who have taken MATH 254.

MATH 243
Analysis 2
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics

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

MATH 314
Advanced Calculus
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 Terms
 Instructors
 Charles Roth
 Jeremy Macdonald

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
 Instructors
 Courtney Paquette
 Rosalie BélangerRioux

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

MATH 323
Probability
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 141 or equivalent.
 Restriction: Intended for students in Science, Engineering and related disciplines, who have had differential and integral calculus
 Restriction: Not open to students who have taken or are taking MATH 356
 Terms
 Instructors
 David A Stephens, Alia Sajjad
 Alia Sajjad, Tharshanna Nadarajah
Complementary Courses (27 credits)
27 credits selected as follows:
612 credits selected from the following:

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

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.

MATH 335
Computational Algebra
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 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.
 Terms
 This course is not scheduled for the 20212022 academic year
 Instructors
 There are no professors associated with this course for the 20212022 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
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
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.

MATH 208
Intro to Statistical Computing
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Basic data management. Data visualization. Exploratory data analysis and descriptive statictics. Writing functions. Simulation and parallel computing. Communication data and documenting code for reproducible research.
Offered by: Mathematics and Statistics

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 20212022 academic year
 Instructors
 There are no professors associated with this course for the 20212022 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

MATH 319
Intro to Partial Diff Equas
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

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

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 20212022 academic year
 Instructors
 There are no professors associated with this course for the 20212022 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

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 in some detail.
Offered by: Mathematics and Statistics

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 20212022 academic year
 Instructors
 There are no professors associated with this course for the 20212022 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.

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.

MATH 407
Dynamic Programming
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 Terms
 This course is not scheduled for the 20212022 academic year
 Instructors
 There are no professors associated with this course for the 20212022 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
 Instructors
 Adrian Roshan Vetta, Djivede A Kelome, Sahir R Bhatnagar, Erica E Moodie, Christian Genest, Yi Yang, Anush Tserunyan
 Djivede A Kelome

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

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

MATH 427
Statistical Quality Control
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 Terms
 This course is not scheduled for the 20212022 academic year
 Instructors
 There are no professors associated with this course for the 20212022 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 20212022 academic year
 Instructors
 There are no professors associated with this course for the 20212022 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.

MATH 478
Comput. Meth. in Applied Math
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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
Offered by: Mathematics and Statistics

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

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 20212022 academic year
 Instructors
 There are no professors associated with this course for the 20212022 academic year

MATH 545
Intro to Time Series Analysis
4 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
If necessary, 6 additional credits in Mathematics or related disciplines selected in consultation with the Adviser.