Program Requirement:
The B.A.; Major Concentration in Mathematics aims to provide an overview of the foundations of mathematics.
Guidelines for Course Selection
Students who received advanced standing or the CEGEP equivalent of the 100-level Math courses listed below are no longer required to take them. Whenever an exemption without credits is granted for a 200-level and above required Math course, the latter must be replaced with a complementary course chosen in consultation with a program advisor.
Where appropriate, Honours-level courses may be substituted for their Majors-level counterparts. Students planning to undertake graduate studies in mathematics are urged to make such substitutions. If there is no major counterpart available for a course, please see a departmental advisor to discuss its inclusion into your program as a complementary course in the lower section.
Students interested in computer science should consider the courses MATH 317, MATH 318, MATH 327, MATH 340, MATH 417, and take the Minor Concentration Computer Science.
Students interested in probability and statistics should consider either taking the Minor Concentration Statistics under option C or taking the major concentration in statistics.
Students interested in applied mathematics should consider the courses MATH 317, MATH 319, MATH 324, MATH 326, MATH 327, and MATH 417.
Students interested in careers in business, industry or government should consider the courses MATH 317, MATH 319, MATH 327, MATH 417, MATH 423, and MATH 447.
Students who have done well in MATH 242 and MATH 235 at the end of their first term should consider, in consultation with their adviser and the instructors of the courses involved, the possibility of entering an Honours program in Mathematics, in Applied Mathematics, in Probability and Statistics, or a Joint Honours program in Mathematics and another discipline.
Required Courses (28 credits)
-
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(s): 1) Not open to students who have taken CEGEP objective 00UQ or equivalent. 2) Not open to students who have taken or are taking MATH 123, except by permission of the Department of Mathematics and Statistics.
- Terms
- Instructors
- Jeremy D Macdonald, Antoine Giard, Miguel Ayala, Romain Branchereau
-
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(s): 1) Not open to students who have taken MATH139 or MATH 150 or CEGEP objective 00UN or equivalent. 2) 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, Marcin Sabok, Artem Kalmykov
-
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(s): Not open to students who have taken CEGEP objective 00UP or equivalent.
- Restriction(s): 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
- Andrei Zlotchevski, Sidney Trudeau, Hazem A Hassan
- Sidney Trudeau
-
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
- Brent Pym, Damien Tageddine
-
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; homomorphisms and quotient groups.
Offered by: Mathematics and Statistics
- Fall
- 3 hours lecture; 1 hour tutorial
- Prerequisite: MATH 133 or equivalent
- Restrictions: Not open to students who have taken or are taking MATH 245.
-
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. Cayley-Hamilton 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 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
- Alia Sajjad
- Tharshanna Nadarajah
Complementary Courses (18 credits)
9-18 credits from:
* Note: Either MATH 249 or MATH 316 may be taken but not both.
-
MATH 249
Honours Complex Variables
3 Credits*
Offered in the:
- Fall
- Winter
- Summer
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.
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
-
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
- Niky Kamran
-
MATH 316
Complex Variables
3 Credits*
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Algebra of complex numbers, Cauchy-Riemann equations, complex integral, Cauchy's theorems. Taylor and Laurent series, residue theory and applications.
Offered by: Mathematics and Statistics
-
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 318
Mathematical Logic
3 Credits
Offered in the:
- Fall
- Winter
- Summer
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.
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.
- Terms
- Instructors
- Tharshanna Nadarajah
- Masoud Asgharian
-
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
-
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
- Instructors
- There are no professors associated with this course for the 2024-2025 academic year
-
MATH 378
Nonlinear Optimization
3 Credits
Offered in the:
- Fall
- Winter
- Summer
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.
Offered by: Mathematics and Statistics
- Terms
- This course is not scheduled for the 2024-2025 academic year
- Instructors
- There are no professors associated with this course for the 2024-2025 academic year
-
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, interior-point methods, quadratic optimization, applications in game theory.
Offered by: Mathematics and Statistics
-
MATH 451
Intro. to General Topology
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): This course is an introduction to point set topology. Topics include basic set theory and logic, topological spaces, separation axioms, continuity, connectedness,
compactness, Tychonoff Theorem, metric spaces, and Baire spaces.
Offered by: Mathematics and Statistics
- Terms
- This course is not scheduled for the 2024-2025 academic year
- Instructors
- There are no professors associated with this course for the 2024-2025 academic year
0-3 credits from:
-
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
- Terms
- This course is not scheduled for the 2024-2025 academic year
- Instructors
- There are no professors associated with this course for the 2024-2025 academic year
-
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, 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.
Offered by: Mathematics and Statistics
0-9 credits from:
-
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 statistics. 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
-
MATH 319
Partial Differential Equations
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, Sturm-Liouville 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, Poincare-Bendixson 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 2024-2025 academic year
- Instructors
- There are no professors associated with this course for the 2024-2025 academic year
-
MATH 335
Groups, Tilings and Algorithms
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): 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.
Offered by: Mathematics and Statistics
- Prerequisites: MATH 235
- 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 2024-2025 academic year
- Instructors
- There are no professors associated with this course for the 2024-2025 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.
- Terms
- This course is not scheduled for the 2024-2025 academic year
- Instructors
- There are no professors associated with this course for the 2024-2025 academic year
-
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 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
- Jose Andres Correa, Dmitry Jakobson, Tony Humphries, Abbas Khalili Mahmoudabadi, Anmar Khadra, Marcin Sabok, Alia Sajjad, Courtney Paquette, Tharshanna Nadarajah
- Djivede A Kelome
-
MATH 420
Independent Study
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Reading projects permitting independent study under the guidance of a staff member specializing in a subject where no appropriate course is available. Arrangements must be made with an instructor and the Chair before registration.
Offered by: Mathematics and Statistics
- Fall and Winter and Summer
- Requires approval by the chair before registration
- Please see regulations concerning Project Courses under Faculty Degree Requirements
- Terms
- Instructors
- Djivede A Kelome
- Djivede A Kelome
-
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 2024-2025 academic year
- Instructors
- There are no professors associated with this course for the 2024-2025 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
-
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 463
Convex Optimization
3 Credits
Offered in the:
- Fall
- Winter
- Summer
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.
Offered by: Mathematics and Statistics
-
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, Navier-Stokes equations
Offered by: Mathematics and Statistics