![important](/study/2022-2023/files/study.2022-2023/exclamation-point-small.png)
Note: This is the 2023–2024 eCalendar. Update the year in your browser's URL bar for the most recent version of this page, or .
Note: This is the 2023–2024 eCalendar. Update the year in your browser's URL bar for the most recent version of this page, or .
Students may complete this program with a minimum of 60 credits or a maximum of 63 credits depending if they are exempt from MATH 222.
The minimum requirement for entry into the Honours program is that the student has completed with high standing the following courses below or their equivalents.
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.
Terms: Fall 2023, Winter 2024, Summer 2024
Instructors: Trudeau, Sidney; Collins-Woodfin, Elizabeth; Branchereau, Romain (Fall) Gerbelli-Gauthier, Mathilde (Winter) Bellemare, Hugues (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, except by permission of the Department of Mathematics and Statistics.
Restriction C: Not open to students who are taking or have taken MATH 134.
Mathematics & Statistics (Sci) : Functions, limits and continuity, differentiation, L'Hospital's rule, applications, Taylor polynomials, parametric curves, functions of several variables.
Terms: Fall 2023
Instructors: Roth, Charles (Fall)
Fall
3 hours lecture, 2 hours tutorial
Students with no prior exposure to vector geometry are advised to take MATH 133 concurrently. Intended for students with high school calculus who have not received six advanced placement credits
Restriction: Not open to students who have taken CEGEP objective 00UN 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
MATH 150 and MATH 151 cover the material of MATH 139, MATH 140, MATH 141, MATH 222
Mathematics & Statistics (Sci) : Integration, methods and applications, infinite sequences and series, power series, arc length and curvature, multiple integration.
Terms: Winter 2024
Instructors: Roth, Charles (Winter)
Winter
3 hours lecture; 2 hours tutorial
Each Tutorial section is enrolment limited
Prerequisite: MATH 150
Restriction: Not open to students who have taken CEGEP objective 00UP 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
Restriction: Not open to students who have taken MATH 152
In particular, MATH 150/151 and MATH 140/141/222 are considered equivalent.
Students who have not completed an equivalent of MATH 222 on entering the program must consult an academic adviser and take MATH 222 as a required course in the first semester, increasing the total number of program credits from 60 to 63. Students who have successfully completed MATH 150/151 are not required to take MATH 222.
Students who transfer to Honours in Mathematics from other programs will have credits for previous courses assigned, as appropriate, by the Department.
To be awarded the Honours degree, the student must have, at time of graduation, a CGPA of at least 3.00 in the required and complementary Mathematics courses of the program, as well as an overall CGPA of at least 3.00.
45-48 credits
+ Students who have successfully completed MATH 150/151 or an equivalent of MATH 222 on entering the program are not required to take MATH 222.
* Not open to students who have taken MATH 354.
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 2023, Winter 2024, Summer 2024
Instructors: Sabok, Marcin; Allen, Patrick (Fall) Trudeau, Sidney (Winter) Bibby, Sean (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.
Terms: Fall 2023
Instructors: Macdonald, Jeremy; Goren, Eyal Z (Fall)
Fall
3 hours lecture; 1 hour tutorial
Prerequisite: MATH 133 or equivalent
Mathematics & Statistics (Sci) : Linear equations over a field. Introduction to vector spaces. Linear maps and their matrix representation. Determinants. Canonical forms. Duality. Bilinear and quadratic forms. Real and complex inner product spaces. Diagonalization of self-adjoint operators.
Terms: Winter 2024
Instructors: Tserunyan, Anush (Winter)
Mathematics & Statistics (Sci) : Basic point-set topology, metric spaces: open and closed sets, normed and Banach spaces, Hölder and Minkowski inequalities, sequential compactness, Heine-Borel, Banach Fixed Point theorem. Riemann-(Stieltjes) integral, Fundamental Theorem of Calculus, Taylor's theorem. Uniform convergence. Infinite series, convergence tests, power series. Elementary functions.
Terms: Winter 2024
Instructors: Jakobson, Dmitry (Winter)
Mathematics & Statistics (Sci) : First and second order equations, linear equations, series solutions, Frobenius method, introduction to numerical methods and to linear systems, Laplace transforms, applications.
Terms: Winter 2024
Instructors: Humphries, Tony (Winter)
Mathematics & Statistics (Sci) : Sample space, probability axioms, combinatorial probability. Conditional probability, Bayes' Theorem. Distribution theory with special reference to the Binomial, Poisson, and Normal distributions. Expectations, moments, moment generating functions, uni-variate transformations. Random vectors, independence, correlation, multivariate transformations. Conditional distributions, conditional expectation.Modes of stochastic convergence, laws of large numbers, Central Limit Theorem.
Terms: Fall 2023
Instructors: Addario-Berry, Louigi Dana (Fall)
Mathematics & Statistics (Sci) : Data analysis. Estimation and hypothesis testing. Power of tests. Likelihood ratio criterion. The chi-squared goodness of fit test. Introduction to regression analysis and analysis of variance.
Terms: Winter 2024
Instructors: Asgharian, Masoud (Winter)
Mathematics & Statistics (Sci) : Point-set topology in Euclidean space; continuity and differentiability of functions in several variables. Implicit and inverse function theorems. Vector fields, divergent and curl operations. Rigorous treatment of multiple integrals: volume and surface area; and Fubini’s theorem. Line and surface integrals, conservative vector fields. Green's theorem, Stokes’ theorem and the divergence theorem.
Terms: Winter 2024
Instructors: Toth, John A (Winter)
Mathematics & Statistics (Sci) : Review of point-set topology: topological space, dense sets, completeness, compactness, connectedness and path-connectedness, separability. Arzela-Ascoli, Stone-Weierstrass, Baire category theorems. Measure theory: sigma algebras, Lebesgue measure and integration, L^1 functions. Fatou's lemma, monotone and dominated convergence theorem. Egorov, Lusin's theorems. Fubini-Tonelli theorem.
Terms: Fall 2023
Instructors: Vetois, Jerome (Fall)
Mathematics & Statistics (Sci) : Continuation of measure theory. Functional analysis: L^p spaces, linear functionals and dual spaces, Hahn-Banach theorem, Riesz representation theorem. Hilbert spaces, weak convergence. Spectral theory of compact operator. Introduction to Fourier analysis, Fourier transforms.
Terms: Winter 2024
Instructors: Jakobson, Dmitry (Winter)
Mathematics & Statistics (Sci) : Introduction to monoids, groups, permutation groups; the isomorphism theorems for groups; the theorems of Cayley, Lagrange and Sylow; structure of groups of low order. Introduction to ring theory; integral domains, fields, quotient field of an integral domain; polynomial rings; unique factorization domains.
Terms: Fall 2023
Instructors: Darmon, Henri (Fall)
Mathematics & Statistics (Sci) : Introduction to modules and algebras; finitely generated modules over a principal ideal domain. Field extensions; finite fields; Galois groups; the fundamental theorem of Galois theory; application to the classical problem of solvability by radicals.
Terms: Winter 2024
Instructors: Darmon, Henri (Winter)
Mathematics & Statistics (Sci) : In addition to the topics of MATH 320, topics in the global theory of plane and space curves, and in the global theory of surfaces are presented. These include: total curvature and the Fary-Milnor theorem on knotted curves, abstract surfaces as 2-d manifolds, the Euler characteristic, the Gauss-Bonnet theorem for surfaces.
Terms: Winter 2024
Instructors: Kamran, Niky (Winter)
Mathematics & Statistics (Sci) : Functions of a complex variable, Cauchy-Riemann equations, Cauchy's theorem and its consequences. Uniform convergence on compacta. Taylor and Laurent series, open mapping theorem, Rouché's theorem and the argument principle. Calculus of residues. Fractional linear transformations and conformal mappings.
Terms: Fall 2023
Instructors: Hurtubise, Jacques Claude (Fall)
Mathematics & Statistics (Sci) : The project will contain a significant research component that requires substantial independent work consisting of a written report and oral examination or presentation.
Terms: Fall 2023, Winter 2024, Summer 2024
Instructors: Hoheisel, Tim; Pym, Brent; Kamnitzer, Joel; Hurtubise, Jacques Claude; Choksi, Rustum; Allen, Patrick; Darmon, Henri; Goren, Eyal Z; Love, Jonathan; Przytycki, Piotr; Nave, Jean-Christophe; Dagdoug, Mohamed Mehdi; Steele, Russell (Fall) Sabok, Marcin; Goren, Eyal Z; Love, Jonathan; Allen, Patrick (Winter) Dagdoug, Mohamed Mehdi; Hoheisel, Tim; Asgharian, Masoud; Paquette, Courtney; Tserunyan, Anush; Sabok, Marcin; Jakobson, Dmitry; Toth, John A (Summer)
Fall and Winter and Summer
Requires Departmental Approval
Students are advised to start contacting potential project supervisors early during their U2 year.
Prerequisite: appropriate honours courses with approval of the project supervisor
Mathematics & Statistics (Sci) : First order partial differential equations, geometric theory, classification of second order linear equations, Sturm-Liouville problems, orthogonal functions and Fourier series, eigenfunction expansions, separation of variables for heat, wave and Laplace equations, Green's function methods, uniqueness theorems.
Terms: Fall 2023
Instructors: Martine, Gabriel (Fall)
3 credits selected from:
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 2023
Instructors: Hundemer, Axel W (Fall)
Mathematics & Statistics (Sci) : Properties of R. Cauchy and monotone sequences, Bolzano- Weierstrass theorem. Limits, limsup, liminf of functions. Pointwise, uniform continuity: Intermediate Value theorem. Inverse and monotone functions. Differentiation: Mean Value theorem, L'Hospital's rule, Taylor's Theorem.
Terms: Fall 2023
Instructors: Jaksic, Vojkan (Fall)
** It is strongly recommended that students take MATH 254.
0-6 credits from the following courses for which no Honours equivalent exists:
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 2024
Instructors: Nadarajah, Tharshanna (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.
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.
Terms: Fall 2023
Instructors: Lee, Kiwon (Fall)
Prerequisite(s): MATH 133
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 2024
Instructors: Yang, Archer Yi (Winter)
Mathematics & Statistics (Sci) : Simple and compound interest, annuities certain, amortization schedules, bonds, depreciation.
Terms: Winter 2024
Instructors: Kelome, Djivede (Winter)
Winter
Prerequisite: MATH 141
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 2023
Instructors: Fortier, Jérôme (Fall)
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: Fall 2023
Instructors: Hoheisel, Tim (Fall)
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 2023-2024 academic year.
Instructors: There are no professors associated with this course for the 2023-2024 academic year.
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.
Terms: This course is not scheduled for the 2023-2024 academic year.
Instructors: There are no professors associated with this course for the 2023-2024 academic year.
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 2024
Instructors: Paquette, Courtney (Winter)
6-12 credits selected from:
Computer Science (Sci) : Mathematical tools (binary numbers, induction, recurrence relations, asymptotic complexity, establishing correctness of programs), Data structures (arrays, stacks, queues, linked lists, trees, binary trees, binary search trees, heaps, hash tables), Recursive and non-recursive algorithms (searching and sorting, tree and graph traversal). Abstract data types, inheritance. Selected topics.
Terms: Fall 2023, Winter 2024
Instructors: Alberini, Giulia (Fall) Alberini, Giulia (Winter)
Computer Science (Sci) : The design and analysis of data structures and algorithms. The description of various computational problems and the algorithms that can be used to solve them, along with their associated data structures. Proving the correctness of algorithms and determining their computational complexity.
Terms: Winter 2024
Instructors: Devroye, Luc P (Winter)
3 hours
Restrictions: (1) Open only to students in Honours programs. (2) Students cannot receive credit for both COMP 251 and COMP 252.
COMP 252 uses basic combinatorial counting methods that are covered in MATH 240 but not in MATH 235. Students who are unfamiliar with these methods should speak with the instructor for guidance.
Mathematics & Statistics (Sci) : Discrete mathematics. Graph Theory: matching theory, connectivity, planarity, and colouring; graph minors and extremal graph theory. Combinatorics: combinatorial methods, enumerative and algebraic combinatorics, discrete probability.
Terms: Fall 2023
Instructors: Norin, Sergey (Fall)
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: This course is not scheduled for the 2023-2024 academic year.
Instructors: There are no professors associated with this course for the 2023-2024 academic year.
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.
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.
Terms: Winter 2024
Instructors: Przytycki, Piotr (Winter)
Mathematics & Statistics (Sci) : This course consists of the lectures of MATH 326, but will be assessed at the honours level.
Terms: Fall 2023
Instructors: Humphries, Tony (Fall)
Mathematics & Statistics (Sci) : This course consists of the lectures of MATH 346, but will be assessed at the honours level.
Terms: This course is not scheduled for the 2023-2024 academic year.
Instructors: There are no professors associated with this course for the 2023-2024 academic year.
Winter
Prerequisite: Enrolment in Mathematics Honours program or consent of instructor
Restriction: Not open to students who have taken or are taking MATH 346.
Note: Additionally, a special project or projects may be assigned.
Mathematics & Statistics (Sci) : Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations.
Terms: Winter 2024
Instructors: Gantumur, Tsog (Winter)
Mathematics & Statistics (Sci) : The course consists of the lectures of MATH 327 plus additional work involving theoretical assignments and/or a project. The final examination for this course may be different from that of MATH 327.
Terms: This course is not scheduled for the 2023-2024 academic year.
Instructors: There are no professors associated with this course for the 2023-2024 academic year.
Mathematics & Statistics (Sci) : Honours level: 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 2023
Instructors: Przytycki, Piotr (Fall)
Mathematics & Statistics (Sci) : Foundations of optimization and convex analysis, stochastic gradient descent. Divergences, loss functions, empirical loss minimization and parameter estimation. Reproducing kernel Hilbert spaces. Multiple linear regression in the context of machine learning. Classification with support vector machines. Dimensionality reduction, Johnson-Lindenstrauss Lemma. Concentration of measure and learning bounds.
Terms: Fall 2023
Instructors: Oberman, Adam (Fall)
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.
Terms: Fall 2023, Winter 2024, Summer 2024
Instructors: Przytycki, Piotr; Allen, Patrick (Fall) Paquette, Elliot; Devroye, Luc P; Allen, Patrick (Winter) Steele, Russell; Jakobson, Dmitry (Summer)
Fall and Winter and Summer
Please see regulations concerning Project Courses under Faculty Degree Requirements
Requires approval by the chair before registration
Mathematics & Statistics (Sci) : Axioms of set theory, ordinal and cardinal arithmetic, consequences of the axiom of choice, models of set theory, constructible sets and the continuum hypothesis, introduction to independence proofs.
Terms: This course is not scheduled for the 2023-2024 academic year.
Instructors: There are no professors associated with this course for the 2023-2024 academic year.
all MATH 500-level courses.
++ Students with limited programming experience should take COMP 202 or COMP 204 or COMP 208 or equivalent before COMP 250.
Students may select other courses with the permission of the Department.