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Honours Applied Mathematics (63 credits)

Offered by: Mathematics and Statistics     Degree: Bachelor of Arts

Program Requirements

The B.Sc.; Honours in Applied Mathematics provides an in-depth training, at the honours level, in 鈥渄iscrete鈥� or 鈥渃ontinuous鈥� applied mathematics. It gives the foundations and necessary tools to explore some areas such as numerical analysis, continuous and discrete optimization, graph theory, discrete probability. The program also provides the background required to pursue interdisciplinary research at the interface between mathematics and other fields such as biology, physiology, and the biomedical sciences. This program may be completed with a minimum of 60 credits or a maximum of 63 credits.

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.

Program Prerequisites

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:

  • MATH 133 Linear Algebra and Geometry (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    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. Linear transformations. Eigenvalues and diagonalization.

    Terms: Fall 2024, Winter 2025

    Instructors: Macdonald, Jeremy; Ayala, Miguel; Branchereau, Romain; Giard, Antoine (Fall) Pinet, Th茅o (Winter)

    • 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.

  • MATH 150 Calculus A (4 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : Functions, limits and continuity, differentiation, L'Hospital's rule, applications, Taylor polynomials, parametric curves, functions of several variables.

    Terms: Fall 2024

    Instructors: Kelome, Djivede (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(s): 1) Not open to students who have taken or are taking MATH 139 or MATH 140 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.

    • MATH 150 and MATH 151 cover the material of MATH 139, MATH 140, MATH 141, MATH 222

  • MATH 151 Calculus B (4 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : Integration, methods and applications, infinite sequences and series, power series, arc length and curvature, multiple integration.

    Terms: Winter 2025

    Instructors: Roth, Charles (Winter)

    • Winter

    • 3 hours lecture; 2 hours tutorial

    • Each Tutorial section is enrolment limited

    • Prerequisite: MATH 150

    • Restriction(s): 1) Not open to students who have taken or are taking MATH 141 or CEGEP objective 00UP or equivalent. 2) Not open to students who have taken or are taking MATH 122, except by permission of the Department of Mathematic sand Statistics.

In particular, MATH 150/MATH 151 and MATH 140/MATH 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/MATH 151 are not required to take MATH 222.

Note: COMP 202鈥攐r an equivalent introduction to computer programming course鈥攊s a program prerequisite. U0 students may take COMP 202 as a Freshman Science course; new U1 students should take it as an elective in their first semester.

Students who transfer to Honours in Applied 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.

Required Courses

(36-39 credits)

* Students with limited programming experience should take COMP 202 or COMP 204 or COMP 208 or equivalent before COMP 250.
** Students select either MATH 251 or MATH 247, but not both.
*** Students who have successfully completed MATH 150/MATH 151 or an equivalent of MATH 222 on entering the program are not required to take MATH 222.

  • COMP 250 Introduction to Computer Science (3 credits) *

    Offered by: Computer Science (Faculty of Science)

    Overview

    Computer Science (Sci) : Mathematical tools (binary numbers, induction,recurrence relations, asymptotic complexity,establishing correctness of programs). Datastructures (arrays, stacks, queues, linked lists,trees, binary trees, binary search trees, heaps,hash tables). Recursive and non-recursivealgorithms (searching and sorting, tree andgraph traversal). Abstract data types. Objectoriented programming in Java (classes andobjects, interfaces, inheritance). Selected topics.

    Terms: Fall 2024, Winter 2025

    Instructors: Alberini, Giulia (Fall) Alberini, Giulia (Winter)

  • COMP 252 Honours Algorithms and Data Structures (3 credits)

    Offered by: Computer Science (Faculty of Science)

    Overview

    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 2025

    Instructors: Devroye, Luc P (Winter)

    • 3 hours

    • Prerequisite: COMP 250 and either MATH 235 or MATH 240

    • 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.

  • MATH 222 Calculus 3 (3 credits) ***

    Offered by: Mathematics and Statistics (Faculty of Science)

    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 2024, Winter 2025

    Instructors: Pym, Brent; Tageddine, Damien (Fall) Mazakian, Hovsep (Winter)

  • MATH 247 Honours Applied Linear Algebra (3 credits) **

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : Matrix algebra, determinants, systems of linear equations. Abstract vector spaces, inner product spaces, Fourier series. Linear transformations and their matrix representations. Eigenvalues and eigenvectors, diagonalizable and defective matrices, positive definite and semidefinite matrices. Quadratic and Hermitian forms, generalized eigenvalue problems, simultaneous reduction of quadratic forms. Applications.

    Terms: Winter 2025

    Instructors: Hoheisel, Tim (Winter)

    • Winter

    • Prerequisite: MATH 133 or equivalent.

    • Restriction: Intended for Honours Physics and Engineering students

    • Restriction: Not open to students who have taken or are taking MATH 236, MATH 223 or MATH 251

  • MATH 251 Honours Algebra 2 (3 credits) **

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    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 2025

    Instructors: Przytycki, Piotr (Winter)

    • Winter

    • Prerequisites: MATH 235 or permission of the Department

    • Restriction: Not open to students who are taking or have taken MATH 247

  • MATH 255 Honours Analysis 2 (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : Basic point-set topology, metric spaces: open and closed sets, normed and Banach spaces, H脙露lder 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 2025

    Instructors: Vetois, Jerome (Winter)

  • MATH 325 Honours Ordinary Differential Equations (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    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 2025

    Instructors: Lessard, Jean-Philippe (Winter)

    • Fall and Winter

    • (3-0-6)

    • Prerequisite: MATH 222.

    • Restriction: Intended for Honours Mathematics, Physics and Engineering programs.

    • Restriction: Not open to students who have taken MATH 263 (formerly MATH 261), MATH 315

  • MATH 350 Honours Discrete Mathematics (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    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 2024

    Instructors: Norin, Sergey (Fall)

    • Prerequisites: MATH 235 or MATH 240 and MATH 251 or MATH 223.

    • Restrictions: Not open to students who have taken or are taking MATH 340. Intended for students in mathematics or computer science honours programs.

    • Intended for students in mathematics or computer science honours programs.

  • MATH 356 Honours Probability (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    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 2024

    Instructors: Asgharian, Masoud (Fall)

    • Fall

    • Prerequisite(s): MATH 243 or MATH 255, and MATH 222 or permission of the Department.

    • Restriction: Not open to students who have taken or are taking MATH 323

  • MATH 357 Honours Statistics (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : Sampling distributions. Point estimation. Minimum variance unbiased estimators, sufficiency, and completeness. Confidence intervals. Hypothesis tests, Neyman-Pearson Lemma, uniformly most powerful tests. Likelihood ratio tests for normal samples. Asymptotic sampling distributions and inference.

    Terms: Winter 2025

    Instructors: Khalili, Abbas (Winter)

    • Winter

    • Prerequisite: MATH 356 or equivalent

    • Restriction: Not open to students who have taken or are taking MATH 324

  • MATH 358 Honours Advanced Calculus (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    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鈥檚 theorem. Line and surface integrals, conservative vector fields. Green's theorem, Stokes鈥� theorem and the divergence theorem.

    Terms: Winter 2025

    Instructors: Toth, John A (Winter)

  • MATH 376 Honours Nonlinear Dynamics (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : This course consists of the lectures of MATH 326, but will be assessed at the honours level.

    Terms: Fall 2024

    Instructors: Humphries, Tony (Fall)

    • Fall

    • Prerequisites: MATH 222, MATH 223

    • Restrictions: Intended primarily for Honours students. Not open to students who have taken or are taking MATH 326.

    • Note: Additionally, a special project or projects may be assigned.

  • MATH 470 Honours Research Project (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    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 2024, Winter 2025

    Instructors: Lee, Kiwon; Lin, Jessica; Jakobson, Dmitry; Khadra, Anmar; Darmon, Henri; Nave, Jean-Christophe; Chen, Linan; Correa, Jose Andres; Addario-Berry, Louigi Dana; Norin, Sergey; Neslehova, Johanna (Fall) Kelome, Djivede (Winter)

    • 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

  • MATH 475 Honours Partial Differential Equations (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    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 2024

    Instructors: Choksi, Rustum (Fall)

Complementary Courses (24 credits)

3 credits selected from:

  • MATH 242 Analysis 1 (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    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 2024

    Instructors: Jakobson, Dmitry (Fall)

    • Fall

    • Prerequisite: MATH 141

    • Restriction(s): Not open to students who are taking or who have taken MATH 254.

  • MATH 254 Honours Analysis 1 (3 credits) +

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    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 2024

    Instructors: Hundemer, Axel W (Fall)

    • Prerequisite(s): MATH 141

    • Restriction(s): Not open to students who are taking or who have taken MATH 242.

3 credits from:

  • MATH 235 Algebra 1 (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    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; homomorphisms and quotient groups.

    Terms: Fall 2024

    Instructors: Sabbagh, Magid (Fall)

    • 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 245 Honours Algebra 1 (3 credits) +

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : Honours level: Sets, functions, and relations. Methods of proof. Complex numbers. Divisibility theory for integers and modular arithmetic. Divisibility theory for polynomials. In-depth study of rings, ideals, and quotient rings; fields and construction of fields from polynomial rings; groups, subgroups, and cosets, homomorphisms, and quotient groups.

    Terms: Fall 2024

    Instructors: Goren, Eyal Z (Fall)

    • Prerequisites: Prerequisites: MATH 133 or equivalent

    • Restrictions: Not open to students who have taken or are taking MATH 235.

+ It is strongly recommended that students take both MATH 245 and MATH 254.

Advising Notes:
Students interested in continuous applied mathematics are urged to choose these as part of their Complementary Courses: MATH 454, MATH 455 and MATH 478, and are advised to choose additional courses from MATH 387, MATH 397, MATH 555, MATH 574, MATH 578, MATH 579, MATH 580, MATH 581.

Students interested in discrete applied mathematics are advised to choose from these as part of their Complementary Courses: COMP 362, COMP 490, MATH 456, MATH 457, MATH 517, MATH 547, MATH 550, MATH 552.

3 credits selected from:

  • MATH 249 Honours Complex Variables (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    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.

    Terms: Winter 2025

    Instructors: Pym, Brent (Winter)

    • 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 466 Honours Complex Analysis (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    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, Rouch茅's theorem and the argument principle. Calculus of residues. Fractional linear transformations and conformal mappings.

    Terms: Fall 2024

    Instructors: Hurtubise, Jacques Claude (Fall)

3 credits selected from:

  • MATH 387 Honours Numerical Analysis (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    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: 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.

    • Taught in alternate years

    • Winter (even years)

    • Prerequisites: MATH 325 or MATH 315, COMP 202 or permission of instructor.

    • Corequisites: MATH 255 or MATH 243.

    • Restriction: Intended primarily for Honours students.

  • MATH 397 Honours Matrix Numerical Analysis (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    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 2024-2025 academic year.

    Instructors: There are no professors associated with this course for the 2024-2025 academic year.

0-6 credits from the following courses for which no Honours equivalent exists.

  • MATH 204 Principles of Statistics 2 (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    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 2025

    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.

  • MATH 208 Introduction to Statistical Computing (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    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 2024

    Instructors: Lee, Kiwon (Fall)

  • MATH 308 Fundamentals of Statistical Learning (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    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 2025

    Instructors: Yang, Archer Yi (Winter)

  • MATH 329 Theory of Interest (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : Simple and compound interest, annuities certain, amortization schedules, bonds, depreciation.

    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 and Philosophy of Mathematics (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    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, 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 2024

    Instructors: Fortier, J茅r么me (Fall)

  • MATH 430 Mathematical Finance (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    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 2025

    Instructors: Kelome, Djivede (Winter)

  • MATH 451 Introduction to General Topology (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    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 2024-2025 academic year.

    Instructors: There are no professors associated with this course for the 2024-2025 academic year.

  • MATH 462 Machine Learning (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : Introduction to supervised learning: decision trees, nearest neighbors, linear models, neural networks. Probabilistic learning: logistic regression, Bayesian methods, naive Bayes. Classification with linear models and convex losses. Unsupervised learning: PCA, k-means, encoders, and decoders. Statistical learning theory: PAC learning and VC dimension. Training models with gradient descent and stochastic gradient descent. Deep neural networks. Selected topics chosen from: generative models, feature representation learning, computer vision.

    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 478 Computational Methods in Applied Mathematics (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    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, Navier-Stokes equations

    Terms: Winter 2025

    Instructors: Nave, Jean-Christophe (Winter)

0-12 credits selected from:

  • COMP 362 Honours Algorithm Design (3 credits)

    Offered by: Computer Science (Faculty of Science)

    Overview

    Computer Science (Sci) : Basic algorithmic techniques, their applications and limitations. Problem complexity, how to deal with problems for which no efficient solutions are known.

    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.

    • 3 hours

    • Prerequisite: COMP 252

    • Restriction: Not open to students who have taken or are taking COMP 360.

    • Note: COMP 362 can be used instead of COMP 360 to satisfy prerequisites.

  • MATH 352 Problem Seminar (1 credit)

    Offered by: Mathematics and Statistics (Faculty of Science)

    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 2024

    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 365 Honours Groups, Tilings and Algorithms (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    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: 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.

    • Prerequisite: MATH 235

    • Restrictions: Not open to students who have taken or are taking MATH 335.

  • MATH 377 Honours Number Theory (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : This course consists of the lectures of MATH 346, but will be assessed at the honours level.

    Terms: Winter 2025

    Instructors: Branchereau, Romain (Winter)

    • 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.

  • MATH 398 Honours Euclidean Geometry (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    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鈥檚 theorem. Isometries. Homothety. Inversion.

    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.

    • Prerequisite: MATH 133 or equivalent or permission of instructor.

    • Restrictions: Not open to students taking or have take MATH 348.

  • MATH 454 Honours Analysis 3 (3 credits) ++

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : Measure theory: sigma-algebras, Lebesgue measure in R^n and integration, L^1 functions, Fatou's lemma, monotone and dominated convergence theorem, Egorov鈥檚 theorem, Lusin's theorem, Fubini-Tonelli theorem, differentiation of the integral, differentiability of functions of bounded variation, absolutely continuous functions, fundamental theorem of calculus.

    Terms: Fall 2024

    Instructors: Chen, Linan (Fall)

    • Prerequisite(s): MATH 255

    • Restriction: Not open to students who have taken MATH 354.

  • MATH 455 Honours Analysis 4 (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : Review of point-set topology: topological spaces, dense sets, completeness, compactness, connectedness and path-connectedness, separability, Baire category theorem, Arzela-Ascoli theorem, Stone-Weierstrass theorem..Functional analysis: L^p spaces, linear functionals and dual spaces, Hilbert spaces, Riesz representation theorems. Fourier series and transform, Riemann-Lebesgue Lemma,Fourier inversion formula, Plancherel theorem, Parseval鈥檚 identity, Poisson summation formula.

    Terms: Winter 2025

    Instructors: Lin, Jessica (Winter)

    • Prerequisite: MATH 454 or equivalent.

    • Restriction(s): Not open to students who have taken MATH 355.

  • MATH 456 Honours Algebra 3 (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    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 2024

    Instructors: Darmon, Henri (Fall)

  • MATH 457 Honours Algebra 4 (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    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 2025

    Instructors: Darmon, Henri (Winter)

    • Prerequisite: MATH 456 or equivalent

    • Restriction(s): Not open to students who have taken MATH 371.

  • MATH 458 Honours Differential Geometry (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    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 2025

    Instructors: Mutanguha, Jean Pierre (Winter)

  • MATH 462 Machine Learning (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : Introduction to supervised learning: decision trees, nearest neighbors, linear models, neural networks. Probabilistic learning: logistic regression, Bayesian methods, naive Bayes. Classification with linear models and convex losses. Unsupervised learning: PCA, k-means, encoders, and decoders. Statistical learning theory: PAC learning and VC dimension. Training models with gradient descent and stochastic gradient descent. Deep neural networks. Selected topics chosen from: generative models, feature representation learning, computer vision.

    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 480 Honours Independent Study (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    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 2024, Winter 2025

    Instructors: Addario-Berry, Louigi Dana (Fall) Kelome, Djivede (Winter)

    • Fall and Winter and Summer

    • Please see regulations concerning Project Courses under Faculty Degree Requirements

    • Requires approval by the chair before registration

  • MATH 488 Honours Set Theory (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    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: Winter 2025

    Instructors: Sabok, Marcin (Winter)

    • Fall

    • Prerequisites: MATH 251 or MATH 255 or permission of instructor

    • Restrictions :Not open to students who have taken or are taking MATH 590.

++ Not open to students who have taken MATH 354.

All MATH 500-level courses.

Other courses with the permission of the Department.

Faculty of Arts—2024-2025 (last updated Sep. 5, 2024) (disclaimer)
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