麻豆AV

Program Requirements

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 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, Summer 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 140 Calculus 1 (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Review of functions and graphs. Limits, continuity, derivative. Differentiation of elementary functions. Antidifferentiation. Applications.

  Terms: Fall 2024, Winter 2025, Summer 2025

  Instructors: Sabok, Marcin; Trudeau, Sidney; Kalmykov, Artem (Fall) Huang, Peiyuan; Trudeau, Sidney (Winter)

  • 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

• MATH 141 Calculus 2 (4 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : The definite integral. Techniques of integration. Applications. Introduction to sequences and series.

  Terms: Fall 2024, Winter 2025, Summer 2025

  Instructors: Hassan, Hazem; Trudeau, Sidney; Zlotchevski, Andrei (Fall) Trudeau, Sidney; Poulin, Antoine; Syroka, Bartosz (Winter)

  • 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

• 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, Summer 2025

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

  • Prerequisite: MATH 141. Familiarity with vector geometry or Corequisite: MATH 133

  • Restriction: Not open to students who have taken or are taking MATH 150, MATH 151, MATH206, or MATH 262.

• 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 236 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 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.

  Terms: Winter 2025

  Instructors: Macdonald, Jeremy (Winter)

  • Winter

  • Prerequisite: MATH 235

• 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 243 Analysis 2 (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Definition and properties of Riemann integral, Fundamental Theorem of Calculus, Taylor's theorem. Infinite series: alternating, telescoping series, rearrangements, conditional and absolute convergence, convergence tests. Power series and Taylor series. Elementary functions. Introduction to metric spaces.

  Terms: Winter 2025

  Instructors: Hundemer, Axel (Winter)

  • Winter

  • Prerequisite: MATH 242 or MATH 254.

• MATH 323 Probability (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Sample space, events, conditional probability, independence of events, Bayes' Theorem. Basic combinatorial probability, random variables, discrete and continuous univariate and multivariate distributions. Independence of random variables. Inequalities, weak law of large numbers, central limit theorem.

  Terms: Fall 2024, Winter 2025, Summer 2025

  Instructors: Sajjad, Alia (Fall) Nadarajah, Tharshanna (Winter)

  • 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

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 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 314 Advanced Calculus (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Derivative as a matrix. Chain rule. Implicit functions. Constrained maxima and minima. Jacobians. Multiple integration. Line and surface integrals. Theorems of Green, Stokes and Gauss. Fourier series with applications.

  Terms: Fall 2024, Winter 2025

  Instructors: Martine, Gabriel (Fall) Borthwick, Jack Anthony (Winter)

  • Prerequisites: MATH 133, MATH 222

  • Restriction: Not open to students who have taken or are taking MATH 248 or MATH 358.

• MATH 315 Ordinary Differential Equations (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions.

  Terms: Fall 2024, Winter 2025

  Instructors: Paquette, Courtney (Fall) Kamran, Niky (Winter)

  • Prerequisite: MATH 222.

  • Corequisite: MATH 133.

  • Restriction: Not open to students who have taken or are taking MATH 325.

• MATH 316 Complex Variables (3 credits) *

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Algebra of complex numbers, Cauchy-Riemann equations, complex integral, Cauchy's theorems. Taylor and Laurent series, residue theory and applications.

  Terms: Fall 2024

  Instructors: Kamran, Niky (Fall)

  • Fall

  • Prerequisites: MATH 314 or equivalent and MATH 243.

  • Restriction: Not open to students who have taken or are taking MATH 249, MATH 366, MATH 381 or MATH 466.

• MATH 317 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: Fall 2024

  Instructors: Duchesne, Gabriel William (Fall)

  • Fall

  • Prerequisites: MATH 315 or MATH 325 or MATH 263, and COMP 202 or permission of instructor.

  • Restrictions: Not open to students who have taken COMP 350

• MATH 318 Mathematical Logic (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Propositional logic: truth-tables, formal proof systems, completeness and compactness theorems, Boolean algebras; first-order logic: formal proofs, G枚del's completeness theorem; axiomatic theories; set theory; Cantor's theorem, axiom of choice and Zorn's lemma, Peano arithmetic; G枚del's incompleteness theorem.

  Terms: Fall 2024

  Instructors: Fortier, J茅r么me (Fall)

  • Fall

  • Prerequisite(s): MATH 235 or MATH 240 or MATH 242.

• MATH 324 Statistics (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference.

  Terms: Fall 2024, Winter 2025

  Instructors: Nadarajah, Tharshanna (Fall) Asgharian, Masoud (Winter)

  • Fall and Winter

  • Prerequisite: MATH 323 or equivalent

  • Restriction: Not open to students who have taken or are taking MATH 357

  • You may not be able to receive credit for this course and other statistic courses. Be sure to check the Course Overlap section under Faculty Degree Requirements in the Arts or Science section of the Calendar.

• MATH 340 Discrete Mathematics (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Discrete Mathematics and applications. Graph Theory: matchings, planarity, and colouring. Discrete probability. Combinatorics: enumeration, combinatorial techniques and proofs.

  Terms: Winter 2025

  Instructors: Norin, Sergey (Winter)

  • Winter

  • Prerequisites: MATH 235 or MATH 240 or MATH 242.

  • Corequisites: MATH 223 or MATH 236.

  • Restriction: Restriction: Not open to students who have taken or are taking MATH 350.

• MATH 346 Number Theory (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Divisibility. Congruences. Quadratic reciprocity. Diophantine equations. Arithmetical functions.

  Terms: Winter 2025

  Instructors: Branchereau, Romain (Winter)

  • Winter

  • Prerequisite: MATH 235 or consent of instructor

  • Restriction: Not open to students who have taken or are taking MATH 377.

• MATH 378 Nonlinear Optimization (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  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: 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.

  • Prerequisites: MATH 223 or MATH 247 or MATH 236 or MATH 251. MATH 248 or MATH 314 or MATH 358. MATH 243 or MATH 255.

  • Not open to students who have taken MATH 560.

• MATH 417 Linear Optimization (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  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.

  Terms: Fall 2024

  Instructors: Hoheisel, Tim (Fall)

  • Prerequisites: COMP 202, and MATH 223 or MATH 236, and MATH 314 or equivalent

  • Restriction: Not open to students who have taken or are taking MATH 487 or MATH 517.

• 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.

  • Prerequisites: MATH 242 or MATH 254

0-3 credits from:

• 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.

  • Winter

  • Prerequisite: MATH 141

• 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)

  • Fall

  • Prerequisites: MATH 133, MATH 141.

0-9 credits from:

• 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)

  • Prerequisite(s): MATH 133

• 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)

  • Prerequisite(s): MATH 208, one of MATH 223, MATH 236, MATH 247, MATH 251; MATH 323 or MATH 356.

• MATH 319 Partial Differential Equations (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  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.

  Terms: Winter 2025

  Instructors: Lin, Jessica (Winter)

  • Winter

  • Prerequisites: MATH 223 or MATH 236, MATH 314 or equivalent, MATH 315

  • Not open to students who have taken or are taking MATH 475.

• MATH 326 Nonlinear Dynamics and Chaos (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Linear systems of differential equations, linear stability theory. Nonlinear systems: existence and uniqueness, numerical methods, one and two dimensional flows, phase space, limit cycles, Poincare-Bendixson theorem, bifurcations, Hopf bifurcation, the Lorenz equations and chaos.

  Terms: Fall 2024

  Instructors: Humphries, Tony (Fall)

  • Fall

  • Prerequisites: MATH 222, MATH 223

  • Restriction: Not open to students who have taken or are taking MATH 376

• MATH 327 Matrix Numerical Analysis (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : An overview of numerical methods for linear algebra applications and their analysis. Problem classes include linear systems, least squares problems and eigenvalue problems.

  Terms: 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.

  • Winter

  • Prerequisites: MATH 223 or MATH 236 or MATH 247 or MATH 251, COMP 202 or consent of instructor.

• MATH 335 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.

  • Prerequisites: MATH 235

  • Restriction(s): Not open to students who have taken or are taking MATH 365.

  • Note: This course is intended primarily for students in the Major Program in Mathematics and the Joint Major Program in Mathematics and Computer Science.

• MATH 348 Euclidean Geometry (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Points and lines in a triangle. Quadrilaterals. Angles in a circle. Circumscribed and inscribed circles. Congruent and similar triangles. Area. Power of a point with respect to a circle. Ceva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.

  • Restriction: Not open to students who have taken MATH 398.

• 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 410 Majors Project (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : A supervised project.

  Terms: Fall 2024, Winter 2025

  Instructors: Khadra, Anmar; Nadarajah, Tharshanna; Correa, Jose Andres; Jakobson, Dmitry; Humphries, Tony; Paquette, Courtney; Sabok, Marcin; Sajjad, Alia; Khalili, Abbas (Fall) Kelome, Djivede (Winter)

  • Prerequisite: Students must have 21 completed credits of the required mathematics courses in their program, including all required 200 level mathematics courses.

  • Requires departmental approval.

• MATH 420 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: Kelome, Djivede (Fall) Choksi, Rustum (Winter)

  • Fall and Winter and Summer

  • Requires approval by the chair before registration

  • Please see regulations concerning Project Courses under Faculty Degree Requirements

• MATH 423 Applied Regression (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  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.

  Terms: Fall 2024

  Instructors: Steele, Russell (Fall)

  • Fall

  • Prerequisites: MATH 324, and MATH 223 or MATH 236

• MATH 427 Statistical Quality Control (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Introduction to quality management; variability and productivity. Quality measurement: capability analysis, gauge capability studies. Process control: control charts for variables and attributes. Process improvement: factorial designs, fractional replications, response surface methodology, Taguchi methods. Acceptance sampling: operating characteristic curves; single, multiple and sequential acceptance sampling plans for variables and attributes.

  Terms: This course is not scheduled for the 2024-2025 academic year.

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

  • Prerequisites: MATH 203 or equivalent, and MATH 204 or MATH 324.

• 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)

  • Prerequisite(s): MATH 243 or MATH 255, and MATH 323 or MATH 356, and MATH 133 or equivalent.

• MATH 447 Introduction to Stochastic Processes (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Conditional probability and conditional expectation, generating functions. Branching processes and random walk. Markov chains, transition matrices, classification of states, ergodic theorem, examples. Birth and death processes, queueing theory.

  Terms: Winter 2025

  Instructors: Paquette, Elliot (Winter)

  • Winter

  • Prerequisite: MATH 323

  • Restriction: Not open to students who have taken or are taking MATH 547.

• MATH 463 Convex Optimization (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  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 2025

  Instructors: Paquette, Courtney (Winter)

  • Prerequisites: MATH 223 or MATH 247 or MATH 236 or MATH 251. MATH 248 or MATH 314 or MATH 358. MATH 243 or MATH 255. COMP 202 or COMP 204 or COMP 208 or equivalent.

  • Restriction: Not open to students who have taken or are taking MATH 563.

• 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)

  • Prerequisites: MATH 315 or MATH 325 or MATH 263; MATH 317 or MATH 387 or COMP 350 or MECH 309; or permission of the instructor

  • This course will be taught in the winter semester.