Program Requirements
The B.Sc.; Major in Mathematics provides a general overview of Mathematics including a rigorous foundation and the exploration of the different branches of Mathematics.
Program Prerequisites
Students entering the Major program are normally expected to have completed the courses below or their equivalents. Otherwise, they will be required to make up any deficiencies in these courses over and above the 54 credits of required courses.
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MATH 133 Linear Algebra and Geometry (3 credits)
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.
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MATH 140 Calculus 1 (3 credits)
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
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MATH 141 Calculus 2 (4 credits)
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)
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
Guidelines for Selection of Courses in the Major Program
The following informal guidelines should be discussed with the student's adviser. Where appropriate, Honours courses may be substituted for equivalent Major courses. Students planning to pursue graduate studies are encouraged to make such substitutions.
Students interested in computer science are advised to choose courses from the following: MATH 317, MATH 318, MATH 327, MATH 335, MATH 340, MATH 417 and to complete the Computer Science Minor.
Students interested in probability and statistics are advised to take MATH 204, MATH 324, MATH 423, MATH 447, MATH 523, MATH 525.
Students interested in applied mathematics should take MATH 317, MATH 319, MATH 324, MATH 326, MATH 327, MATH 417.
Students considering a career in secondary school teaching are advised to take MATH 318, MATH 338, MATH 346, MATH 348.
Students interested in careers in business, industry or government are advised to select courses from the following list:
MATH 317, MATH 319, MATH 327, MATH 329, MATH 417, MATH 423, MATH 430, MATH 447, MATH 523, MATH 525.
Required Courses (27 credits)
Note: Students who have done well in MATH 235 and MATH 242 should consider entering the Honours stream by registering in MATH 251 and MATH 255 instead of MATH 236 and MATH 243.
* Students may select either MATH 249 or MATH 316 but not both.
** Students who have successfully completed a course equivalent to MATH 222 with a grade of C or better may omit MATH 222, but must replace it with 3 credits of complementary courses.
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MATH 222 Calculus 3 (3 credits) **
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)
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MATH 235 Algebra 1 (3 credits)
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)
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MATH 236 Algebra 2 (3 credits)
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
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MATH 242 Analysis 1 (3 credits)
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)
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MATH 243 Analysis 2 (3 credits)
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 W (Winter)
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MATH 249 Honours Complex Variables (3 credits) *
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)
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MATH 314 Advanced Calculus (3 credits)
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)
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MATH 315 Ordinary Differential Equations (3 credits)
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)
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MATH 316 Complex Variables (3 credits) *
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)
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MATH 323 Probability (3 credits)
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)
Complementary Courses (27 credits)
6-12 credits selected from the following:
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MATH 317 Numerical Analysis (3 credits)
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)
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MATH 324 Statistics (3 credits)
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.
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MATH 335 Groups, Tilings and Algorithms (3 credits)
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.
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MATH 340 Discrete
Mathematics (3 credits)
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)
15-21 credits selected from the following: at least 6 credits must be at the 400 or 500 level.
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MATH 204 Principles of Statistics 2 (3 credits)
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.
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MATH 208 Introduction to Statistical Computing (3 credits)
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
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MATH 308 Fundamentals of Statistical Learning (3 credits)
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)
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MATH 318 Mathematical Logic (3 credits)
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)
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MATH 319 Partial Differential
Equations
(3 credits)
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)
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MATH 326 Nonlinear Dynamics and Chaos (3 credits)
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)
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MATH 327 Matrix Numerical Analysis (3 credits)
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.
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MATH 329 Theory of Interest (3 credits)
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
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MATH 338 History and Philosophy of Mathematics (3 credits)
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)
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MATH 346 Number Theory (3 credits)
Overview
Mathematics & Statistics (Sci) : Divisibility. Congruences. Quadratic reciprocity. Diophantine equations. Arithmetical functions.
Terms: Winter 2025
Instructors: Branchereau, Romain (Winter)
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MATH 348 Euclidean Geometry (3 credits)
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.
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MATH 352 Problem Seminar (1 credit)
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.
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MATH 378 Nonlinear Optimization
(3 credits)
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.
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MATH 410 Majors Project (3 credits)
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.
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MATH 417 Linear Optimization (3 credits)
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)
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MATH 423 Applied Regression (3 credits)
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)
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MATH 427 Statistical Quality Control (3 credits)
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.
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MATH 430 Mathematical Finance (3 credits)
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)
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MATH 447 Introduction to Stochastic Processes (3 credits)
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)
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MATH 451 Introduction to General
Topology (3 credits)
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.
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MATH 462 Machine Learning
(3 credits)
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.
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MATH 463 Convex Optimization (3 credits)
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)
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MATH 478 Computational Methods in Applied Mathematics
(3 credits)
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)
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MATH 510 Quantitative Risk Management (4 credits)
Overview
Mathematics & Statistics (Sci) : Basics concepts in quantitative risk management: types of financial risk, loss distribution, risk measures, regulatory framework. Empirical properties of financial data, models for stochastic volatility. Extreme-value theory models for maxima and threshold exceedances. Multivariate models, copulas, and dependence measures. Risk aggregation.
Terms: Winter 2025
Instructors: Neslehova, Johanna (Winter)
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MATH 523 Generalized Linear Models (4 credits)
Overview
Mathematics & Statistics (Sci) : Exponential families, link functions. Inference and parameter estimation for generalized linear models; model selection using analysis of deviance. Residuals. Contingency table analysis, logistic regression, multinomial regression, Poisson regression, log-linear models. Multinomial models. Overdispersion and Quasilikelihood. Applications to experimental and observational data.
Terms: Winter 2025
Instructors: Steele, Russell (Winter)
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MATH 525 Sampling Theory and Applications (4 credits)
Overview
Mathematics & Statistics (Sci) : Simple random sampling, domains, ratio and regression estimators, superpopulation models, stratified sampling, optimal stratification, cluster sampling, sampling with unequal probabilities, multistage sampling, complex surveys, nonresponse.
Terms: Winter 2025
Instructors: Dagdoug, Mohamed Mehdi (Winter)
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MATH 545 Introduction to Time Series Analysis (4 credits)
Overview
Mathematics & Statistics (Sci) : Stationary processes; estimation and forecasting of ARMA models; non-stationary and seasonal models; state-space models; financial time series models; multivariate time series models; introduction to spectral analysis; long memory models.
Terms: Winter 2025
Instructors: Stephens, David (Winter)
If necessary, 6 additional credits in Mathematics or related disciplines selected in consultation with the Adviser.
