Program Requirements
The B.Sc.; Honours in Probability and Statistics provides training, at the honours level, in probability and statistics, with a solid mathematical core, and basic training in computing. With a suitable selection of complementary courses, the program can focus on probability, mathematical statistics, applied statistics, actuarial science and finance, or data science. With satisfactory performance in an appropriate selection of courses, this program can lead to the professional accreditation A.Stat from the Statistical Society of Canada, which is regarded as the entry level requirement for a Statistician practicing in Canada.
Program Requirements (63 credits)
Students may complete this program with a minimum of 60 credits or a maximum of 63 credits depending on whether or not they are required to take 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 or their equivalents:

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 2023, Winter 2024, Summer 2024
Instructors: Trudeau, Sidney; CollinsWoodfin, Elizabeth; Branchereau, Romain (Fall) GerbelliGauthier, Mathilde (Winter)
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.

MATH 150 Calculus A (4 credits)
Overview
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

MATH 151 Calculus B (4 credits)
Overview
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/MATH 151 and MATH 140/MATH 141/MATH 222 are considered equivalent.
Required Courses (2831 credits)
* Students with limited programming experience should take COMP 202/COMP 204/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.
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: Students with limited knowledge of computer programming should take COMP 202/COMP 204/COMP 208 or equivalent before COMP 250. U0 students may take COMP 202 as a Freshman Science course; new U1 students should take one of these courses as an elective in their first semester.
Note: Students who wish to take MATH 204 as a complementary course are strongly advised to take MATH 203 beforehand, in their first semester or their first year.
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.

COMP 250 Introduction to Computer Science (3 credits) *
Overview
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 nonrecursive 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)

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 2023
Instructors: Lee, Kiwon (Fall)
Prerequisite(s): MATH 133

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 2023, Winter 2024, Summer 2024
Instructors: Sabok, Marcin; Allen, Patrick (Fall) Trudeau, Sidney (Winter)

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; 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

MATH 247 Honours Applied Linear Algebra (3 credits) **
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 2024
Instructors: Hoheisel, Tim (Winter)

MATH 251 Honours Algebra 2 (3 credits) **
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 selfadjoint operators.
Terms: Winter 2024
Instructors: Tserunyan, Anush (Winter)

MATH 255 Honours Analysis 2 (3 credits)
Overview
Mathematics & Statistics (Sci) : Basic pointset topology, metric spaces: open and closed sets, normed and Banach spaces, HÃ¶lder and Minkowski inequalities, sequential compactness, HeineBorel, 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)

MATH 356 Honours Probability (3 credits)
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, univariate 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: AddarioBerry, Louigi Dana (Fall)

MATH 357 Honours Statistics (3 credits)
Overview
Mathematics & Statistics (Sci) : Data analysis. Estimation and hypothesis testing. Power of tests. Likelihood ratio criterion. The chisquared goodness of fit test. Introduction to regression analysis and analysis of variance.
Terms: Winter 2024
Instructors: Asgharian, Masoud (Winter)

MATH 470 Honours Research Project (3 credits)
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 2023
Instructors: Hoheisel, Tim; Pym, Brent; Kamnitzer, Joel; Hurtubise, Jacques Claude; Choksi, Rustum; Allen, Patrick; Darmon, Henri; Goren, Eyal Z; Love, Jonathan; Przytycki, Piotr; Nave, JeanChristophe; Dagdoug, Mohamed Mehdi; Steele, Russell (Fall)
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 533 Regression and Analysis of Variance (4 credits)
Overview
Mathematics & Statistics (Sci) : Multivariate normal and chisquared distributions; quadratic forms. Multiple linear regression estimators and their properties. General linear hypothesis tests. Prediction and confidence intervals. Asymptotic properties of least squares estimators. Weighted least squares. Variable selection and regularization. Selected advanced topics in regression. Applications to experimental and observational data.
Terms: Fall 2023
Instructors: Dagdoug, Mohamed Mehdi (Fall)
Complementary Courses (32 credits)
Advising notes:
 Students wishing to pursue mathematical statistics in graduate school are advised to take MATH 587 and recommended to take honours mathematics courses as complementary courses in Part II, in particular MATH 358, MATH 454 (preferably prior to MATH 587), and MATH 455.
 Students wishing to pursue applied statistics and/or careers as statisticians in industry or government are advised to take MATH 523, MATH 524, MATH 547, at least one of MATH 525 and MATH 558, and as many courses as possible from Part III of the list of Complementary Courses below. Students interested in obtaining the AStat accreditation from the Statistical Society of Canada should discuss their course selection with the academic adviser.
Students with interest in probability are advised to choose from the following as part of their Complementary Courses: MATH 547, MATH 587, MATH 589.
 Students with interest in actuarial science are advised to choose from the following as part of their Complementary Courses: MATH 329, MATH 430, MATH 524, MATH 545, MATH 547.
 Students with interest in data science and machine learning are advised to choose from the following as part of their Complementary Courses: COMP 206, COMP 251, COMP 370, COMP 424, COMP 551, MATH 308, MATH 350, MATH 378, MATH 462 and MATH 517,MATH 562, and MATH 563.
Part I: 3 credits selected from:
* It is strongly recommended that students take MATH 254.

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 2023
Instructors: Hundemer, Axel W (Fall)

MATH 254 Honours Analysis 1 (3 credits) *
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 2023
Instructors: Jaksic, Vojkan (Fall)
Part II: 611 credits in mathematics and computer science selected from:
+ Students can select either MATH 248 or MATH 358, but not both.
++ Students may obtain credit for both MATH 455 and MATH 587.

COMP 206 Introduction to Software Systems (3 credits)
Overview
Computer Science (Sci) : Comprehensive overview of programming in C, use of system calls and libraries, debugging and testing of code; use of developmental tools like make, version control systems.
Terms: Fall 2023, Winter 2024
Instructors: Vybihal, Joseph P; BérubéVallières, Mathieu (Fall) Vybihal, Joseph P; Errington, Jacob (Winter)

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

MATH 248 Honours Vector Calculus (3 credits) +
Overview
Mathematics & Statistics (Sci) : Partial derivatives and differentiation of functions in several variables; Jacobians; maxima and minima; implicit functions. Scalar and vector fields; orthogonal curvilinear coordinates. Multiple integrals; arc length, volume and surface area. Line and surface integrals; irrotational and solenoidal fields; Green's theorem; the divergence theorem. Stokes' theorem; and applications.
Terms: Fall 2023
Instructors: Kamran, Niky (Fall)

MATH 325 Honours Ordinary Differential Equations (3 credits)
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 2024
Instructors: Humphries, Tony (Winter)

MATH 350 Honours Discrete Mathematics
(3 credits)
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 2023
Instructors: Norin, Sergey (Fall)

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: This course is not scheduled for the 20232024 academic year.
Instructors: There are no professors associated with this course for the 20232024 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.

MATH 358 Honours Advanced Calculus (3 credits) +
Overview
Mathematics & Statistics (Sci) : Pointset 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)

MATH 376 Honours Nonlinear Dynamics (3 credits)
Overview
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)

MATH 387 Honours 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: Winter 2024
Instructors: Gantumur, Tsog (Winter)

MATH 397 Honours Matrix Numerical Analysis (3 credits)
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 20232024 academic year.
Instructors: There are no professors associated with this course for the 20232024 academic year.

MATH 398 Honours Euclidean Geometry
(3 credits)
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’s theorem. Isometries. Homothety. Inversion.
Terms: Fall 2023
Instructors: Przytycki, Piotr (Fall)

MATH 454 Honours Analysis 3 (3 credits)
Overview
Mathematics & Statistics (Sci) : Review of pointset topology: topological space, dense sets, completeness, compactness, connectedness and pathconnectedness, separability. ArzelaAscoli, StoneWeierstrass, 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. FubiniTonelli theorem.
Terms: Fall 2023
Instructors: Vetois, Jerome (Fall)

MATH 455 Honours Analysis 4 (3 credits) ++
Overview
Mathematics & Statistics (Sci) : Continuation of measure theory. Functional analysis: L^p spaces, linear functionals and dual spaces, HahnBanach 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)

MATH 458 Honours Differential Geometry (3 credits)
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 FaryMilnor theorem on knotted curves, abstract surfaces as 2d manifolds, the Euler characteristic, the GaussBonnet theorem for surfaces.
Terms: Winter 2024
Instructors: Kamran, Niky (Winter)

MATH 466 Honours Complex Analysis (3 credits)
Overview
Mathematics & Statistics (Sci) : Functions of a complex variable, CauchyRiemann 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)

MATH 475 Honours Partial Differential Equations (3 credits)
Overview
Mathematics & Statistics (Sci) : First order partial differential equations, geometric theory, classification of second order linear equations, SturmLiouville 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)

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, NavierStokes equations
Terms: This course is not scheduled for the 20232024 academic year.
Instructors: There are no professors associated with this course for the 20232024 academic year.

MATH 480 Honours Independent Study (3 credits)
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 2023
Instructors: Przytycki, Piotr; Allen, Patrick (Fall)
Fall and Winter and Summer
Please see regulations concerning Project Courses under Faculty Degree Requirements
Requires approval by the chair before registration

MATH 527D1 Statistical Data Science
Practicum (3 credits)
Overview
Mathematics & Statistics (Sci) : The holistic skills required for doing statistical data science in practice. Data science life cycle from a statisticscentric perspective and from the perspective of a statistician working in the larger data science environment. Groupbased projects with industry, government, or university partners. Statistical collaboration and consulting conducted in coordination with the Data Science Solutions Hub (DaS^2H) of the Computational and Data Systems Initiative (CDSI).
Terms: Fall 2023
Instructors: Correa, Jose Andres; Kolaczyk, Eric (Fall)

MATH 527D2 Statistical Data Science
Practicum (3 credits)
Overview
Mathematics & Statistics (Sci) : See MATH 527D1 for course description.
Terms: Winter 2024
Instructors: Correa, Jose Andres; Kolaczyk, Eric (Winter)
Corequisites: MATH 423
No credit will be given for this course unless both MATH 527D1 and MATH 527D2 are successfully completed in consecutive terms
and any 500level course offered by the Department of Mathematics and Statistics not listed in Part III below.
Part III: 1823 credits in probability and statistics selected as follows:
1523 credits selected from:
+++ Students must take MATH 204 before taking MATH 357 or MATH 533. Moreover, it is strongly advised to take MATH 203 before taking MATH 204.

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 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.

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 2024
Instructors: Yang, Archer Yi (Winter)

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, loglinear models. Multinomial models. Overdispersion and Quasilikelihood. Applications to experimental and observational data.
Terms: Winter 2024
Instructors: Steele, Russell (Winter)

MATH 524 Nonparametric Statistics (4 credits)
Overview
Mathematics & Statistics (Sci) : Distribution free procedures for 2sample problem: Wilcoxon rank sum, SiegelTukey, Smirnov tests. Shift model: power and estimation. Single sample procedures: Sign, Wilcoxon signed rank tests. Nonparametric ANOVA: KruskalWallis, Friedman tests. Association: Spearman's rank correlation, Kendall's tau. Goodness of fit: Pearson's chisquare, likelihood ratio, KolmogorovSmirnov tests. Statistical software packages used.
Terms: This course is not scheduled for the 20232024 academic year.
Instructors: There are no professors associated with this course for the 20232024 academic year.

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 2024
Instructors: Dagdoug, Mohamed Mehdi (Winter)

MATH 545 Introduction to Time Series Analysis (4 credits)
Overview
Mathematics & Statistics (Sci) : Stationary processes; estimation and forecasting of ARMA models; nonstationary and seasonal models; statespace models; financial time series models; multivariate time series models; introduction to spectral analysis; long memory models.
Terms: This course is not scheduled for the 20232024 academic year.
Instructors: There are no professors associated with this course for the 20232024 academic year.

MATH 547 Stochastic Processes (4 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: This course is not scheduled for the 20232024 academic year.
Instructors: There are no professors associated with this course for the 20232024 academic year.

MATH 556 Mathematical Statistics 1 (4 credits)
Overview
Mathematics & Statistics (Sci) : Distribution theory, stochastic models and multivariate transformations. Families of distributions including locationscale families, exponential families, convolution families, exponential dispersion models and hierarchical models. Concentration inequalities. Characteristic functions. Convergence in probability, almost surely, in Lp and in distribution. Laws of large numbers and Central Limit Theorem. Stochastic simulation.
Terms: Fall 2023
Instructors: Asgharian, Masoud (Fall)
Fall
Prerequisite: MATH 357 or equivalent

MATH 557 Mathematical Statistics 2 (4 credits)
Overview
Mathematics & Statistics (Sci) : Sampling theory (including largesample theory). Likelihood functions and information matrices. Hypothesis testing, estimation theory. Regression and correlation theory.
Terms: Winter 2024
Instructors: Asgharian, Masoud (Winter)
Winter
Prerequisite: MATH 556

MATH 558 Design of Experiments (4 credits)
Overview
Mathematics & Statistics (Sci) : Introduction to concepts in statistically designed experiments. Randomization and replication. Completely randomized designs. Simple linear model and analysis of variance. Introduction to blocking. Orthogonal block designs. Models and analysis for block designs. Factorial designs and their analysis. Rowcolumn designs. Latin squares. Model and analysis for fixed row and column effects. Splitplot designs, model and analysis. Relations and operations on factors. Orthogonal factors. Orthogonal decomposition. Orthogonal plot structures. Hasse diagrams. Applications to real data and ethical issues.
Terms: Winter 2024
Instructors: Sajjad, Alia (Winter)

MATH 559 Bayesian Theory and Methods (4 credits)
Overview
Mathematics & Statistics (Sci) : Subjective probability, Bayesian statistical inference and decision making, de Finetti’s representation. Bayesian parametric methods, optimal decisions, conjugate models, methods of prior specification and elicitation, approximation methods. Hierarchical models. Computational approaches to inference, Markov chain Monte Carlo methods, Metropolis—Hastings. Nonparametric Bayesian inference.
Terms: Fall 2023
Instructors: Stephens, David (Fall)

MATH 587 Advanced Probability Theory 1 (4 credits)
Overview
Mathematics & Statistics (Sci) : Probability spaces. Random variables and their expectations. Convergence of random variables in Lp. Independence and conditional expectation. Introduction to Martingales. Limit theorems including Kolmogorov's Strong Law of Large Numbers.
Terms: Fall 2023
Instructors: AddarioBerry, Louigi Dana (Fall)

MATH 589 Advanced Probability Theory 2 (4 credits)
Overview
Mathematics & Statistics (Sci) : Characteristic functions: elementary properties, inversion formula, uniqueness, convolution and continuity theorems. Weak convergence. Central limit theorem. Additional topic(s) chosen (at discretion of instructor) from: Martingale Theory; Brownian motion, stochastic calculus.
Terms: Winter 2024
Instructors: Paquette, Elliot (Winter)
Winter
Prerequisites: MATH 587 or equivalent
03 credits from the following courses for which no Honours equivalent exists:

MATH 329 Theory of Interest (3 credits)
Overview
Mathematics & Statistics (Sci) : Simple and compound interest, annuities certain, amortization schedules, bonds, depreciation.
Terms: Winter 2024
Instructors: Kelome, Djivede (Winter)
Winter
Prerequisite: MATH 141

MATH 378 Nonlinear Optimization
(3 credits)
Overview
Mathematics & Statistics (Sci) : Optimization terminology. Convexity. First and secondorder optimality conditions for unconstrained problems. Numerical methods for unconstrained optimization: Gradient methods, Newtontype methods, conjugate gradient methods, trustregion methods. Least squares problems (linear + nonlinear). Optimality conditions for smooth constrained optimization problems (KKT theory). Lagrangian duality. Augmented Lagrangian methods. Activeset method for quadratic programming. SQP methods.
Terms: Fall 2023
Instructors: Hoheisel, Tim (Fall)

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 20232024 academic year.
Instructors: There are no professors associated with this course for the 20232024 academic year.
08 credits selected from:
+++ Students may select either MATH 594 or MATH 598 but not both.

COMP 370 Introduction to Data
Science (3 credits)
Overview
Computer Science (Sci) : Comprehensive introduction to the data science process. Orientation to the use and configuration of core data science toolkits, data collection and annotation fundamentals, principles of responsible data science, the use of quantitative tools in data science, and presentation of data science findings.
Terms: Fall 2023
Instructors: Ruths, Derek (Fall)

COMP 424 Artificial Intelligence (3 credits)
Overview
Computer Science (Sci) : Introduction to search methods. Knowledge representation using logic and probability. Planning and decision making under uncertainty. Introduction to machine learning.
Terms: Fall 2023
Instructors: Meger, David (Fall)

COMP 451 Fundamentals of Machine Learning (3 credits)
Overview
Computer Science (Sci) : Introduction to the computational, statistical and mathematical foundations of machine learning. Algorithms for both supervised learning and unsupervised learning. Maximum likelihood estimation, neural networks, and regularization.
Terms: Fall 2023
Instructors: Ravanbakhsh, Siamak (Fall)

COMP 551 Applied Machine Learning (4 credits)
Overview
Computer Science (Sci) : Selected topics in machine learning and data mining, including clustering, neural networks, support vector machines, decision trees. Methods include feature selection and dimensionality reduction, error estimation and empirical validation, algorithm design and parallelization, and handling of large data sets. Emphasis on good methods and practices for deployment of real systems.
Terms: Fall 2023, Winter 2024
Instructors: PrémontSchwarz, Isabeau; Rabbany, Reihaneh (Fall) Li, Yue; PrémontSchwarz, Isabeau (Winter)

COMP 579 Reinforcement Learning (4 credits)
Overview
Computer Science (Sci) : Bandit algorithms, finite Markov decision processes, dynamic programming, MonteCarlo Methods, temporaldifference learning, bootstrapping, planning, approximation methods, on versus off policy learning, policy gradient methods temporal abstraction and inverse reinforcement learning.
Terms: Winter 2024
Instructors: Precup, Doina; PrémontSchwarz, Isabeau (Winter)

COMP 588 Probabilistic Graphical Models (4 credits)
Overview
Computer Science (Sci) : Representation, inference and learning with graphical models; directed and undirected graphical models; exact inference; approximate inference using deterministic optimization based methods, stochastic sampling based methods; learning with complete and partial observations.
Terms: This course is not scheduled for the 20232024 academic year.
Instructors: There are no professors associated with this course for the 20232024 academic year.

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: This course is not scheduled for the 20232024 academic year.
Instructors: There are no professors associated with this course for the 20232024 academic year.

MATH 462 Honours Mathematics for Machine Learning (3 credits)
Overview
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, JohnsonLindenstrauss Lemma. Concentration of measure and learning bounds.
Terms: Fall 2023
Instructors: Oberman, Adam (Fall)

MATH 562 Theory of Machine Learning (4 credits)
Overview
Mathematics & Statistics (Sci) : Concentration inequalities, PAC model, VC dimension, Rademacher complexity, convex optimization, gradient descent, boosting, kernels, support vector machines, regression and learning bounds. Further topics selected from: Gaussian processes, online learning, regret bounds, basic neural network theory.
Terms: This course is not scheduled for the 20232024 academic year.
Instructors: There are no professors associated with this course for the 20232024 academic year.
Prerequisites: MATH 462 or COMP 451 or (COMP 551, MATH 222, MATH 223 and MATH 324) or ECSE 551.
Restrictions: Not open to students who have taken or are taking COMP 562. Not open to students who have taken COMP 599 when the topic was "Statistical Learning Theory" or "Mathematical Topics for Machine Learning". Not open to students who have taken COMP 598 when the topic was"Mathematical Foundations of Machine Learning".

MATH 594 Topics in Mathematics and Statistics
(4 credits) +++
Overview
Mathematics & Statistics (Sci) : This course covers a topic in mathematics and/or statistics.
Terms: This course is not scheduled for the 20232024 academic year.
Instructors: There are no professors associated with this course for the 20232024 academic year.
Prerequisites: At least 30 credits in required or complementary courses from the Honours Mathematics, Honours Applied Mathematics, or Honours Probability and Statistics programs. Additional prerequisites may be imposed by the Department of Mathematics and Statistics depending on the nature of the topic.
Restrictions: Requires permission of the Department of Mathematics and Statistics

MATH 598 Topics in Probability and Statistics (4 credits) +++
Overview
Mathematics & Statistics (Sci) : This course covers a topic in probability and/or statistics.
Terms: Fall 2023, Winter 2024
Instructors: Paquette, Elliot (Fall) Stephens, David (Winter)
Prerequisite(s): At least 30 credits in required or complementary courses from the Honours in Probability and Statistics program including MATH 356. Additional prerequisites may be imposed by the Department of Mathematics and Statistics depending on the nature of the topic.
Restriction(s): Requires permission of the Department of Mathematics and Statistics.