Statistics Honours (B.A.) (63 credits)
Offered by: Mathematics and Statistics (Faculty of Science)
Degree: Bachelor of Science; Bachelor of Arts
Program credit weight: 63
Program Description
The B.Sc.: Honours in Statistics provides training, at the honours level, in 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.
Degree Requirements — B.Sc.
This program is offered as part of a Bachelor of Science (B.Sc.) degree.
To graduate, students must satisfy both their program requirements and their degree requirements.
- The program requirements (i.e., the specific courses that make up this program) are listed under the Course Tab (above).
- The degree requirements—including the mandatory Foundation program, appropriate degree structure, and any additional components—are outlined on the Degree Requirements page.
Students are responsible for ensuring that this program fits within the overall structure of their degree and that all degree requirements are met. Consult the Degree Planning Guide on the SOUSA website for additional guidance.
Degree Requirements — B.A. students
To be eligible for a B.A. degree, a student must fulfil all Faculty and program requirements as indicated in Degree Requirements for the Faculty of Arts.
We recommend that students consult an Arts OASIS advisor for degree planning.
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 Calculus 3..
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:
| Course | Title | Credits |
|---|---|---|
| MATH 133 | Linear Algebra and Geometry. | 3 |
Linear Algebra and Geometry. Terms offered: Summer 2025, Fall 2025, Winter 2026 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. | ||
| MATH 150 | Calculus A. | 4 |
Calculus A. Terms offered: this course is not currently offered. Functions, limits and continuity, differentiation, L'Hospital's rule, applications, Taylor polynomials, parametric curves, functions of several variables. | ||
| MATH 151 | Calculus B. | 4 |
Calculus B. Terms offered: this course is not currently offered. Integration, methods and applications, infinite sequences and series, power series, arc length and curvature, multiple integration. | ||
In particular, MATH 150 Calculus A./MATH 151 Calculus B. and MATH 140 Calculus 1./MATH 141 Calculus 2./MATH 222 Calculus 3. are considered equivalent.
Required Courses (25-28 credits)
Students who have not completed an equivalent of MATH 222 Calculus 3. on entering the program must consult an academic adviser and take MATH 222 Calculus 3. 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 Calculus A./MATH 151 Calculus B. are not required to take MATH 222 Calculus 3..
Note: Students with limited knowledge of computer programming should take COMP 202 Foundations of Programming./COMP 204 Computer Programming for Life Sciences./COMP 208 Computer Programming for Physical Sciences and Engineering . or equivalent before COMP 250 Introduction to Computer Science.. U0 students may take COMP 202 Foundations of Programming. 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 Principles of Statistics 2. as a complementary course are strongly advised to take MATH 203 Principles of Statistics 1. 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.
| Course | Title | Credits |
|---|---|---|
| COMP 250 | Introduction to Computer Science. 1 | 3 |
Introduction to Computer Science. Terms offered: Fall 2025, Winter 2026 Mathematical tools (binary numbers, induction,recurrence relations, asymptotic complexity,establishing correctness of programs). Datastructures (arrays, stacks, queues, linked lists,trees, binary trees, binary search trees, heaps,hash tables). Recursive and non-recursivealgorithms (searching and sorting, tree andgraph traversal). Abstract data types. Objectoriented programming in Java (classes andobjects, interfaces, inheritance). Selected topics. | ||
| MATH 208 | Introduction to Statistical Computing. | 3 |
Introduction to Statistical Computing. Terms offered: Fall 2025 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. | ||
| MATH 222 | Calculus 3. 2 | 3 |
Calculus 3. Terms offered: Summer 2025, Fall 2025, Winter 2026 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. | ||
| MATH 247 | Honours Applied Linear Algebra. 3 | 3 |
Honours Applied Linear Algebra. Terms offered: Winter 2026 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. | ||
| MATH 251 | Honours Algebra 2. 3 | 3 |
Honours Algebra 2. Terms offered: Winter 2026 Linear equations over a field. Introduction to vector spaces. Linear maps and their matrix representation. Determinants. Canonical forms. Duality. Bilinear and quadratic forms. Real and complex inner product spaces. Diagonalization of self-adjoint operators. | ||
| MATH 255 | Honours Analysis 2. | 3 |
Honours Analysis 2. Terms offered: Winter 2026 Basic point-set topology, metric spaces: open and closed sets, normed and Banach spaces, Hölder and Minkowski inequalities, sequential compactness, Heine-Borel, Banach Fixed Point theorem. Riemann-(Stieltjes) integral, Fundamental Theorem of Calculus, Taylor's theorem. Uniform convergence. Infinite series, convergence tests, power series. Elementary functions. | ||
| MATH 356 | Honours Probability. | 3 |
Honours Probability. Terms offered: Fall 2025 Sample space, probability axioms, combinatorial probability. Conditional probability, Bayes' Theorem. Distribution theory with special reference to the Binomial, Poisson, and Normal distributions. Expectations, moments, moment generating functions, uni-variate transformations. Random vectors, independence, correlation, multivariate transformations. Conditional distributions, conditional expectation.Modes of stochastic convergence, laws of large numbers, Central Limit Theorem. | ||
| MATH 357 | Honours Statistics. | 3 |
Honours Statistics. Terms offered: Winter 2026 Sampling distributions. Point estimation. Minimum variance unbiased estimators, sufficiency, and completeness. Confidence intervals. Hypothesis tests, Neyman-Pearson Lemma, uniformly most powerful tests. Likelihood ratio tests for normal samples. Asymptotic sampling distributions and inference. | ||
| MATH 470 | Honours Research Project. | 3 |
Honours Research Project. Terms offered: Summer 2025, Fall 2025, Winter 2026 The project will contain a significant research component that requires substantial independent work consisting of a written report and oral examination or presentation. | ||
| MATH 533 | Regression and Analysis of Variance. | 4 |
Regression and Analysis of Variance. Terms offered: Fall 2025 Multivariate normal and chi-squared 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. | ||
- 1
Students with limited programming experience should take COMP 202 Foundations of Programming./COMP 204 Computer Programming for Life Sciences./COMP 208 Computer Programming for Physical Sciences and Engineering . or equivalent before COMP 250 Introduction to Computer Science..
- 2
Students who have successfully completed MATH 150 Calculus A./MATH 151 Calculus B. or an equivalent of MATH 222 Calculus 3. on entering the program are not required to take MATH 222 Calculus 3..
- 3
Students select either MATH 251 Honours Algebra 2. or MATH 247 Honours Applied Linear Algebra., but not both.
Complementary Courses (35 credits)
Advising notes:
Students wishing to pursue mathematical statistics in graduate school are advised to take MATH 587 Advanced Probability Theory 1. and recommended to take honours mathematics courses as complementary courses in Part II, in particular MATH 358 Honours Advanced Calculus., MATH 454 Honours Analysis 3. (preferably prior to MATH 587 Advanced Probability Theory 1.), and MATH 455 Honours Analysis 4..
Students wishing to pursue applied statistics and/or careers as statisticians in industry or government are advised to take MATH 523 Generalized Linear Models., MATH 524 Nonparametric Statistics., MATH 547 Stochastic Processes., at least one of MATH 525 Sampling Theory and Applications. and MATH 558 Design of Experiments., and as many courses as possible from Part III of the list of Complementary Courses below. Students interested in obtaining the A-Stat 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:
| Course | Title | Credits |
|---|---|---|
| MATH 547 | Stochastic Processes. | 4 |
Stochastic Processes. Terms offered: this course is not currently offered. 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. | ||
| MATH 587 | Advanced Probability Theory 1. | 4 |
Advanced Probability Theory 1. Terms offered: Fall 2025 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. | ||
| MATH 589 | Advanced Probability Theory 2. | 4 |
Advanced Probability Theory 2. Terms offered: Winter 2026 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. | ||
Students with interest in actuarial science are advised to choose from the following as part of their Complementary Courses:
| Course | Title | Credits |
|---|---|---|
| MATH 329 | Theory of Interest. | 3 |
Theory of Interest. Terms offered: Winter 2026 Simple and compound interest, annuities certain, amortization schedules, bonds, depreciation. | ||
| MATH 430 | Mathematical Finance. | 3 |
Mathematical Finance. Terms offered: this course is not currently offered. 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. | ||
| MATH 524 | Nonparametric Statistics. | 4 |
Nonparametric Statistics. Terms offered: Fall 2025 Distribution free procedures for 2-sample problem: Wilcoxon rank sum, Siegel-Tukey, Smirnov tests. Shift model: power and estimation. Single sample procedures: Sign, Wilcoxon signed rank tests. Nonparametric ANOVA: Kruskal-Wallis, Friedman tests. Association: Spearman's rank correlation, Kendall's tau. Goodness of fit: Pearson's chi-square, likelihood ratio, Kolmogorov-Smirnov tests. Statistical software packages used. | ||
| MATH 545 | Introduction to Time Series Analysis. | 4 |
Introduction to Time Series Analysis. Terms offered: this course is not currently offered. 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. | ||
| MATH 547 | Stochastic Processes. | 4 |
Stochastic Processes. Terms offered: this course is not currently offered. 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. | ||
Students with interest in data science and machine learning are advised to choose from the following as part of their Complementary Courses:
| Course | Title | Credits |
|---|---|---|
| COMP 206 | Introduction to Software Systems. | 3 |
Introduction to Software Systems. Terms offered: Fall 2025, Winter 2026 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. | ||
| COMP 251 | Algorithms and Data Structures. | 3 |
Algorithms and Data Structures. Terms offered: Fall 2025, Winter 2026 Data Structures: priority queues, balanced binary search trees, hash tables, graphs. Algorithms: topological sort, connected components, shortest paths, minimum spanning trees, bipartite matching, network flows. Algorithm design: greedy, divide and conquer, dynamic programming, randomization. Mathematicaltools: proofs of asymptotic complexity and program correctness, Master theorem. | ||
| COMP 370 | Introduction to Data Science. | 3 |
Introduction to Data Science. Terms offered: Fall 2025 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. | ||
| COMP 424 | Artificial Intelligence. | 3 |
Artificial Intelligence. Terms offered: Fall 2025 Introduction to search methods. Knowledge representation using logic and probability. Planning and decision making under uncertainty. Introduction to machine learning. | ||
| COMP 551 | Applied Machine Learning. | 4 |
Applied Machine Learning. Terms offered: Fall 2025, Winter 2026 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. | ||
| MATH 308 | Fundamentals of Statistical Learning. | 3 |
Fundamentals of Statistical Learning. Terms offered: Winter 2026 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. | ||
| MATH 350 | Honours Discrete Mathematics . | 3 |
Honours Discrete Mathematics . Terms offered: Fall 2025 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. | ||
| MATH 378 | Nonlinear Optimization . | 3 |
Nonlinear Optimization . Terms offered: Fall 2025 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. | ||
| MATH 462 | Machine Learning . | 3 |
Machine Learning . Terms offered: this course is not currently offered. 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. | ||
| MATH 517 | Honours Linear Optimization. | 4 |
Honours Linear Optimization. Terms offered: this course is not currently offered. Honours level introduction to linear optimization and its applications: duality theory, fundamental theorem, sensitivity analysis, convexity, simplex algorithm, interiorpoint methods, quadratic optimization, applications in game theory. | ||
| MATH 562 | Theory of Machine Learning. | 0-4 |
Theory of Machine Learning. Terms offered: Winter 2026 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. | ||
| MATH 563 | Honours Convex Optimization . | 4 |
Honours Convex Optimization . Terms offered: Winter 2026 Honours level 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. | ||
Part I
3 credits selected from:
| Course | Title | Credits |
|---|---|---|
| MATH 242 | Analysis 1. | 3 |
Analysis 1. Terms offered: Fall 2025 A rigorous presentation of sequences and of real numbers and basic properties of continuous and differentiable functions on the real line. | ||
| MATH 254 | Honours Analysis 1. 1 | 3 |
Honours Analysis 1. Terms offered: Fall 2025 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. | ||
3 credits from:
| Course | Title | Credits |
|---|---|---|
| MATH 235 | Algebra 1. | 3 |
Algebra 1. Terms offered: Fall 2025 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. | ||
| MATH 245 | Honours Algebra 1. 1 | 3 |
Honours Algebra 1. Terms offered: Fall 2025 Honours level: Sets, functions, and relations. Methods of proof. Complex numbers. Divisibility theory for integers and modular arithmetic. Divisibility theory for polynomials. In-depth study of rings, ideals, and quotient rings; fields and construction of fields from polynomial rings; groups, subgroups, and cosets, homomorphisms, and quotient groups. | ||
- 1
It is strongly recommended that students take both MATH 245 and MATH 254.
Part II
6-11 credits in mathematics and computer science selected from:
| Course | Title | Credits |
|---|---|---|
| COMP 206 | Introduction to Software Systems. | 3 |
Introduction to Software Systems. Terms offered: Fall 2025, Winter 2026 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. | ||
| COMP 252 | Honours Algorithms and Data Structures. | 3 |
Honours Algorithms and Data Structures. Terms offered: Winter 2026 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. | ||
| MATH 248 | Honours Vector Calculus. 1 | 3 |
Honours Vector Calculus. Terms offered: Fall 2025 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. | ||
| MATH 325 | Honours Ordinary Differential Equations. | 3 |
Honours Ordinary Differential Equations. Terms offered: Winter 2026 First and second order equations, linear equations, series solutions, Frobenius method, introduction to numerical methods and to linear systems, Laplace transforms, applications. | ||
| MATH 350 | Honours Discrete Mathematics . | 3 |
Honours Discrete Mathematics . Terms offered: Fall 2025 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. | ||
| MATH 352 | Problem Seminar. | 1 |
Problem Seminar. Terms offered: this course is not currently offered. 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. | ||
| MATH 358 | Honours Advanced Calculus. 1 | 3 |
Honours Advanced Calculus. Terms offered: Winter 2026 Point-set topology in Euclidean space; continuity and differentiability of functions in several variables. Implicit and inverse function theorems. Vector fields, divergent and curl operations. Rigorous treatment of multiple integrals: volume and surface area; and Fubini’s theorem. Line and surface integrals, conservative vector fields. Green's theorem, Stokes’ theorem and the divergence theorem. | ||
| MATH 376 | Honours Nonlinear Dynamics. | 3 |
Honours Nonlinear Dynamics. Terms offered: Fall 2025 This course consists of the lectures of MATH 326, but will be assessed at the honours level. | ||
| MATH 387 | Honours Numerical Analysis. | 3 |
Honours Numerical Analysis. Terms offered: Winter 2026 Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations. | ||
| MATH 397 | Honours Matrix Numerical Analysis. | 3 |
Honours Matrix Numerical Analysis. Terms offered: this course is not currently offered. 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. | ||
| MATH 398 | Honours Euclidean Geometry . | 3 |
Honours Euclidean Geometry . Terms offered: Fall 2025 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. | ||
| MATH 454 | Honours Analysis 3. | 3 |
Honours Analysis 3. Terms offered: Fall 2025 Measure theory: sigma-algebras, Lebesgue measure in R^n and integration, L^1 functions, Fatou's lemma, monotone and dominated convergence theorem, Egorov’s theorem, Lusin's theorem, Fubini-Tonelli theorem, differentiation of the integral, differentiability of functions of bounded variation, absolutely continuous functions, fundamental theorem of calculus. | ||
| MATH 455 | Honours Analysis 4. 2 | 3 |
Honours Analysis 4. Terms offered: Winter 2026 Review of point-set topology: topological spaces, dense sets, completeness, compactness, connectedness and path-connectedness, separability, Baire category theorem, Arzela-Ascoli theorem, Stone-Weierstrass theorem..Functional analysis: L^p spaces, linear functionals and dual spaces, Hilbert spaces, Riesz representation theorems. Fourier series and transform, Riemann-Lebesgue Lemma,Fourier inversion formula, Plancherel theorem, Parseval’s identity, Poisson summation formula. | ||
| MATH 458 | Honours Differential Geometry. | 3 |
Honours Differential Geometry. Terms offered: Winter 2026 In addition to the topics of MATH 320, topics in the global theory of plane and space curves, and in the global theory of surfaces are presented. These include: total curvature and the Fary-Milnor theorem on knotted curves, abstract surfaces as 2-d manifolds, the Euler characteristic, the Gauss-Bonnet theorem for surfaces. | ||
| MATH 466 | Honours Complex Analysis. | 3 |
Honours Complex Analysis. Terms offered: this course is not currently offered. Functions of a complex variable, Cauchy-Riemann equations, Cauchy's theorem and its consequences. Uniform convergence on compacta. Taylor and Laurent series, open mapping theorem, Rouché's theorem and the argument principle. Calculus of residues. Fractional linear transformations and conformal mappings. | ||
| MATH 475 | Honours Partial Differential Equations. | 3 |
Honours Partial Differential Equations. Terms offered: Fall 2025 First order partial differential equations, geometric theory, classification of second order linear equations, Sturm-Liouville problems, orthogonal functions and Fourier series, eigenfunction expansions, separation of variables for heat, wave and Laplace equations, Green's function methods, uniqueness theorems. | ||
| MATH 478 | Computational Methods in Applied Mathematics . | 3 |
Computational Methods in Applied Mathematics . Terms offered: this course is not currently offered. 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 | ||
| MATH 480 | Honours Independent Study. | 3 |
Honours Independent Study. Terms offered: Summer 2025, Fall 2025, Winter 2026 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. | ||
| MATH 527D1 | Statistical Data Science Practicum. | 3 |
Statistical Data Science Practicum. Terms offered: Fall 2025 The holistic skills required for doing statistical data science in practice. Data science life cycle from a statistics-centric perspective and from the perspective of a statistician working in the larger data science environment. Group-based 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). | ||
| MATH 527D2 | Statistical Data Science Practicum. | 3 |
Statistical Data Science Practicum. Terms offered: Winter 2026 See MATH 527D1 for course description. | ||
and any 500-level course offered by the Department of Mathematics and Statistics not listed in Part III below.
- 1
Students can select either MATH 248 Honours Vector Calculus. or MATH 358 Honours Advanced Calculus., but not both.
- 2
Students may obtain credit for both MATH 455 Honours Analysis 4. and MATH 587 Advanced Probability Theory 1..
Part III
18-23 credits in probability and statistics selected as follows:
15-23 credits selected from:
| Course | Title | Credits |
|---|---|---|
| MATH 204 | Principles of Statistics 2. 1 | 3 |
Principles of Statistics 2. Terms offered: Winter 2026 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. | ||
| MATH 308 | Fundamentals of Statistical Learning. | 3 |
Fundamentals of Statistical Learning. Terms offered: Winter 2026 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. | ||
| MATH 511 | Analysis of Categorical Data. | 4 |
Analysis of Categorical Data. Terms offered: Winter 2026 Probability distributions for categorical data, Analysis of 2X2 contingency tables, Multiway contingency tables, The Logistic regression, Logistic regression for categorical predictors, Logit models for nominal and ordinal responses, Log-linear models and modelling ordinal associations in contingency tables, Unsupervised learning techniques for categorical data, Non Linear Principal component analysis, Applications of unsupervised learning techniques using R, Item Response Theory, Rasch model. Some topics may be included or excluded as the time permits. | ||
| MATH 523 | Generalized Linear Models. | 4 |
Generalized Linear Models. Terms offered: Winter 2026 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. | ||
| MATH 524 | Nonparametric Statistics. | 4 |
Nonparametric Statistics. Terms offered: Fall 2025 Distribution free procedures for 2-sample problem: Wilcoxon rank sum, Siegel-Tukey, Smirnov tests. Shift model: power and estimation. Single sample procedures: Sign, Wilcoxon signed rank tests. Nonparametric ANOVA: Kruskal-Wallis, Friedman tests. Association: Spearman's rank correlation, Kendall's tau. Goodness of fit: Pearson's chi-square, likelihood ratio, Kolmogorov-Smirnov tests. Statistical software packages used. | ||
| MATH 525 | Sampling Theory and Applications. | 4 |
Sampling Theory and Applications. Terms offered: Winter 2026 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. | ||
| MATH 545 | Introduction to Time Series Analysis. | 4 |
Introduction to Time Series Analysis. Terms offered: this course is not currently offered. 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. | ||
| MATH 547 | Stochastic Processes. | 4 |
Stochastic Processes. Terms offered: this course is not currently offered. 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. | ||
| MATH 556 | Mathematical Statistics 1. | 4 |
Mathematical Statistics 1. Terms offered: Fall 2025 Distribution theory, stochastic models and multivariate transformations. Families of distributions including location-scale 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. | ||
| MATH 557 | Mathematical Statistics 2. | 4 |
Mathematical Statistics 2. Terms offered: Winter 2026 Sufficiency, minimal and complete sufficiency, ancillarity. Fisher and Kullback-Leibler information. Elements of decision theory. Theory of estimation and hypothesis testing from the Bayesian and frequentist perspective. Elements of asymptotic statistics including large-sample behaviour of maximum likelihood estimators, likelihood-ratio tests, and chi-squared goodness-of-fit tests. | ||
| MATH 558 | Design of Experiments. | 4 |
Design of Experiments. Terms offered: this course is not currently offered. 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. Row-column designs. Latin squares. Model and analysis for fixed row and column effects. Split-plot 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. | ||
| MATH 559 | Bayesian Theory and Methods. | 4 |
Bayesian Theory and Methods. Terms offered: this course is not currently offered. 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. | ||
| MATH 587 | Advanced Probability Theory 1. | 4 |
Advanced Probability Theory 1. Terms offered: Fall 2025 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. | ||
| MATH 589 | Advanced Probability Theory 2. | 4 |
Advanced Probability Theory 2. Terms offered: Winter 2026 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. | ||
- 1
Students must take MATH 204 Principles of Statistics 2. before taking MATH 357 Honours Statistics. or MATH 533 Regression and Analysis of Variance.. Moreover, it is strongly advised to take MATH 203 Principles of Statistics 1. before taking MATH 204 Principles of Statistics 2..
0-3 credits from the following courses for which no Honours equivalent exists:
| Course | Title | Credits |
|---|---|---|
| MATH 329 | Theory of Interest. | 3 |
Theory of Interest. Terms offered: Winter 2026 Simple and compound interest, annuities certain, amortization schedules, bonds, depreciation. | ||
| MATH 378 | Nonlinear Optimization . | 3 |
Nonlinear Optimization . Terms offered: Fall 2025 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. | ||
| MATH 427 | Statistical Quality Control. | 3 |
Statistical Quality Control. Terms offered: Fall 2025 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. | ||
0-8 credits selected from:
| Course | Title | Credits |
|---|---|---|
| COMP 370 | Introduction to Data Science. | 3 |
Introduction to Data Science. Terms offered: Fall 2025 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. | ||
| COMP 424 | Artificial Intelligence. | 3 |
Artificial Intelligence. Terms offered: Fall 2025 Introduction to search methods. Knowledge representation using logic and probability. Planning and decision making under uncertainty. Introduction to machine learning. | ||
| COMP 451 | Fundamentals of Machine Learning. | 3 |
Fundamentals of Machine Learning. Terms offered: this course is not currently offered. 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. | ||
| COMP 551 | Applied Machine Learning. | 4 |
Applied Machine Learning. Terms offered: Fall 2025, Winter 2026 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. | ||
| COMP 579 | Reinforcement Learning. | 4 |
Reinforcement Learning. Terms offered: Winter 2026 Bandit algorithms, finite Markov decision processes, dynamic programming, Monte-Carlo Methods, temporal-difference learning, bootstrapping, planning, approximation methods, on versus off policy learning, policy gradient methods temporal abstraction and inverse reinforcement learning. | ||
| COMP 588 | Probabilistic Graphical Models. | 4 |
Probabilistic Graphical Models. Terms offered: Winter 2026 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. | ||
| MATH 430 | Mathematical Finance. | 3 |
Mathematical Finance. Terms offered: this course is not currently offered. 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. | ||
| MATH 462 | Machine Learning . | 3 |
Machine Learning . Terms offered: this course is not currently offered. 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. | ||
| MATH 510 | Quantitative Risk Management. | 4 |
Quantitative Risk Management. Terms offered: Winter 2026 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. | ||
| MATH 562 | Theory of Machine Learning. | 4 |
Theory of Machine Learning. Terms offered: Winter 2026 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. | ||
| MATH 594 | Topics in Mathematics and Statistics . 1 | 4 |
Topics in Mathematics and Statistics . Terms offered: this course is not currently offered. This course covers a topic in mathematics and/or statistics. | ||
| MATH 598 | Topics in Probability and Statistics. 1 | 4 |
Topics in Probability and Statistics. Terms offered: Fall 2025, Winter 2026 This course covers a topic in probability and/or statistics. | ||