Department of Mathematics and Statistics

Students are expected to participate in a weekly seminar in which they are required to present material on a topic that relates to their research.

An introduction to graph theory, one of the central disciplines of discrete mathematics. Topics include: graphs, subgraphs, trees, connectivity, Euler tours, Hamiltonian cycles, matchings, independent sets, cliques, colourings, and planarity.  (Offered jointly with MATH-401*.) Three term-hours; lectures.
EXCLUSION: MATH-401*

Enumerative combinatorics is concerned with counting the number of elements of finite sets with prescribed conditions. The techniques covered include inclusion-exclusion, bijective proofs, double-counting arguments, recurrence relations, and generating functions. (Offered jointly with MATH-402*.) Three term hours; lectures.
EXCLUSION: MATH-402*

Construction and properties of finite fields. Polynomials, vector spaces, block codes over finite fields. Hamming distance and other code parameters. Bounds relating code parameters. Cyclic codes and their structure as ideals. Weight distribution. Special codes and their relation to designs and projective planes. Decoding algorithms. (Offered jointly with MATH/MTHE 406*.) Three term-hours; lectures.

Subject matter may vary from year to year. Three term-hours; lectures.

An introduction to the study of systems of polynomial equations in one or many variables. Topics covered include the Hilbert basis theorem, the Nullstellenstaz, the dictionary between ideals and affine varieties, and projective geometry (Offered jointly with MATH 413*). Three term-hours; lectures.

Time estimates for arithmetic and elementary number theory algorithms (division algorithm, Euclidean algorithm, congruences), modular arithmetic, finite fields, quadratic residues. Design of simple cryptographic systems; public key, RSA systems. Primality and factoring: pseudoprimes, Pollard's rho-method, index calculus. Elliptic curve cryptography. (Offered jointly with MATH/MTHE-418*.) Three term hours; lectures.

Topics include: global properties of flows and diffeomorphisms; invariant sets and dynamics; bifurcations of fixed and periodic points; stability and chaos. (Offered jointly with MATH-427*.) Three term-hours; lectures.

A generalization of linear algebra and calculus to infinite dimensional spaces. Now questions about continuity and completeness become crucial, and algebraic, topological, and analytical arguments need to be combined. We focus mainly on Hilbert spaces and the need for Functional Analysis will be motivated by its application to Quantum Mechanics. (Offered jointly with MATH 429.) Three term hours; lectures.

This course covers core topics in modern control theory: Linearization, existence and uniqueness of trajectories for nonlinear and linear systems, the transition matrix,controllability, observability, minimal realizations, feedback stabilization, linear state observers, optimal control theory, the linear quadratic regulator, dynamic programming. (Offered jointly with MTHE-430*.) Three term-hours; lectures.

Continuum mechanics lays the foundations for the study of the mechanical behavior of solids and fluids. Topics include vector and tensor analysis, stress, strain and deformation, and balance laws with constitutive models for applications in fluid mechanics and elasticity. (Offered jointly with MTHE 433.) Three term hours; lectures.

Theory of convex sets and functions; separation theorems; primal-dual properties; geometric treatment of optimization problems; algorithmic procedures for solving constrained optimization programs;engineering and economics applications. (Offered jointly with MATH-434). Three term-hours; lectures.

This is a course in advanced mathematical methods used to construct models of biological phenomena in ecology, epidemiology, and evolutionary biology. The course will focus on population models, starting with individual-based models based on assumptions on the distribution of individual traits, then scaling up to stochastic models for small populations and deterministic models for large populations. Three term-hours; lectures.

Geometric modelling, including configuration space, tangent bundle, kinetic energy, inertia, and force. Euler-Lagrange equations using affine connections. The last part of the course develops one of the following three applications: mechanical systems with nonholonomic constraints; control theory for mechanical systems; equilibria and stability. (Offered jointly with MATH/MTHE-439*) Three term-hours; lectures.

Subject matter may vary from year to year. Three term-hours; lectures.

Subject matter may vary from year to year. Three term-hours; lectures.

Differentiable structures, smooth manifolds and submanifolds, immersions and submersions, vector fields and differential forms, orientation and integration, de Rham cohomology. Three term-hours; lectures.

Stabilization and optimization of controlled dynamical systems under probabilistic uncertainty. Topics include: review of probability, controlled Markov chains, martingale and Lyapunov methods for stochastic stability, dynamic programming, partially observed models and non-linear filtering, the Kalman Filter, average cost problems, learning and computational methods, decentralized stochastic control, and stochastic control in continuous-time. (Offered jointly with MTHE- 472*.) Three term hours, fall or winter; lectures.

An introduction to the fundamental principles of the theory of communication. Topics include:information measures, entropy, mutual information, divergence; modeling of information sources, discrete memoryless sources, Markov sources, entropy rate, source redundancy, fundamentals of lossless data compression, block encoding, variable-length encoding, Kraft inequality, design of Shannon-Fano and Huffman codes; fundamentals of channel coding, channel capacity, noisy channel coding theorem, channels with memory, lossless information transmission theorem; continuous-alphabet sources and channels, differential entropy, capacity of discrete-time and band-limited continuous-time Gaussian channels; rate-distortion theory, lossy data compression, rate-distortion theorem, lossy information transmission theorem. (Offered jointly with MATH/MTHE-474*). Three term hours; lectures.

Fundamentals of the theoretical and practical (algorithmic) aspects of lossless and lossy data compression. Topics include: adaptive Huffman coding, arithmetic coding, the fundamental performance limits of universal lossless coding, Lempel-Ziv and related dictionary based methods, the Burrows-Wheeler transform, elements of Kolmogorov complexity theory, rate-distortion theory, scalar and vector quantization, applications to speech and image coding. (Offered jointly with MATH/MTHE-477*.)

PREREQUISITE: MATH-874*

This course covers performance models for data networking, delay models and loss models; analysis of multiple access systems, routing, and flow control; multiplexing; priority systems; satellite multiple access, wireless networking, wireless sensor networks. Knowledge of networking protocols is not required. (Offered jointly with MATH/MTHE-484*.) Three term hours; lectures.

PREREQUISITE: STAT-855*

This course provides basic knowledge in real and complex analysis at the graduate level on the following topics: Lebesgue measure and integration theory; elementary Hilbert space theory; examples of Banach space techniques. Three term-hours, fall; lectures.

This course provides basic knowledge in real and complex analysis at the graduate level on the following topics: basic theory of Fourier transforms; basic elements of spectral theory and Banach algebras; complex analysis. Three term-hours, winter; lectures.

This course provides basic knowledge in algebra at the graduate level on the following topics: elementary theory of groups; elementary theory of rings and modules; Galois theory. Three term-hours, fall; lectures.

This course provides basic knowledge in algebra at the graduate level on the following topics: representation theory of finite groups through characters; advanced theory of modules; advanced theory of rings. Three term-hours, winter; lectures.

This course provides basic knowledge in probability at the graduate level. Topics will include: basic notions and concepts of Probability Theory; characteristic functions; law of large numbers and central limit theorem; martingales; stochastic processes. Three term-hours, winter; lectures.

This course provides basic knowledge in mathematical statistics at the graduate level. Topics will include: Classical and Bayesian inference, Multivariate Gaussian distribution and its applications in Statistics; decision theory; basic techniques of non-parametric estimation. Three term-hours, fall; lectures.

This course provides basic knowledge in mathematical statistics at the graduate level. Topics will include: Weak convergence in metric spaces; Delta method; Method of moments; M-estimation; Asymptotic normality and efficiency; Likelihood ratio test; U statistics; Bootstrap; Applications in Statistics. Three term-hours, winter; lectures.

Advanced topics course, normally offered in the summer term, by a research institute in Canada or abroad can be taken for credit with the permission of the Supervisor and Coordinator of Graduate Studies and in cooperation with Institute organizers. Grades are assigned on a PASS - FAIL basis.

Subject matter will vary from year to year. Three term-hours; Seminar or reading course.

Subject matter will vary from year to year. Three term-hours; Seminar or reading course.

Subject matter will vary from year to year. Three term-hours; Seminar or reading course.

Subject matter will vary from year to year. Three term-hours; seminar or reading course.

Subject matter will vary from year to year. Three term-hours; seminar or reading course.

Subject matter will vary from year to year. Three term-hours; seminar or reading course.

Subject matter will vary from year to year. Three term-hours; seminar or reading course.

Subject matter will vary from year to year. Three term-hours; seminar or reading course.

Subject matter will vary from year to year. Three term-hours; seminar or reading course.

Subject matter will vary from year to year. Three term-hours; Seminar or reading course.

Subject matter will vary from year to year. Three term-hours; Seminar or reading course.

Subject matter will vary from year to year. Three term-hours; Seminar or reading course.

Subject matter will vary from year to year. Three term-hours; Seminar or reading course.

Subject matter will vary from year to year. Three term-hours; Seminar or reading course.

Subject matter will vary from year to year. Three term-hours; Seminar or reading course.

Subject matter will vary from year to year. Three term-hours; Seminar or reading course.

Subject matter will vary from year to year. Three term-hours; Seminar or reading course.

Subject matter will vary from year to year. Three term-hours; Seminar or reading course.

Subject matter will vary from year to year. Three term-hours; Seminar or reading course.

Subject matter will vary from year to year. Three term-hours; Seminar or reading course.

Subject matter will vary from year to year. Three term-hours; Seminar or reading course.

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Decision theory and Bayesian inference; principles of optimal statistical procedures; maximum likelihood principle; large sample theory for maximum likelihood estimates; principles of hypotheses testing and the Neyman-Pearson theory; generalized likelihood ratio tests; the chi-square, t, F and other distributions. (Offered jointly with STAT-463*.) Three term hours; lectures.

Many systems evolve with an inherent amount of randomness in time and/or space. The focus of this course is on developing and analyzing methods for analyzing time series. Because most of the common time--domain methods are unreliable, the emphasis is on frequency--domain methods, i.e. methods that work and expose the bias that plagues most time--domain techniques. Slepian sequences (discrete prolate spheroidal sequences) and multi--taper methods of spectrum estimation are covered in detail. (Offered jointly with MTHE-454*.) Three term-hours; lectures.

Markov chains, birth and death processes, random walk problems, elementary renewal theory, Markov processes, Brownian motion and Poisson processes, queuing theory, branching processes. (Offered jointly with MTHE/STAT-455*.) Three term hours; lectures.

This course is an introduction to Bayesian analysis and decision theory. Topics covered will include: elements of decision theory; Bayesian point estimation, set estimation, and hypothesis testing; special priors; computations for Bayesian analysis. (Offered jointly with STAT-456.)

Introduction to the theory and application of statistical algorithms. Topics may include classification, smoothing, model selection, optimization, sampling, supervised and unsupervised learning. (Offered jointly with STAT-457).

Introduction to the statistical packages SAS and R; classification; spline and smoothing spline; regularization, ridge regression and Lasso; model selection; resampling methods; importance sampling; Markov chain Monte Carlo; Metropolis-Hasting algorithm; Gibbs sampling; optimization. (Offered jointly with STAT-462.) Three term hours; lectures.

Autocorrelation and autocovariance, stationarity; ARIMA models; model identification and forecasting; spectral analysis. Applications to biological, physical and economic data. (Offered jointly with STAT-464*.) Three term-hours; lectures.

An overview of the statistical and lean manufacturing tools and techniques used in the measurement and improvement of quality in business, government and industry today. Topics include management and planning tools, Six Sigma approach, statistical process charting, process capability analysis, measurement system analysis. (Offered jointly with STAT-465*.) Three term-hours; lectures.

Introduction to the basic knowledge in programming, data management, and exploratory data analysis using SAS software: data manipulation and management; output delivery system; advanced text file generation, statistical procedures and data analysis, macro language, structure query language, and SAS applications in clinical trial, administrative financial data. (Offered jointly with STAT 466*). Three term-hours; lectures.

Simple random sampling; Unequal probability sampling; Stratified sampling; Cluster sampling; Multi‐stage sampling; Analysis of variance and covariance; Block designs; Fractional factorial designs; Split‐plot designs; Response surface methodology; Robust parameter designs for products and process improvement. (Offered jointly with STAT-471*.) Three term hours; lectures.

An introduction to advanced regression methods for binary, categorical, and count data. Major topics include maximum-likelihood method, binomial and Poisson regression, contingency tables, log linear models, and random effect models. The generalized linear models will be discussed both in theory and in applications to real data from a variety of sources.(Offered jointly with STAT-473*.)

Introduces the theory and application of survival analysis: survival distributions and their applications, parametric and nonparametric methods, proportional hazards models, counting process and proportional hazards regression, planning and designing clinical trials. (Offered jointly with STAT-486*.) Three term-hours; lectures.

Under the guidance of the supervisor, students will carry out a practicum project in a health research group/site and practise biostatistical methods and data analysis, or conduct methodology research in a biostatistical project. Students will summarize the results of the project in a written report that will be reviewed and orally defended.

Subject matter will vary from year to year. Three term-hours; Seminar or reading course.

Subject matter will vary from year to year. Three term-hours; Seminar or reading course.

Subject matter will vary from year to year. Three term-hours; Seminar or reading course.

Subject matter will vary from year to year. Three term-hours; Seminar or reading course.

Subject matter will vary from year to year. Three term-hours; Seminar or reading course.

Subject matter will vary from year to year. Three term-hours; Seminar or reading course.