# Course Descriptions

These are the currect course descriptions of graduate courses in MATH and STAT from the university gradute calendar. Use the Filter Courses bar to narrow your search within each subject.

## Mathematics

### MATH 800 - Comprehensive Review of a Selected Topic in Mathematics

The student will conduct an in-depth literature review of a selected area in Mathematics and prepare a report pertaining to the selected topic. The topic will be chosen in consultation with the supervisor and the Department Head. A final examinaton (written, oral or both) will be conducted by a committe of the Department.

### MATH 802 - Major Essay in Mathematics

Essay on a selected topic for students in the course-based MSc program in Mathematics.

### MATH 803 - Approved Summer School

This course is available to full-time Mathematics graduate students in good standing. Students will participate in a summer school offered by an approved institute. The school and credit award must be approved by the Graduate Coordinator for Mathematics and Statistics (or designee).

***Prerequisite: Approval of Department Head.***

*Note: Students may only take MATH 803 once in their program.*

### MATH 810 - Measure & Integration

Integration and measure theory, spaces of continuous functions, and Lp spaces.

### MATH 812 - Complex Analysis

Riemann mapping theorem, analytic continuation, Riemann surfaces.

### MATH 813 - Functional Analysis

Banach spaces, Banach algebras, and operator theory.

### MATH 814 - Operator Algebras

C*-algebras and von Neumann algebras.

### MATH 816 - Introduction to Quantum Information Theory

A first course in the mathematics of quantum information theory. Topics include information measures, quantum states and observables, qubits, entanglement, quantum channels, entropy, and measurements.

### MATH 818 - Intro to Lie Algebras and Representation Theory

The course is an introduction to the structure of finite dimensional complex semisimple Lie algebras, via root systems, as well as their finite dimensional irreducible representations, through highest weight modules.

### MATH 819 - Topics in Analysis

Advanced study of selected areas of analysis.

### MATH 820 - Introduction to Commutative Algebra

A first graduate course in commutative algebra. Topics include prime and maximal ideals, radicals, Nakayama's Lemma, exact sequences, tensor products, localization, Noetherian and Artinian rings and selected additional topics.

### MATH 821 - Number Theory

Topics from analytic and algebraic number theory.

### MATH 822 - Linear Algebra

Vector spaces, linear transformations and matrices, canonical forms, multilinear algebra.

### MATH 823 - Algebra

Advanced study of group theory, Galois theory, and ring and module theory.

### MATH 824 - Topics in Algebra

Advanced study of selected areas of algebra.

### MATH 825 - Matrix Analysis

Matrix canonical forms, norms, spectral theory, perturbation theory, special classes of matrices.

### MATH 826 - Combinatorial Matrix Theory

Amtrices arising from directed and undirected graphs, and related connections between matrix theory and combinational mathematics.

### MATH 827 - Graph Theory

Advanced study of selected areas of graph theory.

### MATH 828 - Combinatorics

Advanced study of selected areas of combinatorics.

### MATH 831 - Differential Geometry

Differentiable manifolds, the tangent bundle, differential forms, and the general Stokes' theorem.

### MATH 832 - Topics in Differential Geometry and Topology

Advanced study of selected areas of differential geometry and topology.

### MATH 837 - Intro to Algebraic Number Theory

A course on rings of integers of algebraic number fields, Dedekind rings, and Ideal Class Groups.

### MATH 838 - Associative Algebras, Groups, and Representation Theory

An introductory course on the fundamental results concerning associative algebras, groups, and the representation theory of groups and algebras.

### MATH 841 - General Topology

Separability of spaces, paracompactness, metrization theorems, function spaces.

### MATH 842 - Algebraic Topology

Introduction to homotopy groups, and to the homology and cohomology of topological spaces.

### MATH 843 - Homological Algebra

A first graduate course in homological algebra. Topics include modules over rings, chain complexes, homology, projective and injective resolutions, derived functors, abelian categories, derived categories, and selected additional topics.

### MATH 849 - Topics in Topology

Advanced study of selected areas of topology.

### MATH 869 - Numerical Analysis

Advanced study of selected areas of numerical analysis.

### MATH 881 - Partial Differential Equations

The Cauchy problem, the Fredholm alternaive in Banach space, the potential equation, the Dirichlet problem, the heat equation, Green's functions, and the separation of variables.

### MATH 882 - Topics in Applied Mathematics

Advanced study of selected topics in applied mathematics.

### MATH 890AG - Topics in Combinatorics

This course will include transitivity in graphs, eigenvalues of graphs, homomorphisms of graphs, and some results from extremal set theory, particularly the Erdos-Ko-Rado theorem that can be proven using algebraic graph theory.

### MATH 890AH - Topics in Complex Manifold Theory

definition, examples incl. projective spaces, tori, type decompositions as (1, 0), (0, 1), holomorphic functions, holomorphic forms, sheaves, sheaf cohomology, Dolbeault cohomology, divisors, fiber bundles incl. line bundles and vector bundles, almost complex manifolds, Hermitian metrics, Kaehler metrics, connections

### MATH 890AI - Lie Groups

This course is an introduction to the main fundamental results of Lie Group theory through an extensive study of the classical groups.

### MATH 890AK - Extremal combinatorics

An introduction to extremal combinatorics and extremal set theory.

### MATH 890AL - Permutation Groups

A course in the theory of permutation groups, with an emphasis on actions of finite permutation groups on combinatorial structures, such as graphs, designs and geometries.

### MATH 890AM - Topics In Analysis II

Advanced study of selected areas of analysis and operator algebras.

### MATH 890AN - Advanced Topics in Functional Analysis

Locally convex topologies, geometry of Banach spaces, bounded and

unbounded operators on Banach spaces, spectral theory.

### MATH 890AP - Quiver representations of algebras

The algebra of a quiver; Auslander-Reiten quivers; classification of finite dimensional algebras and their representation theory in terms of quivers.

### MATH 890AQ - Matrix Analysis and Entrywise Positivity Preservers

This course is an advanced course in matrix analysis and will concentrate on the topic of entrywise positivity preservers. Preservers are functions that operate on the individual entries of matrices and preserve the cone of positive semidefinite matrices.

### MATH 890AT - Design Theory

This course will be an introduction to design theory. This course will include block designs, symmetric designs, Hadamard matrices and orthogonal arrays. We also study distance regular graphs, projective and affine space. We will look at focus on constructions and bounds of designs as well as connections to other areas of math.

### MATH 890AU - Combinatorial Association Scheme

This class will be on Association Schemes with a combinatorial perspective. The course will look at specific association scheme arising in graph theory, such as distance regular graphs, strongly regular graphs and the Johnson scheme. Including a focus on the symmetric group and how it applies to Schurian association schemes.

### MATH 890AV - Continuum Mechanics

Tensor analysis, fundamentals of continuum mechanics, Navier-Stokes equations.

### MATH 900 - Seminar

Preparation and presentation of a one-hour lecture to graduate students and faculty.

### MATH 901 - Research

Thesis research.

### MATH 902 - Research Tools in Mathematics

This course teaches students about the computing and library resources available in the Mathematics and Statistics department. This course also includes an introduction to using LaTeX for preparing papers, writing research proposals, and giving academic presentations.

### MATH 903 - Comprehensive Exam 1

Students must complete a comprehensive exam in one of the following topics: Matrix Theory and Linear Algebra, Commutative Algebra, Abstract Algebra, or Combinatorics and Graph Theory. It is evaluated on a pass/fail basis.

### MATH 904 - Comprehensive Exam 2

Students must complete a comprehensive exam in one of the following topics: Topology, Algebraic Topology, Functional Analysis, Measure and Integration, Differential Geometry, or Probability Theory. It is evaluated on a pass/fail basis.

### MATH 905 - Research Proposal

Students are required to submit a written research proposal for their PhD thesis research project during its early stages. The candidate will give a seminar before the department to defend their proposal. The topic must be approved by the research supervisor and the candidate's PhD committee. It is evaluated on a pass/fail basis. This course is required of all PhD students in Mathematics, and will usually be completed following the completion of MATH 903 and 904.

## Statistics

### STAT 754 - Linear Statistical Models

Simple linear regression; multiple linear regression; diagnostics and remedial measures for regression models; remedial measures and alternative regression techniques; multicollinearity diagnostics.

*Note: Students transferring to the MSc Thesis-Based Program or PhD Program from the MSc Course-Based Program may not receive any credit for completion of STAT 754.*

### STAT 757 - Sampling Theory

Simple random sampling, sample size, estimation of ratios and ratio estimators, stratified sampling, cluster sampling, non-response in surveys and non-sampling errors.

*Note: Students transferring to the MSc Thesis-Based Program or PhD Program from the MSc Course-Based Program may not receive any credit for completion of STAT 757.*

### STAT 800 - Comprehensive Review

The student will conduct an in-depth literature review of a selected area in Statistics and prepare a report pertaining to the selected topic. The topic will be chosen in consultation with the supervisor and the Department Head. A final examination (written, oral or both) will be conducted by a committee in the Department.

### STAT 802 - Major Essay in Statistics

Essay on a selected topic for students in the course-based MSc program in Statistics.

### STAT 803 - Approved Summer School

This course is available to full-time Statistics graduate students in good standing. Students will participate in a summer school offered by an approved institute. The school and credit award must be approved by the Graduate Coordinator for Mathematics and Statistics (or designee).

***Prerequisite: Approval of Department Head.***

*Note: Students may only take STAT 803 once in their program.*

### STAT 818 - Time Series Analysis and Forecasting

A first graduate course in time series models and analysis. Topics include deterministic and stochastic models, stationary and non-stationary time series models, state space models, spectral analysis, and selected additional topics. This course includes a lab component.

*Note: Students may receive credit for one of STAT 818, STAT 418, or ACSC 418.*

### STAT 819 - Advanced Applications of Fourier Analysis in Life Sciences

Advanced applications of Fourier Analysis. Topics include confidence intervals, hypothesis testing, modelling linear relationships, time series and Fourier analysis. Advanced applications of Fourier Analysis in life sciences will be reviewed. The list of applications may vary.

### STAT 826 - Advanced Survival Analysis

Life table, survival distributions, types of censoring, estimation and inference for basic survival quantities, proportional hazards regression model, goodness of fit tests.

### STAT 851 - Probability

Probability measures; distribution functions; sequences of random variables; characteristic functions; modes of convergence; convergence theorems; weak and strong laws of large numbers; Central Limit Theorem

### STAT 852 - Statistical Inference

Detailed theoretical development of statistical interference; statistical models; exponential families, sufficiency; completeness; properties of point estimation; testing hypothesis and confidence regions; asymptotic properties of estimators.

### STAT 853 - Limit Theorems

Probability inequalities, weak limit theorems (central limit theorem, weak law of large numbers), strong limit theorems (strong law of large numbers, law of iterated logarithm).

### STAT 855 - Generalized Linear Models

Generalized linear models, exponential family, likelihood-based inference, analysis of contingency tables, estimation procedures.

### STAT 856 - Stochastic Processes

A first graduate course in stochastic processes. Topics include Markov chains, Poisson process, renewal theory, Brownian motions and selected additional topics. This class is cross-listed with STAT 456 and ACSC 456.

### STAT 858 - Statistical Modeling of Dependence and Extremes

A first graduate course in extreme value theory and copula dependence modelling. Topics include copula models, dependence measures, order statistics, maximum domains of attraction, extreme value distribution, peak over threshold method, generalized Pareto distribution and selected additional topics.

***Prerequisite: STAT 851 or permission of the Department Head.***

### STAT 859 - Design of Experiments

Completely randomized designs, randomized block designs, factorial and fractional factorial designs, nested designs, fixed and random effects models.

### STAT 862 - Advanced Topics in Stochastic Processes

This is an advanced course in stochastic processes. Topics include: Measure theoretic probability theory, stopping theorems, Poisson process, renewal processes, Markov processes, Brownian motion, Gaussian processes, martingales, stochastic integration, and applications.

### STAT 870 - Bootstrap Methods

A first course in Bootstrap techniques. Topics include bootstrap and jackknife procedures, confidence intervals, hypotheses testing, standard errors, regression models. Additional topics may vary. jackknife procedures, confidence intervals, hypotheses testing, standard errors, regression models. Additional topics may vary.

### STAT 872 - Large Sample Methods

Asymptotic behavior of estimators and test statistics, asymptotic relative efficiency, large sample theory for regression models.

### STAT 890AD - Analysis of Longitudinal Data

Exploring longitudinal data. General linear model for longitudinal data. Parametric model for the convariance structure. Generalized linear model for longitudinal data. Likelihood-based methods for categorical data. Missing values for longitudinal data.

### STAT 890AF - Directed Readings in Stochastic Processes

Directed readings in Stochastic Processes as selected by the instructor.

### STAT 890AG - Statistical Analysis with Missing Data

Missing data is a major issue in statistical analysis. This course introduces the four common approaches for inference in models with missing values, including maximum likelihood, multiple imputation, fully Bayesian, and weighted estimating equations. Computational tools (e.g. the EM algorithm and the Gibbs' sampler) will be discussed.

### STAT 890AI - Multivariate Statistical Modelling

Univariate generalized linear models, models for multicategorical responses, multivariate extensions of generalized linear models, selecting and checking models, semi and nonparametric approaches to regression analysis.

### STAT 890AJ - Statistical Analysis for Language Assessment

This course explores statistical methods for language test validity and reliability. The main focus will be on Rasch models.

### STAT 890AR - Stochastic Differential Equations for Finance

Modelling of mathematical finances in continuous time, stochastic integrals Itô's formula

### STAT 890AS - Advanced Applied Multivariate Statistics in Educational Psychology

The purpose of this course is to teach the application of multivariate analysis to research problems in Educational Psychology. This course will include advanced instruction in applied multivariate analysis, including: simple linear regression, multiple regression, nonlinear regression, time-series analysis, logistic regression, MANOVA, factor analysis, between-groups comparison, profile analysis, structural equation modeling and path analysis. The course is designed to broaden one’s understanding of applied statistics, and designing quantitative studies.

### STAT 890AT - Regression Models for Time Series Analysis

Times Series Following Generalized Linear Models: Regression Models for Binary Time Series; Regression Models for Categorical Time Series; Regression for Count Time Series; Other models and Alternative ApproachesSTAT Space Models: Prediction and Interpolation

### STAT 890AW - Statistics in the Health Science

Function-Based Inference; Likelihood Tenet; Martingale; Bayes Factor; Empirical Likelihood; Jackknife and Bootstrap.

### STAT 890AX - Computational Statistics

A general introduction to computational methods in statistics including optimization, statistical estimation algorithms, bootstrapping/jackknife procedures, Monte Carlo sampling, generating random deviates, computation in the R programming language.

### STAT 900 - Seminar

Preparation and presentation of a one-hour lecture to graduate students and faculty.

### STAT 901 - Research

Thesis research

### STAT 902 - Research Tools in Statistics

This course teaches students about the computing and library resources available in the Mathematics and Statistics department. This course also includes an introduction to using LaTeX for preparing papers, writing research proposals, and giving academic presentations.

### STAT 903 - Comprehensive Exam 1

Students must complete a comprehensive exam in Probability Theory. The exam will also include one of the following elective topics: Stochastic Processes, Dependence and Extremes, Limit Theorems, or Measure and Integration. It is evaluated on a pass/fail basis.

### STAT 904 - Comprehensive Exam 2

Students must complete a comprehensive exam in Statistical Inference. The exam will also include one of the following elective topics: Generalized Linear models, Survival Analysis, Experimental Design, Time Series Analysis, Linear Models, or Sampling Theory. It is evaluated on a pass/fail basis.

### STAT 905 - Research Proposal

Students are required to submit a written research proposal for their PhD thesis research project during its early stages. The candidate will give a seminar before the department to defend their proposal. The topic must be approved by the research supervisor and the candidate's PhD committee. It is evaluated on a pass/fail basis. This course is required of all PhD students is Statistics, and will usually be completed following the completion of STAT 903 and 904.