IX. Graduate Programs
Mathematics and Statistics
Courses
Mathematics
| MATH*6011 Dynamical Systems I U [0.50] |
|---|
| Basic theorems on existence, uniqueness and differentiability; phase space, flows, dynamical systems; review of linear systems, Floquet theory; Hopf bifurcation; perturbation theory and structural stability; differential equations on manifolds. Applications drawn from the biological, physical, and social sciences. |
| MATH*6012 Dynamical Systems II U [0.50] |
|---|
| The quantitative theory of dynamical systems defined by differential equations and discrete maps, including: generic properties; bifurcation theory; the center manifold theorem; nonlinear oscillations, phase locking and period doubling; the Birkhoff-Smale homoclinic theorem; strange attractors and deterministic chaos. |
| MATH*6021 Optimization I U [0.50] |
|---|
| A study of the basic concepts in: linear programming, convex programming, non-convex programming, geometric programming and related numerical methods. |
| MATH*6022 Optimization II U [0.50] |
|---|
| A study of the basic concepts in: calculus of variations, optimal control theory, dynamic programming and related numerical methods. |
| MATH*6031 Functional Analysis U [0.50] |
|---|
| Review of metric, normed, and inner product spaces; Banach contraction principle; brief introduction to measure and integration; elementary Fourier analysis; adjoint and compact operators; nonlinear operators and the Frechet derivative; Baire category theorem; principle of uniform boundedness; open mapping theorem; principle ot uniform boundedness; closed graph theorem. |
| MATH*6041 Partial Differential Equations I U [0.50] |
|---|
| Classification of partial differential equations. The Hyperbolic type, the Cauchy problem, range of influence, well- and ill-posed problems, successive approximation, the Riemann function. The elliptic type: fundamental solutions, Dirichlet and Neumann problems. The parabolic type: boundary conditions, Green's functions and separation of variables. Introduction to certain non-linear equations and transformations methods. |
| MATH*6042 Partial Differential Equations II U [0.50] |
|---|
| A continuation of some of the topics of Partial Differential Equations I. Also, systems of partial differential equations, equations of mixed type and non-linear equations. |
| MATH*6051 Mathematical Modelling U [0.50] |
|---|
| Selected advanced topics in mathematical modelling, possibly in conjunction with the departmental Mathematics and Statistics Clinic. |
| MATH*6071 Biomathematics U [0.50] |
|---|
| The application of mathematics to model and analyze biological systems. Specific models to illustrate the different mathematical approaches employed when considering different levels of biological function. |
| MATH*6091 Topics in Analysis U [0.50] |
|---|
| Selected topics from topology, real analysis, complex analysis, and functional analysis. |
| MATH*6181 Topics in Applied Mathematics I U [0.50] |
|---|
| This course provides graduate students, either individually or in groups, with the opportunity to pursue topics in applied mathematics under the guidance of graduate faculty. Course topics will normally be advertised by faculty in the semester prior to their offering. Courses may be offered in any of lecture, reading/seminar, or individual project formats. |
| MATH*6182 Topics in Applied Mathematics II U [0.50] |
|---|
| This course provides graduate students, either individually or in groups, with the opportunity to pursue topics in applied mathematics under the guidance of graduate faculty. Course topics will normally be advertised by faculty in the semester prior to their offering. Courses may be offered in any of lecture, reading/seminar, or individual project formats. |
| MATH*6400 Numerical Analysis I U [0.50] |
|---|
| Topics selected from numerical problems in: matrix operations, interpolation, approximation theory, quadrature, ordinary differential equations, partial differential equations, integral equations, nonlinear algebraic and transcendental equations. |
| MATH*6410 Numerical Analysis II U [0.50] |
|---|
| One or more topics selected from those discussed in Numerical Analysis I, but in greater depth. |
| MATH*6990 Mathematics Seminar U [0.00] |
|---|
| Students will review mathematical literature and present a published paper. |
Statistics
| STAT*6700 Stochastic Processes U [0.50] |
|---|
| The content of this course is to introduce Brownian motion leading to the development of stochastic integrals thus providing a stochastic calculus. The content of this course will be delivered using concepts from measure theory and so familiarity with measures, measurable spaces, etc., will be assumed. |
| STAT*6721 Stochastic Modelling U [0.50] |
|---|
| Topics include the Poisson process, renewal theory, Markov chains, Martingales, random walks, Brownian motion and other Markov processes. Methods will be applied to a variety of subject matter areas. |
| STAT*6741 Statistical Analysis for Reliability and Life Testing U [0.50] |
|---|
| Statistical failure models, order statistics, point and interval estimation procedures for life time distributions, testing reliability hypotheses, Bayes methods in reliability, system reliability. |
| STAT*6761 Survival Analysis U [0.50] |
|---|
| Kaplan-Meier estimation, life-table methods, the analysis of censored data, survival and hazard functions, a comparison of parametric and semi-parametric methods, longitudinal data analysis. |
| STAT*6801 Advanced Data Analysis I U [0.50] |
|---|
| Residual analysis, deletion residuals, influential points,added variable plots, constructed variables, families of transformations, jackknife and bootstrap methods, local linear regression, regression splines and cubic smoothing splines. |
| STAT*6802 Advanced Data Analysis II U [0.50] |
|---|
| Generalized linear and generalized additive models, linear and nonlinear mixed effects models, parameteric and semiparametric analysis of longitudinal and clustered data, generalized estimating equations, applications to categorical and spatial data. |
| STAT*6821 Multivariate Analysis U [0.50] |
|---|
| This is an advanced course in multivariate analysis and one of the primary emphases will be on the derivation of some of the fundamental classical results of multivariate analysis. In addition, topics that are more current to the field will also be discussed such as: multivariate adaptive regression splines; projection pursuit regression; and wavelets. |
| STAT*6841 Statistical Inference U [0.50] |
|---|
| Bayesian and likelihood methods, large sample theory, nuisance parameters, profile, conditional and marginal likelihoods, EM algorithms and other optimization methods, estimating functions, MonteCarlo methods for exploring posterior distributions and likelihoods, data augmentation, importance sampling and MCMC methods. |
| STAT*6850 Advanced Biometry U [0.50] |
|---|
| Topics on advanced techniques for analyzing data from biological systems. In particular, univariate discrete models, stochastic processes as it relates to population dynamics and growth models with time dependencies, generalized discrete models for spatial patterns in wildlife, the theoretical foundation and recent results in aquatic bioassays, and other topics relating to the student's research interest. |
| STAT*6860 Linear Statistical Models U [0.50] |
|---|
| Generalized inverses of matrices; distribution of quadratic and linear forms; regression or full rank model; models not of full rank; hypothesis testing and estimation for full and non-full rank cases; estimability and testability; reduction sums of squares; balanced and unbalanced data; mixed models; components of variance. |
| STAT*6870 Experimental Design U [0.50] |
|---|
| This is an advanced course in experimental design which emphasizes proofs of some of the fundamental results in the topic. The topics will include: design principles; design linear models; designs with several factors; confounding in symmetrical factorials; fractional factorials. |
| STAT*6880 Sampling Theory U [0.50] |
|---|
| Theory of equal and unequal probability sampling. Topics in: simple random, systematic, and stratified sampling; ratio and regression estimates; cluster sampling and subsampling; double sampling procedure and repetitive surveys; nonsampling errors. |
| STAT*6950 Statistical Methods for the Life Sciences F [0.50] |
|---|
| Analysis of variance, completely randomized, randomized complete block and latin square designs; planned and unplanned treatment comparisons; random and fixed effects; factorial treatment arrangements; simple and multiple linear regression; analysis of covariance with emphasis on the life sciences. STAT*6950 and STAT*6960 are intended for graduate students of other departments and may not normally be taken for credit by mathematics and statistics graduate students. |
| STAT*6960 Design of Experiments and Data Analysis for the Life Sciences W [0.50] |
|---|
| Principles of design; randomized complete block; latin square and extensions the split plot and extension; incomplete block designs; confounding and fractional replication of factorial arrangements; response surfaces the analysis of series of experiments; the general linear model; multiple regression and data analytic techniques. STAT*6950 and STAT*6960 are intended for graduate students of other departments and may not normally be taken for credit by mathematics and statistics graduate students. |
| STAT*6970 Statistical Consulting Internship U [0.25] |
|---|
| This course provides experience in statistical consulting in a laboratory and seminar environment. The student will participate in providing statistical advice and/or statistical analyses and participate in seminar discussions of problems arising from research projects in various disciplines. |