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Course Criteria
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3.00 Credits
Introduction to the linear algebra of finite-dimensional vector spaces. Includes systems of equations, matrices, determinants, inner product spaces, spectral theory. Prerequisite: Math 310 or permission of instructor. Math 309 is not an explicit prerequisite but students already should be familiar with such basic topics from matrix theory as matrix operations, linear systems, row reduction, and Gaussian elimination. Material in early chapters on these topics are covered very quickly.
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3.00 Credits
Introduction to groups, rings, and fields. Includes permutation groups, group, and ring homomorphisms, field extensions, connections with linear algebra. Prerequisite: Math 429 or permission of the instructor.
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3.00 Credits
Life table analysis and testing; mortality, and failure rates; Kaplan-Meier or product-limit estimators, hypothesis testing and estimation in the presence of random arrivals and departures; and the Cox proportional hazards model. Techniques of survival analysis are used in medical research, industrial planning, and the insurance industry. Prerequisites: Math 309 and 3200, or permission of the instructor.
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3.00 Credits
Introduction to affine and projective algebraic varieties; the Zariski topology; regular and rational mappings; simple and singular points; divisors and differential forms; genus; the Riemann-Roch theorem. Prerequisites: Math 318, 429, and 430, or permission of the instructor.
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3.00 Credits
Introduction to statistical methods based in linear algebra. Topics include multivariate normal distributions; the distribution of quadratic forms; linear regression and ANOVAs; general linear hypotheses; principal component and linear discriminant models; multivariate linear regressions and MANOVAs; canonical correlations. If time allows, additional topics such as factor analysis; variance component and mixed models; factorial and fractional factorial models. Short computer programs are written in a language such as SAS or R. Prerequisites: Math 3200 and Math 309 (or Math 429), or permission of the instructor.
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3.00 Credits
Computer arithmetic, error propagation, condition number and stability; mathematical modeling, approximation and convergence; roots of functions; calculus of finite differences; implicit and explicit methods for initial value and boundary value problems; numerical integration; numerical solution of linear systems, matrix equations, and eigensystems; Fourier transforms; optimization. Various software packages may be introduced and used. Prerequisites: CSE 126, 131 or 200 (or other computer background with permission of the instructor); Math 217 and 309.
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3.00 Credits
Topic may vary with each offering of the course. Prerequisite: Math 449 or permission of the instructor.
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3.00 Credits
Topic and prerequisites may vary with each offering.
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3.00 Credits
An introduction to the Bayesian approach to statistical inference for data analysis in a variety of applications. Topics include: comparison of Bayesian and frequentist methods, Bayesian model specification, choice of priors, computational methods, empirical Bayes method, hands-on Bayesian data analysis using appropriate software. Prerequisite: Math 493 or permission of the instructor.
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3.00 Credits
An introduction to programming in SAS (Statistical Analysis System) and applied statistics using SAS: contingency tables and Mantel-Haenszel tests; general linear models and matrix operations; simple, multilinear, and stepwise regressions; ANOVAs with nested and crossed interactions; ANOVAs and regressions with vector-valued data (MANOVAs). Topics chosen from discriminant analysis, principal components analysis, logistic regression, survival analysis, and generalized linear models. Prerequisites: Math 3200 and 493 (or 493 concurrently).
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