Math Courses
5000 level and above are graduate courses.
4000 level are undergraduate courses that may be taken for graduate credit.
MATH COURSES
4103 Finite Dimensional Vector Spaces
Linear functions, matrix representation of linear transformations, scalar product, special representation of linear transformations. Prerequisite: MATH 3083
4113 Introduction to Abstract Algebra II
Topics in abstract algebra including finite abelian groups, linear groups, factorization in commutative rings, quadratic field extensions, Gaussian integers. Wedderburn's theorem, and multilinear algebra. Prerequisite: MATH 3113.
4153 Mathematical Modeling
Mathematical techniques for formulating, analyzing, and criticizing models taken from the biological, social, and physical sciences. Techniques include graphical methods, stability, optimization, and phase plane analysis. Prerequisite: MATH 3404.
4163 Dynamic Models in Biology
Mathematical and computational techinques for developing,executing, and analyzing dynamic models arising in the biological sciences. Both discrete and continuous time models are studied. Applications include population dynamics, cellular dynamics, and the spread of infectious diseases. Prerequisite: MATH 2554.
4253 Symbolic Logic I
Rigorous analyses of the concepts of proof, consistency, equivalence,validity, implication, and truth. Full coverage of truth-functionallogic and quantification theory (predicate calculus). Discussionof the nature and limits of mechanical procedures (algorithms) for proving theorems in logic and mathematics. Informal accountsof the basic facts about infinite sets. (Same as PHIL 4253)
4353 Numerical Linear Algebra
Numerical methods for problems of linear algebra, including the solution of very large systems, eigenvalues, and eigenvectors. Prerequisite: MATH 3083.
4363 Numerical Analysis
General iterative techniques, error analysis, root finding, interpolation, approximation, numerical integration, numerical solution of differential equations. Prerequisite: MATH 3404
4503 Differential Geometry and Vector Calculus
Topics include: Vector differential and integral calculus, Stokes Theorem in 3-space, classical differential geometry in 3-space (curves, surfaces), differential forms, general Stokes Theorem, applications to hydrodynamics, and electromagnetism. Prerequisites: MATH 2574.
4513 Advanced Calculus I
The real and complex number systems basic set theory and topology sequences and series continuity differentiation Taylors theorem Emphasis is placed on careful mathematical reasoning. Prerequisite: MATH 2574 and MATH 3083.
4523 Advanced Calculus II
The Riemann-Stieljes integral uniform convergence of functions Fourier series, implicit function theorem, Jacobians, and derivatives of higher order. Prerequisite: MATH 4513.
504V Special Topics for Teachers
Current topics in mathematics of interest to secondary schoool teachers. May be repeated for credit. Prerequisite: graduate standing and consent.
510V Mathematics Seminar
Members of the faculty and advanced students meet for presentation and discussion of topics. Prerequsite: graduate standing.
5123 Algebra I
What the beginning graduate student should know about algebra: groups, rings, modules, algebras, categories, homological algebra, Galois theory, Lie algebras. Prerequisite: MATH 3113.
5133 Algebra II
Continuation of 5123. Prerequisite: MATH 5123.
5303 Ordinary Differential Equations
Existence, uniqueness, stability, qualitative behavior, and numerical solutions. Prerequisites: programming experience, MATH 3404 and MATH 4513.
5313 Partial Differential Equations
Classification, boundary value problems, applications, numerical solutions. Prerequisites: MATH 3423 and MATH 4513.
5363 Scientific Computation and Numerical Methods
An introduction to numerical methods used in solving various problems in engineering and the sceinces.
5453 Functional Analysis I
Linear vector spaces, linear operators. Prerequisite: MATH 5513.
5503 Theory of Functions of Real Variable I
Real number system, Lebesque measure, Lebesque integral, convergence theorems, differentiation of monotone functions, absolute continuity and the fundamental theorem of calculus L^P spaces, Holder and Minkowski inequalities, and bounded linear functionals on the L^P spaces. Prerequisite: MATH 4523.
5513 Theory of Functions of a Real Variable II
Measure and integration on abstract measure spaces, signed measures, Hahn decomposition, Radon-Nikdoym theorem, Lebesque decomposition, measures on algebras and their extensions, product measures, and Fubini's theorem. Prerequisite: MATH 5503.
5523 Theory of Functions of Complex Variable I
Complex numbers, analytic functions, power series, complex integration, Cauchy's Theorem and integral formula, maximum principle, singularities, Laurent series, Mobius maps. Prerequisite: MATH 4513.
5533 Theory of Functions of Complex Variable II
Riemann Mapping Theorem, analytic continuation, harmonic functions, entire functions. Prerequisite: MATH 5523.
5703 Foundations of Topology
Metric and general topological spaces, separation axioms, Urysohn's lemma, Tietze extension theorem, connectedness, compactness, and the Tychonoff theorem. Prerequisite: MATH 4513.
5713 Algebraic Topology
Homotopy, singular and relative homology, excision theorem, the Mayer-Vietoris sequence, Beti numbers, and the Euler characteristic. Prerequisite: MATH 5703.
600V Master's Thesis
Prerequisite: graduate standing.
610V Directed Readings
619V Topics in Algebra
Current research interest in algebra.
659V Topics in Analysis
Current research inrerests in analysis.
679V Topics in Topology
Current research interests in topology.
700V Doctoral Dissertation
STAT COURSES
4001L Statistics Laboratory
Emphasis on use of integrated statistical packages to complement statistical methodology being concurrently in STAT 4003. Corequisite: STAT 4003.
4003 Statistical Methods
Concepts of probability, sampling, regression, and experimental design. Prerequisite: MATH 2554. Corequisite: STAT 4001L.
4033 Nonparametric Statistical Methods
Chi square tests, Kolmogorov-Smirnov goodness-of-fit tests, the Mann-Whitney and Wilcoxon two-sample tests, and various nonparametric measures of association. Prerequisites: MATH 1203 and junior standing.
4043 Sampling Techniques
Considers optimum techniques of simple random, stratified random, cluster, systematic and multistage sampling from finite populations subject to cost precision constraints. Wide range of applications. Prerequisite: STAT 4003.
4373 Experimental Design
Topics in design and analysis of planned experiments including randomized block, Latin square, split plot, and BIB designs, use of fractional factorial replication, and repeated measures. Prerequisite: STAT 4003.
5103 Theory of Statistics
Fundamentals of probability, distribution theory, and random variables; expected value, moments and generating functions; classic parametric families of distributions; central limit theorems, inequalities, and laws of large numbers. Prerequisite: MATH 2574.
5113 Statistical Inference
Statistical theory of estimation and testing hypotheses. Prerequisite: STAT 5103.
5313 Regression Analysis I
Matrix formulation of least squares and multiple regression models. Estimability and use of the generalized inverse in analysis of variance and covariance models of less than full rank. Computational aspects are emphasized.
5333 Analysis of Categorical Responses
A modern treatment, including extensions of classical probit analysis, multivariate logistic models, GSK model, loglinear models in analysis of multiway contingency tables, and nonmetric multidimensional scaling. Prerequisites: STAT 5313.
5343 Stochastic Processes
Markov chains, branching processes, birth-death processes, queuing theory with applications. Prerequisite: STAT 5103.
5353 Methods of Multivariate Analysis II
Hotelling's T2 procedures, multivariate analysis of variance, discriminant function analysis in problems of classification, multidimensional scaling, and cluster analysis. Prerequisite: STAT 5313.
5383 Time Series Analysis
Identification, estimation and forecasting of time series. Spectral analysis including the fast Fourier transform. Computational aspects are emphasized.
Prerequisite: STAT 5103.
5413 Spatial Statistics
Applied spatial statistics, covering univariate spatial modeling (kriging), multivariate spatial modeling (cokriging), methods of estimation and inference, and spatial sampling designs. Special relevance to remote sensing. Prerequisite: STAT 5313.
610V Research in Statistics
Prerequisite: graduate standing.
639V Topics in Statistics
Current state of the art or methodology in one of the topics: Multivariate Analysis, Time Series Analysis, Sequential Analysis, Factor Analysis or Biostatistics.