| Math 1595 | Graduate Seminar (1-0) |
| Conferences and discussions of various topics in mathematics and statistics by faculty, graduate students, and outside speakers. Required of all graduate students during each semester of full-time enrollment. May not be counted more than once toward the degree requirement. Course web page | |
| MATH 5310 | Introduction to Applied Functional Analysis (3-0) |
| Elements of functional analysis for applications in statistics, optimization and computational partial differential equations (PDEs): normed spaces, Banach spaces, Lebesgue spaces, basic inequalities, inner product, Hilbert spaces, orthogonal projections, Riesz theorem, elements of Sobolev spaces. Prerequisites: MATH 2313 and MATH 3323. Course web page | |
| MATH 5311 | Applied Mathematics (3-0) |
| Mathematics 5311 is designed to introduce the student to those areas of mathematics that are useful in engineering and science. Topics are chosen from Differential Equations, Fourier Series, Calculus of Variations, and Theory of Algorithms. The course may be repeated once as content changes. Prerequisite: Instructor approval. Course web page | |
| MATH 5314 | Partial Differential Equations (3-0) |
| Partial derivatives and differential operators, classification of equations with emphasis on elliptic, parabolic and hyperbol physics, maximum principle and well-posedness, boundary formulations, Lax-Milgram lemma, overview of existence an Prerequisite: MATH 5310. Course web page | |
| MATH 5321 | Principles of Analysis (3-0) |
| Investigation of convergence, continuity, differentiability, compactness and connectedness, the Riemann-Stieljes integral, and sequences of functions. Prerequisite: MATH 3341. Course web page | |
| MATH 5325 | Principles of Algebra (3-0) |
| Groups, including subgroups, quotient spaces and homomorphisms, Ring Theory, including ideals and quotients, homomorphisms and polynomial rings. An introduction to modules and fields, including field extensions. Prerequisites: MATH 3325 and department approval. Course web page | |
| MATH 5329 | Numerical Analysis (3-0) |
| Introduction to approximation theory, interpolation, numerical differentiation and integration, solutions of linear and non-linear equations, numerical solution of differential equations, optimization. Emphasis is on error analysis and stability. Several practical examples and computer programs will be covered. Prerequisites: MATH 3323 and a working knowledge of a high-level programming language. Course web page | |
| MATH 5330 | Computational Methods of Linear Algebra (3-0) |
| Numerical methods involved in the computation of solutions of linear systems of equations, eigenvalues, linear least squares solutions; linear programming; error analysis. Prerequisites: MATH 3323 and a working knowledge of a high-level programming language. Course web page | |
| MATH 5331 | Real Variables (3-0) |
| Lebesgue integration, integration with respect to measure, absolute continuity, Fundamental Theorem of Calculus for the Lebesgue integral. Prerequisite: MATH 5321. Course web page | |
| MATH 5335 | Techniques in Optimization (3-0) |
| An introduction to the formulation of optimization problems and their numerical solution with application to problems in science and engineering. Emphasis on deterministic and stochastic techniques such as Newton type methods and simulated annealing. Prerequisites: Math 1411 with a grade of "C" or better and knowledge of a high- level programming language. Course web page | |
| MATH 5336 | Analysis of Categorical Data (3-0) |
| Exact nonparametric methods of inference using fast numerical algorithms to permute the observed data in all possible ways. Prerequisite: Department approval. Course web page | |
| MATH 5341 | General Topology (3-0) |
| Topics include: Separation, compactness, connectedness, paracompactness, metric spaces and metrization of toplogical spaces. Prerequisite: MATH 5321. Course web page | |
| MATH 5343 | Numerical Solution of Partial Differential Equations (3-0) |
| Introduction to finite difference and finite element methods for the solution of elliptic, parabolic, and hyperbolic partial differential equations. Prerequisites: (1) MATH 2326 or MATH 3326; MATH 3323; and MATH 4329, each with a "C" or better or their equivalents and (2) knowledge of a high level programming language. Course web page | |
| MATH 5351 | Complex Variables (3-0) |
| Complex integration and the calculus of residues. Analytical continuation and expansions of the analytic function. Entire, meromorphic, and periodic functions. Prerequisite: MATH 5321 or its equivalent as approved by the instructor. Course web page | |
| MATH 5360 | Introduction to Research in Mathematics Education (3-0) |
| An introduction to current research literature in mathematics education focusing on the relations between theories of cognition and learning and philosophies of mathematics. Topics may include constructivism, Vygotskian theory, genetic epistemology, and technological cognition. The course may be repeated once for credit as content changes. Prerequisites: MATH 3300 with a grade of "C" or better and department approval. Course web page | |
| MATH 5365 | Technology in the Mathematics Classroom (3-0) |
| An introduction to technology used in mathematics education such as graphing calculators, computer algebra systems, course specific software and the use of the Internet, and an exploration of its appropriate and effective use in the mathematics classroom. Prerequisite: Department approval. Course web page | |
| MATH 5370 | Seminar (3-0) |
| Various topics not included in regular courses will be discussed. May be repeated once for credit as the topics vary. Prerequisite: Instructor approval. | |
| MATH 5380 | Mathematical Statistics I (3-0) |
| The probabilistic foundations of mathematical statistics. Probability spaces, random variables, univariate and multivariate probability distributions, conditional distributions, expectation, generating functions, multivariate transformations, modes of convergence, and limit theorems. Prerequisite: STAT 3330 or its equivalent as approved by instructor. Course web page | |
| MATH 5381 | Mathematical Statistics II (3-0) |
| A continuation of Mathematical Statistics I. Parametric statistical models, sufficiency, exponential families, methods of estimation, comparison of estimators, confidence intervals, hypothesis testing, optimal tests, likelihood ratio tests, large sample theory. Prerequisite: MATH 5380. Course web page | |
| MATH 5385 | Statistics in Research (3-0) |
| An introduction to statistical modeling of a univariate response conditional on a test of explanatory variables. Classical formulation of multiple linear regression and analysis of variance. Some discussion of experimental design from power considerations. Selected topics from generalized linear models, nonparametric regression, and quasi-likelihood estimation. Emphasis is on model building, fitting, validation, and subsequent inferences. Analysis of real data using major statistical software packages. Prerequisite: MATH 3323, STAT 4380, or instructor approval. Course web page | |
| MATH 5386 | Stochastic Processes (3-0) |
| Random walks, discrete time Markov chains, and Poisson Process. Further topics such as continuous time Markov chains, branching processes, renewal theory, and estimation in branching processes. Prerequisites: (1) MATH 4341 and (2) STAT 3330 or MATH 5380. Course web page | |
| MATH 5388 | Multivariate Data Analysis (3-0) |
| Statistical analysis of a multivariate response. Multivariate multiple linear regression, principal components, factor analysis, canonical correlation, and discriminate analysis. Applications with the use of statistical packages will be considered. Prerequisite: MATH 5385 or equivalent. Course web page | |
| MATH 5390 | Nonparametric Statistics (3-0) |
| Distribution-free statistical methods; nonparametric one and two sample tests and analysis of variance; goodness-of-fit tests; nonparametric measures of association; and robust procedures. Prerequisite: MATH 5380 or equivalent. Course web page | |
| MATH 5391 | Time Series Analysis (3-0) |
| Time domain and frequency domain aspects of discrete time stationary processes, correlation functions, power spectra, filtering, linear systems, and arma models for non-stationary series. An introduction to the analysis of multiple time series. Some use of statistical software will be included. Prerequisite: MATH 5380. Course web page | |
| MATH 5392 | Statistical Computing (3-0) |
| A study of stochastic simulation and select numerical methods used in statistical computation. Prerequisites: A high-level programming language, linear algebra, and STAT 4380 or equivalent. Course web page | |
| MATH 5396 | Graduate Research (0-0-3) |
| A written report on an appropriate subject in mathematics or statistics is required. May not be counted towards the 24 hours of course work in the thesis option, but may be substituted for three hours of thesis credit. May not be repeated for credit. Prerequisite: Instructor approval. | |
| MATH 5398 | Thesis (0-0-3) |
| Initial work on the thesis. | |
| MATH 5399 | Thesis (0-0-3) |
| Continuous enrollment required while work on thesis continues. Prerequisite: MATH 5398 or department approval. | |