### Courses

**MATH 5195. Graduate Seminar.**

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.

**1 Credit Hour**

**1 Total Contact Hour**

0 Lab Hour

1 Lecture Hour

0 Other Hour

**MATH 5310. Elemnts of Applied Functl Anal.**

Elements of Applied Functional Analysis (3-0) Elements of functional analysis for applications in statistics, optimization and computational partial differential equations (PDEs): normed space, Banach spaces, L spaces, basic inequalities, inner product, Hilbert spaces, orthogonal projections, Riesz theorem, elements of Sobolev spaces.

**MATH 5311. Applied Mathematics.**

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. .

**3 Credit Hours**

**3 Total Contact Hours**

0 Lab Hours

3 Lecture Hours

0 Other Hours

**MATH 5314. Partial Differential Equations.**

Partial Differential Equations (3-0) Partial derivatives and differential operators, classification of partial differential equations with emphasis on elliptic, parabolic and hyperbolic, examples from physics, maximum principle and well-posedness, boundary conditions, weak formulations, Lax-Milgram lemma, overview of existence and uniqueness results.

**3 Credit Hours**

**3 Total Contact Hours**

0 Lab Hours

3 Lecture Hours

0 Other Hours

**Prerequisite(s):** (MATH 5310 w/C or better)

**MATH 5315. Finite Element Methods I.**

Galerkin method and its convergence, piecewise-affine and higher-order FEM in one spatial dimension, adaptivity, general concept of nodal elements, unisolvency, local and global finite element interpolants, conformity, continuous elements in two and three dimensions.

**MATH 5321. Principles of Analysis.**

Principles of Analysis (3-0) Investigation of convergence, continuity, differentiability, compactness and connectedness, the Riemann-Stieljes integral, and sequences of functions.

**3 Credit Hours**

**3 Total Contact Hours**

0 Lab Hours

3 Lecture Hours

0 Other Hours

**Prerequisite(s):** (MATH 3341 w/C or better)

**MATH 5325. Principles of Algebra.**

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.

**3 Credit Hours**

**3 Total Contact Hours**

0 Lab Hours

3 Lecture Hours

0 Other Hours

**Prerequisite(s):** (MATH 3325 w/C or better)

**MATH 5329. Numerical Analysis.**

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.

**3 Credit Hours**

**3 Total Contact Hours**

0 Lab Hours

3 Lecture Hours

0 Other Hours

**Prerequisite(s):** (MATH 3323 w/C or better)

**MATH 5330. Comp Methods of Linear Algebra.**

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.

**3 Credit Hours**

**3 Total Contact Hours**

0 Lab Hours

3 Lecture Hours

0 Other Hours

**Prerequisite(s):** (MATH 3323 w/C or better)

**MATH 5331. Real Variables.**

Real Variables (3-0) Lebesgue integration, integration with respect to measure, absolute continuity, fundamental theorem of calculus for the lebesgue integral.

**3 Credit Hours**

**3 Total Contact Hours**

0 Lab Hours

3 Lecture Hours

0 Other Hours

**Prerequisite(s):** (MATH 5321 w/C or better)

**MATH 5335. Techniques in Optimization.**

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.

**3 Credit Hours**

**3 Total Contact Hours**

0 Lab Hours

3 Lecture Hours

0 Other Hours

**Prerequisite(s):** (MATH 1411 w/C or better ) OR (MATH 1312 w/C or better ) OR (MATH 2313 w/C or better ) OR (MATH 2326 w/C or better ) OR (MATH 1411A w/C or better AND MATH 1411B w/C or better AND MATH 1411C w/C or better)

**MATH 5341. General Topology.**

General Topology (3-0) Topics include: Separation, compactness, connectedness, paracompactness, metric spaces and metrization of toplogical spaces.

**3 Credit Hours**

**3 Total Contact Hours**

0 Lab Hours

3 Lecture Hours

0 Other Hours

**Prerequisite(s):** (MATH 5321 w/C or better)

**MATH 5343. Numer Solution Part Diff Equat.**

Numerical Solutions to Partial Differential Equations (3-0) Introduction to finite difference and finite element methods for the solution of elliptic, parabolic and hyperbolic partial differential equations.

**MATH 5345. Numerical Optimization.**

Numerical Optimization (3-0) A study of numerical algorithms for solving systems of nonlinear equations, unconstrained optimization, and nonlinear least squares problems. Derivation of necessary and sufficient conditions for constrained optimization, and an introduction to interior-point methodology.

**MATH 5346. Interior-Point Methods for Lin.**

Optimization of linear objective functions subject to linear constraints. Development of theory and algorithmic strategies for solving linear programming problems using interior-point methodology.

**MATH 5351. Complex Variables.**

Complex Variables (3-0) Complex integration and the calculus of residues. Analytical continuation and expansions of analytic functions. Entire, meromorphic, and periodic functions.

**3 Credit Hours**

**3 Total Contact Hours**

0 Lab Hours

3 Lecture Hours

0 Other Hours

**Prerequisite(s):** (MATH 5321 w/C or better)

**MATH 5370. Seminar.**

Seminar (3-0) Various topics not included in regular courses will be discussed. May be repeated once for credit as content changes.

**3 Credit Hours**

**3 Total Contact Hours**

0 Lab Hours

3 Lecture Hours

0 Other Hours

**MATH 5380. Mathematical Statistics I.**

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 transfromations, modes of convergence and limit theorems.

**3 Credit Hours**

**3 Total Contact Hours**

0 Lab Hours

3 Lecture Hours

0 Other Hours

**Prerequisite(s):** (STAT 3330 w/C or better)

**MATH 5381. Mathematical Statistics II.**

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 or STAT 5380 each with a grade of C or higher.

**MATH 5385. Statistics in Research.**

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.

**MATH 5388. Multivariate Data Analysis.**

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.

**MATH 5391. Time Series Analysis.**

Time Series Analysis (3-0) Time domain and frequency domain aspects of discrete time stationary processes, correlation functions, power spectra, filtering, linear systems, arma models for non-stationary series. An introduction to the analysis of multiple time series. Some use of statistical software will be included.

**3 Credit Hours**

**3 Total Contact Hours**

0 Lab Hours

3 Lecture Hours

0 Other Hours

**Prerequisite(s):** (MATH 5380 w/C or better)

**MATH 5392. Statistical Computing.**

Statistical Computing (3-0) A study of stochastic simulation and select numerical methods used in statistical computation.

**3 Credit Hours**

**3 Total Contact Hours**

0 Lab Hours

3 Lecture Hours

0 Other Hours

**Prerequisite(s):** (STAT 4380 w/C or better)

**MATH 5396. Graduate Research.**

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.

**3 Credit Hours**

**3 Total Contact Hours**

0 Lab Hours

0 Lecture Hours

3 Other Hours

**MATH 5398. Thesis.**

Thesis (0-0-3).

**3 Credit Hours**

**3 Total Contact Hours**

0 Lab Hours

0 Lecture Hours

3 Other Hours

**MATH 5399. Thesis.**

Thesis (0-0-3).

**3 Credit Hours**

**3 Total Contact Hours**

0 Lab Hours

0 Lecture Hours

3 Other Hours

**Prerequisite(s):** (MATH 5398 w/P or better)

**MATH 6311. Topics in Applied Mathematics.**

This course prepares a student for research in applied mathematics on a specific topic. The topics may vary each semester. Each section is dedicated to a different topic. Course may be repeated for credit.

**3 Credit Hours**

**3 Total Contact Hours**

0 Lab Hours

0 Lecture Hours

3 Other Hours

**MATH 6345. Topics in Optimization.**

The topics may vary each semester. Course may be repeated for credit.

**3 Credit Hours**

**3 Total Contact Hours**

0 Lab Hours

3 Lecture Hours

0 Other Hours

**Prerequisite(s):** (MATH 5345)

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