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Department of Mathematics
Chair Graduate Advisor Graduate Faculty Associate Professors Assistant Professors Professor Emeritus The objectives of the Mathematics
Department's program at the master's level are (1) to
develop the student's ability to do independent research
and prepare for more advanced study in mathematics, and
(2) to give advanced training to professional
mathematicians, mathematics teachers, and those employed
in engineering, scientific, and business areas. The Department of Mathematics offers master's degree programs in mathematics with additional emphasis in applied mathematics, computer science, mathematical education, pure mathematics, and statistics. All students are to use either the thesis or the thesis-substitute plan. All students must complete the following: (a.) General core requirement:
MATH 5300, 5307, 5308, and 5333; In addition: Students in every degree plan must pass a final master's exam. The grade of R (research
in progress) is a permanent grade; it cannot be changed
by completing course requirements in a later semester. To
receive credit for an R-graded course, the student must
continue to enroll in the course until a passing grade is
received. 5300. COMPUTER PROGRAMMING AND
APPLICATIONS 5301. MATHEMATICAL COMPUTER RESOURCES (3-0). Introduction to hardware and software available to the scientific graduate student whose studies involve numerical computations. Utilization of the various mathematic/statistical libraries is emphasized rather than programming of mathematic/statistical routines. Prerequisite: MATH 5300 or its equivalent. 5302. FUNDAMENTALS OF MATHEMATICAL SCIENCES I (3-0). Matrices and operators, linear spaces, multivariable calculus, dynamical systems, applications. Prerequisites: MATH 3318 and 3330 or consent of instructor. 5303. FUNDAMENTALS OF MATHEMATICAL SCIENCES II (3-0). Wave propagation, potential theory, complex variables, transform techniques, perturbation techniques, diffusion, applications. Prerequisite: MATH 5302 or consent of instructor. 5304. GENERAL TOPOLOGY (3-0). Introduction to fundamentals of general topology. Topics include product spaces, the Tychonoff theorem, Tietzes Extension theorem, and metrization theorems. Prerequisite: MATH 4304 or 4335. 5305. STATISTICAL METHODS (3-0). Topics include descriptive statistics, numeracy, and report writing; basic principles of experimental design and analysis; regression analysis; data analysis using the SAS package. Prerequisite: consent of the instructor. 5307. MATHEMATICAL ANALYSIS I (3-0). Elements of topology, real and complex numbers, limits, continuity, and differentiation, functions of bounded variation, Riemann-Stieltjes integrals. Prerequisite: MATH 4335 or consent of Graduate Advisor. 5308. MATHEMATICAL ANALYSIS II (3-0). Analysis in Rn, limits, continuity, Jacobian, extremum problems, multiple integrals, sequences and series of functions, Lebesque integral. Prerequisite: MATH 5307 or consent of Graduate Advisor. 5310. MATHEMATICAL GAME THEORY (3-0). Two person null sum games. Bimatrix games and Nash equilibrium points. Noncooperative games, existence theorem. Cooperative games, core, Shapley value, the nucleolus. Cost allocation. Market games. Simple games and voting. Prerequisite: MATH 3330. 5311. APPLIED PROBABILITY AND STOCHASTIC PROCESSES (3-0). Topics include conditional expectations, law of large numbers and central limit theorem, stochastic processes, including Poisson, renewal, birth-death, and Brownian motion. Prerequisite: MATH 3313 or equivalent. 5312. MATHEMATICAL STATISTICS I (3-0). Basic probability theory, random variables, expectation, probability models, generating functions, transformations of random variables, limit theory. Prerequisite: MATH 5307 or concurrent registration or consent of instructor. 5313. MATHEMATICAL STATISTICS II (3-0). Theories of point estimation (minimum variance unbiased and maximum likelihood), interval estimation and hypothesis testing (Neyman-Pearson and likelihood ratio tests), regression analysis and Bayesian inference. Prerequisite: MATH 5312. 5315. GRAPH THEORY (3-0). Algorithms for problems on graphs. Trees, spanning trees, connectedness, fundamental circuits. Eulerian graphs and Hamiltonian graphs. Graphs and vector spaces, matrices of a graph. Covering and coloring. Flows. Prerequisite: MATH 3314. 5316. COMBINATORIAL OPTIMIZATION (3-0). Shortest paths. Minimum weight spanning trees and matroids. Matchings and optimal assignment. Connectivity. Flows in networks, applications. Prerequisite: MATH 3314. 5317. REAL ANALYSIS FOR THE MATHEMATICAL SCIENCES (3-0). Lebesque measure and integration on Rn. Study of LP spaces. Abstract measure and integration. Prerequisite: MATH 5308. 5318. FUNDAMENTALS OF STOCHASTIC ANALYSIS (3-0). General properties of stochastic processes, processes with independent increments, martingales, limit theorems including invariance principle, Markov processes, stochastic integral, stochastic differential. Prerequisite: MATH 5308. 5319. PROBABILITY THEORY (3-0). Probability spaces, random variables, filtrations, conditional expectations, martingales, strong law of large numbers, ergodic theorem, central limit theorem, Brownian motion and its properties. Prerequisite: MATH 5308. 5320. APPLIED DIFFERENTIAL EQUATIONS (3-0). Fundamentals of the theory of systems of ordinary differential equations: existence, uniqueness, and continuous dependence of solutions on data; linear equations, stability theory and its applications, periodic and oscillatory solutions. Prerequisites: MATH 5307 and 5333. 5321. APPLIED PARTIAL DIFFERENTIAL EQUATIONS (3-0). General first order equations. Basic linear theory for elliptic, hyperbolic, and parabolic second order equations, including existence and uniqueness for initial and boundary value problems. Prerequisites: MATH 5307 and 5333. 5322. COMPLEX VARIABLES I (3-0). Fundamental theory of analytic functions, residues, conformal mapping and applications. Prerequisite: MATH 5307. 5324. APPLIED COMPLEX VARIABLES (3-0). Analytic functions of a complex variable; the line integral, residues, applications; conformal mappings; harmonic functions and applications to physical problems; elements of transform theory. Prerequisite: MATH 3335 or consent of the instructor. 5327. FUNCTIONAL ANALYSIS I (3-0). Introduction to Hilbert and Banach spaces: Hahn-Banach, Banach-Steinhaus, and closed graph theorems. Riesz representation theorem and bounded linear operators in Hilbert space. Prerequisite: MATH 5308. 5328. FUNCTIONAL ANALYSIS II (3-0). The theory of distributions and Sobolev spaces, with applications to differential equations. Compact operators and Fredholm theory. Spectral theory for unbounded operators. Prerequisite: MATH 5327. 5331. ABSTRACT ALGEBRA I (3-0). Zorn's Lemma, groups, including free groups and dihedral groups. Rings including factorization, localization, rings of polynomials, and formal power series. An introduction to modules. Prerequisite: MATH 3321. 5332. ABSTRACT ALGEBRA II (3-0). Modules, including free, projective, and injective. Exact sequences and tensor products of modules. Chain conditions, primary decomposition, Noetherian rings and modules. Prerequisite: MATH 5331. 5333. LINEAR ALGEBRA AND MATRICES (3-0). Liner spaces, linear transformations, vector norms, Gaussian elimination, Jordan form, eigenvalues, quadratic forms, and related topics. Prerequisite: MATH 3330 or consent of instructor. 5334. DIFFERENTIAL GEOMETRY (3-0). Introduction to the theory of curves and surfaces in three dimensional Euclidean space. Prerequisite: MATH 4334 or 4335. 5335. APPLIED VECTOR AND TENSOR ANALYSIS (3-0). Vector algebra, vector and tensor calculus; applications to differential geometry, engineering sciences, and dynamics including surface theory, geodiscs, minimal surfaces, elasticity, particle dynamics, special relativity, and general relativity. Prerequisite: MATH 5302. 5338. NUMERICAL ANALYSIS I (3-0). Solution of equations, interpolation and approximation, numerical differentiation and quadrature, and solution of ordinary differential equations. Prerequisite: MATH 3345. 5339. NUMERICAL ANALYSIS II (3-0). Rigorous treatment of numerical aspects of linear algebra and numerical solution of boundary value problems in ordinary differential equations: also, an introduction to numerical solution of partial differential equations. Prerequisite: MATH 3345. 5341. MATHEMATICS FOR TEACHERS—GEOMETRY (3-0). Selected materials from geometry. 5342. MATHEMATICS FOR TEACHERS—ALGEBRA (3-0). Selected materials from algebra, including probability, statistics, and theory of equations. 5344. MATHEMATICS FOR TEACHERS—COMPUTER (3-0). Selected materials from the literature on the usage of micro-computers in the classroom. 5345. MATHEMATICS FOR TEACHERS—ANALYSIS (3-0). Selected materials from analysis including concepts and topics consistent with precalculus and elementary calculus. 5346. MATHEMATICS FOR TEACHERS—PROBLEM SOLVING (3-0). Instruction in the application of various heuristics or general problem strategies. 5348. ANALYSIS OF NUMERICAL METHODS I (3-0). Rigorous treatment of topics in numerical analysis including roundoff error effects, solution of linear and nonlinear systems, interpolation, and numerical integration. Emphasis on analysis of methods as well as computation. Prerequisites: MATH 3335 and 3345. 5349. ANALYSIS OF NUMERICAL METHODS II (3-0). Continuation of MATH 5348. Topics include QR decomposition, eigenvalue approximation, singular value decomposition, least squares problems, numerical approximation of ODE's and PDE's, and iterative methods for large sparse systems. Emphasis on analysis of methods as well as computation. Prerequisite: MATH 5348. 5350. APPLIED MATHEMATICS I (3-0). Development of models arising in the natural sciences and in engineering. Emphasis will be on the mathematical techniques and theory needed to analyze such models; these include aspects of the theory of differential and integral equations, boundary value problems, theory of distributions and transforms. Prerequisites: MATH 5307 and 5333. 5351. APPLIED MATHEMATICS II (3-0). Continuation of MATH 5350; models arising in the physical sciences whose analysis includes such topics as the theory of operators in a Hilbert space, variational principles, branching theory, perturbation and stability analysis. Prerequisite: MATH 5350. 5355. STATISTICAL THEORY FOR RESEARCH WORKERS (3-0). Designed for graduate students not majoring in mathematics. Topics include basic probability theory, distributions of random variables, point estimation., interval estimation, testing hypotheses, regression, and an introduction to analysis of variance. Graduate credit not given to math majors. Prerequisite: MATH 2325. 5356. APPLIED MULTIVARIATE STATISTICAL ANALYSIS (3-0). Statistical analysis for data collected in several variables, topics including sampling from multivariate normal distribution, Hotelling's T'2, multivariate analysis of variance, discriminant analysis, principal components, and factor analysis. Prerequisite: MATH 5312 or consent of instructor. 5357. SAMPLE SURVEYS (3-0). A comprehensive account of sampling theory and methods, illustrations to show methodology and practice, simple random sampling, stratified random sample, ratio estimates, regression estimates, systematic sampling, cluster sampling, and nonsampling errors. Prerequisite: MATH 5312 or consent of instructor. 5361. APPLIED CALCULUS OF VARIATION (3-0). Functionals, variation, extremization, Euler's equation, direct and indirect approximation methods; applications to mechanics and control theory. Prerequisite: MATH 5302. 5362. MATHEMATICS OF LINEAR PROGRAMMING (3-0). The simplex method and the revised simplex method. Linear algebra for polyhedra and polytopes. Duality theory. Sensitivity analysis. Applications to transportation problems, network flow problems, matrix-games and scheduling problems. Integer programming. Quadratic programming. Prerequisite: MATH 3330. 5363. OSCILLATIONS AND WAVES (3-0). Development of methods and results related to phenomena in nature that exhibit oscillatory motion; mathematical techniques include Fourier series, ordinary and partial differential equations, and the theory of almost periodic functions. Prerequisite: MATH 3318. 5364. INTRODUCTION TO MATHEMATICAL CONTROL THEORY (3-0). Systems in science, engineering, and economics and their mathematical description by means of functional equations (ordinary, partial, integral, delay-type). Basic properties of various classes of systems: observability, controllability, stability, and oscillating systems; optimal control problems and applications. Prerequisite: MATH 3318 or 4320. 5365. BIOMATHEMATICS (3-0). Mathematical techniques used in modeling such as perturbation theory, dimensional analysis, Fourier analysis, and differential equations. Applications to morphogenetics, population dynamics, compartmental systems, and chemical kinetics. Prerequisite: consent of instructor. 5366. INTRODUCTION TO NEURAL AND COGNITIVE MODELING (3-0). Principles of neural network modeling; application of these principles to the simulation of cognitive processes in both brains and machines; models of associative learning, pattern recognition, and classification. Prerequisite: consent of instructor. 5371. NUMERICAL LINEAR ALGEBRA (3-0). Methods and theory related to the numerical solution of linear algebraic systems and eigenvalue-eigenvector problems. Both direct and iterative techniques are developed and discussed for full and sparse systems. Convergence, convergence rates, and error analysis. Prerequisites: MATH 3330 and 3345. 5372. NUMERICAL FUNCTIONAL ANALYSIS (3-0). Numerical implementation of abstract operator methods, including Newton's method for linear and nonlinear algebraic, transcendental, differential, integral, and functional equations; some aspects of approximation theory. Prerequisite: MATH 5308. 5373. NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS (3-0). Theoretical analysis of methods for approximating solutions of initial value problems, boundary value problems, and problems with periodic solutions; existence, uniqueness, convergence, stability, and error analysis are stressed for both single equations and for systems. Prerequisite: MATH 5338 or consent of instructor. 5374. NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS (3-0). Theoretical analysis for numerical methods for approximating solutions of elliptic, parabolic, hyperbolic, mixed, and systems of partial differential equations problems; existence, uniqueness, convergence, stability, and error analysis are stressed. Prerequisite: MATH 5339 or consent of instructor. 5380. SEMINAR (3-0). Current topics in mathematics, may be repeated for credit twice. Prerequisite: consent of instructor. 5391. SPECIAL TOPICS IN MATHEMATICS (3-0). Topics in mathematics assigned individual students or small groups. Faculty members closely supervise the students in their research and study. In areas where there are only three hours offered, the special topics may be used by students to continue their study in the same area. Graded P/F/R. Prerequisite: permission of instructor. 5392. SELECTED TOPICS IN MATHEMATICS (3-0)/(3-1). May vary from semester to semester depending upon need and interest of the students. May be repeated for credit. Prerequisite: permission of instructor. 5395. SPECIAL PROJECT. Graded
P/F/R. Prerequisite: permission of Graduate Advisor. 6313. TOPICS IN PROBABILITY AND STATISTICS (3-0). May be repeated for credit when the content changes. 6391. SPECIAL TOPICS IN MATHEMATICS
(3-0). Faculty directed individual study and research.
May be repeated for credit when the content changes.
Graded P/F/R. A limited number of undergraduate mathematics courses may be applicable to a graduate program in mathematics if approved by the Graduate Advisor. These must be chosen from the following list and shall not exceed six hours total credit. 4303. INTRODUCTION OF TOPOLOGY |
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