2005-2006 CATALOG
Admission to all courses at the 1000-level will be based on performance on the ACT or departmental placement exams. Students with unsatisfactory scores on these exams will be required to pass Developmental Mathematics 107 before registering for any 1000-level course.
Students who show exceptional preparation may replace introductory courses with more advanced ones, with consent of the department based on the student’s performance on a special examination. No student may receive more than nine semester hours credit in courses numbered below 2000.
MATH 1021 Problem Solving and Number Relations for
Elementary Teachers 3 cr.
Offered each semester. Prerequisites: DEVM 0107 or satisfactory performance on either the departmental placement exam or the ACT or SAT. A problem solving approach to the number systems of arithmetic emphasizing the use of logic and sets as the language of mathematics. This course may be used for degree credit only in the College of Education.
MATH 1023 Problem Solving and Geometry for
Elementary Teachers 3 cr.
Offered each semester: Prerequisite: MATH 1021. A problem solving and constructive approach to Euclidean Geometry and three dimensions. This course can be used for degree credit only in the College of Education.
MATH 1031 A Survey of Mathematical Thought 3 cr.
Offered each semester. Prerequisite: Developmental Mathematics 0106 or satisfactory performance on either the departmental placement exam or the ACT or SAT. MATH 1031 is prerequisite to MATH 1032. Credit for both Mathematics 1031, and 2107 or 2111 will not be allowed. Non-technical survey of major branches of mathematics with examples of problems and methods in each.
MATH 1032 A Survey of Mathematical Thought 3 cr.
Offered each semester. Prerequisite: Mathematics 1031. Credit for both Mathematics 1032, and 2107 or 2111 will not be allowed. Non-technical survey of major branches of mathematics with examples of problems and methods in each.
MATH 1115 Algebra 3 cr.
Prerequisite: DEVM 0107 or satisfactory performance on the departmental placement exam, the ACT, or the SAT. Real numbers and equations, functions, polynomial functions and graphs, exponential and logarithmic functions. This course will not serve as a prerequisite to MATH 1126; it will be followed by MATH 1116, 1125, 1140, or 2314 according to major. A strong component of this course will be applications taken from different areas of concentration.
MATH 1116 Trigonometry 3 cr.
Prerequisite: MATH 1115 with a grade of C or better. Introduction to trigonometric functions, graphs of trigonometric functions, trigonometric identities, applications of trigonometry, linear and nonlinear systems, binomial theorem. Designed for students who are not required to take calculus. This course will not serve as a prerequisite to MATH 2107 or 2111. A strong component of this course will be applications taken from different areas of concentration. Credit for both MATH 1116 and 1126 will not be allowed.
MATH 1125 Precalculus Algebra 3 cr.
Prerequisites: MATH 1115 or satisfactory performance on the departmental placement exam, the ACT, or the SAT. Fundamentals, functions, polynomials and rational functions, exponential and logarithmic functions. Designed for students anticipating enrollment in MATH 2107 or 2111. This course will be followed by MATH 1126 and both will be prerequisites to the calculus sequences.
MATH 1126 Precalculus Trigonometry 3 cr.
Prerequisites: MATH 1125 with a grade of C or better. Trigonometric functions of real numbers, trigonometric functions of angles, analytic trigonometry, systems of equations and inequalities, the binomial theorem. Designed for students anticipating enrollment in MATH 2107 or 2111. Credit for both MATH 1116 or 1126 will not be allowed.
MATH 1140 Finite Mathematics 3 cr.
Offered each semester. Prerequisite: MATH 1115 or consent of department. Introduction to set theory and counting techniques, probability, statistics, linear programming and application to behavioral sciences.
MATH 1911 Precalculus 3 cr.
Prerequisite: DEVM 0107 or satisfactory performance on either the departmental placement exam or the ACT (or SAT). Offered each semester. Absolute value equations and inequalities; algebraic, logarithmic, exponential, and trigonometric functions; complex numbers; analytic trigonometry; trigonometry and triangles; systems of linear equations; binomial theorem. Students may not receive credit in both MATH 1911 and either of 1115 1126. This course is designed for students anticipating enrollment in MATH 2107 or MATH 2111.
MATH 2090 History of Mathematics 3 cr.
Prerequisite: credit or registration in MATH 2109 or 2112. A survey starting with the mathematics of the Babylonians and the Egyptians, continuing with the logic, geometry, and number theory of the Greeks; development of logarithms and projective geometry, analytic geometry, calculus, and the beginnings of modern analysis and the origins of modern algebra.
MATH 2100 Introduction to Mathematica 1 cr.
Prerequisite: MATH 1115 or 1126 or 1140 or consent of department. Introduction to Mathematica, a computer algebra package that combines symbolic manipulation, built-in numerical functions, and powerful graphical capabilities for doing mathematics with the help of a computer. Emphasis will be on the use of the package as a tool for solving problems in science, engineering, and business. Programming experience is not required.
MATH 2107 Calculus and Analytic Geometry 3 cr.
Offered each semester. Prerequisite: MATH 1126 with a grade of C or better. MATH 2107 with a grade of C or better recommended is prerequisite to MATH 2108; MATH 2108 with a grade of C or better recommended is prerequisite to MATH 2109. These courses cover the same topics in three semesters that MATH 2111, 2112 cover in two. A student may not receive more than five hours of degree credit for taking MATH 2107 and 2111 or more than six hours for MATH 2107, 2108, and 2111 or more than 10 hours for MATH 2107, 2108, 2109, and MATH 2111, 2112.
MATH 2108 Calculus and Analytic Geometry 3 cr.
Offered each semester. Prerequisite: MATH 1126 with a grade of C or better. MATH 2107 with a grade of C or better recommended is prerequisite to MATH 2108; MATH 2108 with a grade of C or better recommended is prerequisite to MATH 2109. These courses cover the same topics in three semesters that MATH 2111, 2112 cover in two. A student may not receive more than five hours of degree credit for taking MATH 2107 and 2111 or more than six hours for MATH 2107, 2108, and 2111 or more than 10 hours for MATH 2107, 2108, 2109, and MATH 2111, 2112.
MATH 2109 Calculus and Analytic Geometry 4 cr.
Offered each semester. Prerequisite: MATH 1126 with a grade of C or better. MATH 2107 with a grade of C or better recommended is prerequisite to MATH 2108; MATH 2108 with a grade of C or better recommended is prerequisite to MATH 2109. These courses cover the same topics in three semesters that MATH 2111, 2112 cover in two. A student may not receive more than five hours of degree credit for taking MATH 2107 and 2111 or more than six hours for MATH 2107, 2108, and 2111 or more than 10 hours for MATH 2107, 2108, 2109, and MATH 2111, 2112.
MATH 2111 Calculus with Analytic Geometry 5 cr.
Offered each semester. Prerequisite: MATH 1126 with a grade of C or better. MATH 2111 with a grade of C or better recommended is prerequisite to MATH 2112. Brief review of pre-calculus topics; limits, continuity; algebraic and transcendental functions, their derivatives, their inverses and their integrals; fundamental theorems, conic sections, maximum-minimum problems. Integration techniques, polar coordinates, sequences, series, convergence, Taylor series, L’Hospital’s Rule, improper integrals, plane vectors, lines, solids of revolution.
MATH 2112 Calculus with Analytic Geometry 5 cr.
Offered each semester. Prerequisite: MATH 1126 with a grade of C or better. MATH 2111 with a grade of C or better recommended is prerequisite to MATH 2112. Brief review of pre-calculus topics; limits, continuity; algebraic and transcendental functions, their derivatives, their inverses and their integrals; fundamental theorems, conic sections, maximum-minimum problems. Integration techniques, polar coordinates, sequences, series, convergence, Taylor series, L’Hospital’s Rule, improper integrals, plane vectors, lines, solids of revolution.
MATH 2115 Calculus of Several Variables 3 cr.
Offered each semester. Prerequisite: MATH 2109 or 2112 with a grade of C or better recommended or consent of department. Vectors and solid analytic geometry, partial derivatives, multiple integrals, line integrals, Green’s Theorem, divergence, curl and applications.
MATH 2221 Elementary Differential Equations 3 cr.
Offered each semester. Prerequisite: MATH 2109 or 2112 with a grade of C or better recommended or consent of department. Differential equations of first and higher order; constant coefficient equations with and without forcing terms and applications; series solutions; Laplace transforms and systems of differential equations.
MATH 2314 Elementary Statistical Methods 3 cr.
Prerequisite: A grade of C or better in MATH 1115 or MATH 1125 in six hours of mathematics courses numbered at least 1000 or consent of department. Introduction to statistical methods. Topics include data analysis, frequency distributions, probability, inference, estimation, hypothesis testing, regression and correlation.
MATH 2400 Geometry 3 cr.
Spring semester. Prerequisite: MATH 2109 or 2112 or consent of department. Absolute geometry, introduction to non-Euclidean geometries, Euclidean geometries, metric approach.
MATH 2511 Introduction to Linear Algebra 3 cr.
Offered each semester. Prerequisite: MATH 2109 or 2112 or consent of department. Matrices, systems of linear equations, vector spaces, linear transformations, determinants, inner products and norms, eigenvalues and eigenvectors, diagonalization.
MATH 2721 Introduction to Discrete Structures 3 cr.
Prerequisite: MATH 1116 or 1126. An introduction to the discrete structures that serve as a foundation for mathematics and computer science: set theory and mathematical logic; binary relations; counting and algorithm analysis; induction and strings.
MATH 2990 Special Topics 1-3 cr.
Prerequisite: consent of department. May be repeated up to six credit hours. Subject matter may change from semester to semester. Section number will correspond with credit to be earned.
MATH 2998 Independent Study: Readings 1-3 cr.
Prerequisite: consent of department. Course may be repeated to a total of three hours. The course consists of directed readings designed to meet the needs and interests of the individual student; regular conferences between the student and the instructor are required. Section number will correspond with credit to be earned.
MATH 3099 Senior Honor Thesis 1-6 cr.
Prerequisite: consent of department and the director of the Honors Program. Honors thesis research in mathematics under the direction of a faculty member. May be repeated until thesis is accepted for a total of six credits. Section number will correspond with credit earned.
MATH 3221 Methods in Differential Equations 3 cr.
Prerequisites: MATH 2221 - Elementary differential equations, MATH 2115 - Calculus of several variables. The major emphasis of this course will be on techniques and examples. Power series solutions, linear systems, matrix methods, eigenvalues, eigenvectors, partial differential equations, Fourier series, heat equation, wave equation, Laplace’s equation.
MATH 3300 Statistical Computer Packages 1 cr.
Prerequisite: MATH 2314 or consent of department. Introduction to statistical packages, emphasis will be on the use of SAS.
MATH 3512 Introduction to Abstract Algebra 3 cr.
Prerequisite: MATH 2511; MATH 2721 is recommended. An introduction to modern algebraic structures: relations, mappings, semigroups, groups, rings and fields.
MATH 3900 Undergraduate Oral Examination 0 cr.
Required for graduation of all Mathematics majors. A one hour oral examination in which the student will be questioned on mathematical concepts that are familiar to him or her. Successful completion of this examination will satisfy the requirement of demonstrating oral competence. A faculty committee will grade the examination on a pass-fail basis.
MATH 4010 Introduction to Modern Algebra 3 cr.
Prerequisites: MATH 1021 and 1023. Groups, finite groups and permutation groups, rings and fields. Linear algebra, vector spaces, determinants and matrices, linear transformations. This course may be used for degree credit only in the elementary education curriculum at the undergraduate or graduate level.
MATH 4020 Geometry I 3 cr.
Prerequisite: MATH 1023. Incidence and separation in planes and spaces; congruences between lines angles and triangles; parallel postulate; perpendicular lines and planes in space; constructions with ruler and compass. This course may be used for degree credit only in the elementary education curriculum at the undergraduate or graduate level.
MATH 4030 Probability and Finite Mathematics 3 cr.
Prerequisites: MATH 1021 and 1023. Probability theory, convex sets, finite Markov chains, continuous probability theory. This course may be used for degree credit only in the elementary education curriculum at the undergraduate or graduate level.
MATH 4101 Advanced Calculus 3 cr.
Prerequisite: MATH 2115. MATH 4101 is prerequisite to MATH 4102. These courses emphasize a balance between proofs and techniques in intermediate analysis involving one and several variables. Limits, continuity, differentiation, integration and convergence. Series of functions, functional dependence, Jacobian, vector analysis or other techniques of use in applications.
MATH 4102 Advanced Calculus 3 cr.
Prerequisite: MATH 2115. MATH 4101 is prerequisite to MATH 4102. These courses emphasize a balance between proofs and techniques in intermediate analysis involving one and several variables. Limits, continuity, differentiation, integration and convergence. Series of functions, functional dependence, Jacobian, vector analysis or other techniques of use in applications.
MATH 4213 Fourier Series and Transforms 3 cr.
Prerequisite: MATH 2115 and 2221 or consent of department. Fourier series and discrete frequency spectra, Fourier integral and continuous spectra, transformation of special functions, applications in physics and engineering.
MATH 4221 Intermediate Ordinary Differential Equations 3 cr.
Prerequisite: MATH 2221 and 2511 or consent of department. Topics to be selected from the following: introduction to qualitative theory, phase plane analysis of autonomous systems, classification of equilibria, stability theory, Liapunov methods, limit cycles, Poincar Bendixson theorem, introduction to bifurcation theory and chaotic oscillations, Froebenius method for series solutions, special functions, Sturm comparison and separation theorems.
MATH 4224 Partial Differential Equations I 3 cr.
Prerequisite: MATH 2115 and 2221 or consent of department. Basic techniques for solving linear partial differential equations, separation of variables, eigenfunction expansions, integral transforms, Sturm-Liouville boundary value problems, initial value problems and boundary value problems for hyperbolic, parabolic, and elliptic equations, fundamental solutions, maximum principle, classical and modern applications.
MATH 4230 Finite Element Analysis 3 cr.
Prerequisites: MATH 2115, 2221 and 2511. A knowledge of Fortran or consent of department. Variational principle, weighted residual methods, finite element analysis of one and two dimensional steady state and transient boundary value problems involving partial differential equations, software development and implementations.
MATH 4240 Boundary Element Method 3 cr.
Prerequisites: MATH 2115, 2221, and 2511. Some knowledge of computer programming is also required. Weak variational formulation, fundamental solutions, formulation of two- and three-dimensional boundary element equations, potential problems, nonconvex regions, linear elasticity, fluid flows, acoustics, software development.
MATH 4251 Numerical Analysis 3 cr.
Prerequisite: MATH 2115 or consent of department. Numerical solution of systems of linear and nonlinear equations; interpolation, approximation, and minimization of functions; numerical integration.
MATH 4252 Numerical Analysis 3 cr.
Prerequisites: MATH 2221 and 4251, or consent of department. Eigenvalue problems; numerical Fourier transforms; modeling of data; introduction to numerical solution of initial and boundary value problems in ordinary and partial differential equations.
MATH 4270 Introduction to Optimization 3 cr.
Prerequisites: MATH 2115 and 2511 or consent of department. Methods for optimization of physical, economic, and business systems. Convex sets; methods for solving linear programming problems; review of classical methods of optimization; network flow analysis.
MATH 4280 Mathematical Modeling for Continuous Systems 3 cr.
Prerequisite: MATH 2115 and 2221, or consent of department. General principles in mathematical modeling, derivation and analysis of specific models using ordinary and partial differential equations; examples drawn from the applied sciences may include traffic flow, biological systems, mechanical systems, discussion of stability and dependence on parameters.
MATH 4301 Analysis of Variance and Experimental Design 3 cr.
Prerequisite: MATH 2314 or other introductory level statistics course, or consent of department. Only one of MATH 4301 or MATH 6301 may be counted toward a master’s degree in Mathematics. An introduction to the SAS statistical computer package. Basic analysis of variance with fixed and random effects models, multifactor analysis of variance, analysis of covariance. Experimental designs including completely randomized designs, randomized block designs, nested designs, and Latin squares.
MATH 4304 Introduction to Regression Analysis 3 cr.
Prerequisite: MATH 2314 or other introductory level statistics course, or consent of department. Only one of MATH 4304 or 6304 may be counted toward a master’s degree in Mathematics. Linear regression, inferences in regression analysis, aptness of model and remedial measures, matrices, multiple and polynomial regression, indicator variables, multi-collinearity, selection of independent variables, nonlinear regression. SAS will be used for data analysis.
MATH 4310 Matrix Theory For Statistics 3 cr.
Prerequisite: MATH 2511 or the consent of the department. Emphasis is on topics in matrix theory which frequently arise in the study of statistics. Topics in include eigenvalues and eigenvectors, generalized inverses, matrix decomposition, linear systems, matrix derivatives, and special matrices. Topics in statistics are not a portion of this course.
MATH 4311 Introduction to Mathematical Statistics 3 cr.
Prerequisite: MATH 2109 or 2112 or consent of department. MATH 4311 is prerequisite to MATH 4312. Axiomatic probability, discrete and continuous distributions, expectation, estimation, central limit theorem, confidence intervals and tests of hypotheses, regression, Bayesian statistics, other topics.
MATH 4312 Introduction to Mathematical Statistics 3 cr.
Prerequisite: MATH 2109 or 2112 or consent of department. MATH 4311 is prerequisite to MATH 4312. Axiomatic probability, discrete and continuous distributions, expectation, estimation, central limit theorem, confidence intervals and tests of hypotheses, regression, Bayesian statistics, other topics.
MATH 4341 Nonparametric Statistics 3 cr.
Prerequisite: MATH 4301 or 4304, or consent of department. Organizing and summarizing data; one-sample, two-sample, and k-sample tests; tests based on the binomial distribution; confidence intervals; Wilcoxon type tests; Kruskal-Wallis and Friedman tests; contingency tables; tests based on ranks; and Kolgoromov-Smirnoff type statistics.
MATH 4371 Probability Theory 3 cr.
Prerequisite: MATH 2115 or consent of department. Discrete probability theory, Markov chains, elementary limit laws and theorems.
MATH 4372 Applied Stochastic Processes 3 cr.
Prerequisite: MATH 4311 or 4371 or consent of department. Introduction to Poisson processes, Brownian motion, branching processes, and related topics with applications.
MATH 4380 Actuarial Mathematics 3 cr.
Prerequisites: MATH 2115 and MATH 2314 or consent of department. Deterministic and stochastic actuarial modeling, stochastic processes, Markov chains, the Poisson process, Brownian motion, applications of each of the above concepts to actuarial problems.
MATH 4411 Introduction to Complex Analysis 3 cr.
Prerequisite: MATH 2115 or consent of department. Complex plane, analytic functions, Cauchy-Riemann equations, mappings by elementary functions, complex integration, Cauchy’s theorem, Cauchy integral formula and applications, Taylor series, Laurent series, isolated singularities, residue theorem and applications.
MATH 4511 Linear Algebra 3 cr.
Prerequisite: MATH 2511 or 3512. Inner product spaces, dual spaces, canonical forms, the spectral theorem, quadratic forms, operators, the classical groups, multilinear algebra and applications.
MATH 4512 Abstract Algebra 3 cr.
Prerequisite: MATH 3512. Ideals, Euclidean and principal ideal domains, finite fields, Sylow theorems, and solvable groups.
MATH 4518 Elementary Number Theory 3 cr.
Prerequisite: consent of department. Divisibility, congruences, power residues, quadratic residues, certain arithmetic functions and selected topics.
MATH 4524 Mathematical Logic 3 cr.
Prerequisite: MATH 2721 or 3512 or consent of department. Propositional and predicate calculus; formal systems; computability and decidability.
MATH 4611 Topology 3 cr.
Prerequisite: MATH 4101 or consent of department. Topological spaces, continuous maps and homeomorphisms, product spaces, connectedness, separation axioms, compactness, and metric spaces.
MATH 4711 Graph Theory 3 cr.
Prerequisite: MATH 2511 or MATH 2721 or consent of department. An introduction to graph theory and its applications; the basic theorems and algorithms. Paths and cycles, colorings, planarity, directed graphs, networks.
MATH 4721 Combinatorics 3 cr.
Prerequisite: MATH 2511 or 2721 or consent of department. Permutations, combinations, and partitions; inclusion-exclusion principle; generating functions and recurrence relations; matchings; combinatorial designs.
MATH 4990 Special Topics 3 cr.
Prerequisite: consent of department. Six hours maximum will be accepted for graduate credit.
MATH 4991 Special Topics 3 cr.
Prerequisite: consent of department. Six hours maximum will be accepted for graduate credit.
MATH 4992 Special Topics 3 cr.
Prerequisite: consent of department. Six hours maximum will be accepted for graduate credit.
MATH 4998 Selected Readings in Mathematics 1-3 cr.
Prerequisite: consent of department. This course may be repeated to a total of six credits. The course consists of directed readings designed to meet the needs and interests of the individual student; regular conferences between the student and the instructor are required. The section number will correspond with credit to be earned.
MATH 6005 Higher Algebra 3 cr.
Prerequisites: a working knowledge of college algebra and consent of department. (This course is intended for candidates in the M.A. in Science Teaching program.) Topics covered include inequalities, complex numbers, theory of equations, mathematical induction, binomial theorem, progressions, infinite series and applications.
MATH 6006 Analytic and Vector Geometry 3 cr.
Prerequisites: a working knowledge of plane geometry and college algebra and consent of department. (This course is intended for candidates in the M.A. in Science Teaching program.) Plane and solid geometry by analytic methods. Topics covered include vectors, lines, conic sections, translation and rotation of axes, polar coordinates, parametric representations; plane and three-space curves and surfaces.
MATH 6007 Topics in Higher Algebra and Geometry 3 cr.
Prerequisite: MATH 6005 or 6006 or consent of department. (This course is intended for candidates in the M.A. in Science Teaching program.) Topics selected from inequalities, theory of equations, Euclidean geometry, and non-Euclidean geometry.
MATH 6020 Geometry Geometry 3 cr.
Prerequisite: MATH 4020. Space figures: similarity and trigonometry, area and volume measurement, elements of spherical geometry, plane coordinate geometry. This course may be used for degree credit only in the elementary education curriculum.
MATH 6201 Introduction to Applied Mathematics 3 cr.
Prerequisites: MATH 4101. MATH 4101 may be taken concurrently. System of linear ordinary differential equations, fundamental matrices, nonlinear systems of ODE’s, stability, limit cycles, separation of variables, heat equation, wave equation, Laplace’s equation, Sturm-Liouville boundary value problems, Green’s functions, integral transforms, conformal mapping, complex integration.
MATH 6202 Introduction to Applied Mathematics 3 cr.
Prerequisites: MATH 4101 or consent of department. Dynamical systems, elementary bifurcations, chaos, nonlinear PDE, characteristics, shocks, calculus of variations, Euler-Lagrange equation, normed linear spaces, linear operators, convex analysis, optimization.
MATH 6211 Applied Analysis 3 cr.
Prerequisite: MATH 4104 or 4411. Calculus of residues, Fourier and Laplace transforms, orthogonal expansion; special functions; solution of boundary value problems of partial differential equations by various methods; separation of variable, transform techniques; Sturm-Liouville theory; perturbation and asymptotic developments; Green’s functions; the method of characteristics.
MATH 6221 Advanced Differential Equations 3 cr.
Prerequisites: MATH 4101 or 4221. Ordinary differential equations in the real and complex domains, existence and uniqueness theorems, linear systems with constant and periodic coefficients. Linear differential equations or order n, self-adjoint eigenvalue problems, nonlinear equations, and stability theory.
MATH 6224 Partial Differential Equations II 3 cr.
Prerequisite: MATH 4224 or consent of department. Topics in modern linear and nonlinear partial differential equations, distributions and weak solutions, method of characteristics, shock waves, Green functions, fixed point theorems, reaction diffusion equations.
MATH 6230 Advanced Finite Element Analysis 3 cr.
Prerequisites: MATH 4224 or consent of department; Mathematics 4230 is recommended; some knowledge of computer programming is required. Galerkin method, linear triangular elements, bilinear rectangular elements, axisymmetric elements, isoparametric elements, heat transfer by conduction and convection, torsion of noncircular sections, ground water with sources and sinks, biharmonic equation, vibration of membrane, iterative methods, software maintenance and development.
MATH 6242 Functional Analysis 3 cr.
Prerequisite: MATH 4102 or consent of department. Topics will be selected from the following: metric spaces, normed spaces, Banach spaces, functionals, dual spaces and weak topology, inner product spaces, Hilbert spaces, compact operators, spectral analysis, fixed point theorems, implicit function theorem, Fredholm theory.
MATH 6251 Numerical Ordinary Differential Equations 3 cr.
Prerequisite: MATH 4252 or consent of department. Existence and approximation theorems for ordinary differential equations and systems of ordinary differential equations. Convergence, stability, and error analysis.
MATH 6258 Finite Difference Methods 3 cr.
Prerequisites: MATH 2115, 2221 and 2511 or consent of department; Mathematics 4101 is recommended; some knowledge of computer programming is required. Introduction to finite difference methods for solving partial differential equations. Convergence, consistency, stability, description and analysis of various explicit and implicit schemes for parabolic and hyperbolic equations.
MATH 6260 Optimal Control 3 cr.
Prerequisites: MATH 2221 and 4102 or consent of department. The calculus of variations and the Pontryagin maximum principle. Optimal control of linear and nonlinear systems. Algorithms for computing optimal controls.
MATH 6270 Advanced Optimization 3 cr.
Prerequisite: MATH 4101 or consent of department; Mathematics 4270 is recommended. Theory and application of advanced computational methods for extremizing linear and nonlinear functions of many variables including constrained and unconstrained problems. Particular topics include a review of the simplex method an introduction to interior point methods for linear programming problems, descent methods, Newton-like methods, conjugate direction methods, and quadratic and nonlinear programming.
MATH 6290 Topics in Numerical Analysis 3 cr.
Prerequisite: consent of department.
MATH 6300 Statistical Programming with SAS 3 cr.
Prerequisites: Previous experience using the SAS statistical package or consent of department. Proc IML, SAS macros and applications, Monte Carlo methods, resampling methods including bootstrap and jackknife, selected SAS procedures, statistical report writing with SAS.
MATH 6301 Applied Statistics 3 cr.
Prerequisite: MATH 4301 or consent of department. Only one of MATH 4301 or 6301 may be counted toward a master’s degree in mathematics. Data analysis, analysis of variance, regression analysis, nonparametric methods, use of computer packages.
MATH 6303 Multivariate Statistical Analysis 3 cr.
Prerequisite: MATH 6301 or consent of department. Multivariate normal distribution, test of hypothesis on means, multivariate analysis of variance, canonical correlation.
MATH 6304 Regression Analysis 3 cr.
Prerequisite: MATH 6301 or consent of department. Linear regression, regression diagnostics, multiple regression, nonlinear regression. Only one of MATH 4304 or 6304 may be counted toward a master’s degree in Mathematics.
MATH 6311 Mathematical Statistics 3 cr.
Prerequisites: Consent of department. MATH 6311 is prerequisite to MATH 6312. Theory of probability distributions, random variables and functions of random variables, multivariate and conditional distributions, order statistics, sampling distributions, theory of estimation and hypothesis testing.
MATH 6312 Mathematical Statistics 3 cr.
Prerequisites: Consent of department. MATH 6311 is prerequisite to MATH 6312. Theory of probability distributions, random variables and functions of random variables, multivariate and conditional distributions, order statistics, sampling distributions, theory of estimation and hypothesis testing.
MATH 6321 Sampling Theory 3 cr.
Prerequisite: MATH 6311 or consent of department. Simple random sampling with and without replacement, sampling with varying probabilities, stratified sampling, cluster sampling, subsampling, systematic sampling, two-stage sampling, and sequential sampling.
MATH 6331 Categorical Data Analysis 3 cr.
Prerequisite: MATH 6311 and 6312 or consent of department. Analysis of contingency tables, exact small sample tests, large sample inference, logistic regression, logit, probit, extreme value, loglineaer and other generalized linear models, model building and applications.
MATH 6341 Linear Statistical Models 3 cr.
Prerequisite: MATH 6312 or consent of department. Multivariate normal distribution, matrix operations, distributions of quadratic forms, general linear hypotheses, standard models, computing techniques.
MATH 6342 Design of Experiments 3 cr.
Prerequisite: MATH 6341 or consent of department. Matrix methods including calculus, principles of experimental design, techniques of analysis.
MATH 6351 Time Series Analysis 3 cr.
Prerequisite: MATH 6311 or consent of department. Autocorrelation, spectral analysis and filtering, autoregressive (AR) models, moving average (MA) models, ARMA models, ARIMA models, model identification, forecasting, and estimation of parameters.
MATH 6361 Statistical Quality Control 3 cr.
Prerequisite: MATH 4301 or 4304 or consent of department. Management and quality, construction and analysis of control charts for variables and attributes, Markov chain representations of control charts, capability analysis, reliability, continuous sampling plans, acceptance sampling, tolerances.
MATH 6362 Reliability Theory 3 cr.
Prerequisite: MATH 6301 or consent of department. Reliability of coherent systems, distributions in reliability, classes of life distributions, maintenance and replacement policies, availabilities, competing risks, reliability hypothesis testing, estimation of reliability functions, regression models for reliability data, and fault tree analysis.
MATH 6370 Statistical Consulting 3 cr.
Prerequisite: consent of the department. Theory and practice of effective statistical consulting. Communication with clients, problem solving, and report writing. May be repeated for credit. Students may not count more than six semester hours credit for MATH 6370 toward a degree in Mathematics.
MATH 6371 Probability 3 cr.
Prerequisite: MATH 4371 or 4311 or consent of department. Measure theoretic origins, infinite dimensional probability spaces, modes of convergence, laws of large numbers, central limit theorems; certain topics from infinitely divisible laws, stochastic processes, separability, martingales and semi-martingales, ergodic theory, systems theory and stopping rules.
MATH 6372 Mathematics of Financial Derivatives 3 cr.
Prerequisite: credit or concurrent registration in MATH 4311 or the consent of the department. A brief introduction to financial derivatives, normal random variables, geometric brownian motion, stochastic differentiation, stochastic integration, ito’s lemma, the Black-Scholes PDE and its solution.
MATH 6381 Biostatistics 3 cr.
Prerequisite: MATH 6311 or consent of the department. Biostatistical design of medical studies, one- and two-sample inference, counting data, nonparametric, distribution-free and permutation models: robust procedures, simple and multiple regression, multiple comparisons, cross-over designs, discrimination and classification, and other topics.
MATH 6382 Statistical Analysis of Survival Data 3 cr.
Prerequisite: MATH 6311 and 6312 or consent of department. Failure times, censoring mechanisms, failure rates, survival functions, product limit estimators, covariates, Cox model, partial likelihood, exponential regression, rank tests, and other topics.
MATH 6385 Longitudinal Data Analysis 3 cr.
Prerequisite: MATH 6311, 6312 or consent of department. Presentations of longitudinal data, general linear models for longitudinal data, parametric models for covariance structure, analysis of variance methods, marginal models, random effects models, methods for discrete longitudinal data.
MATH 6390 Topics in Probability and Statistics 3 cr.
Prerequisite: consent of department.
MATH 6411 Complex Analysis 3 cr.
Prerequisite: MATH 4411. Analytic continuation, reflection principle, argument principle, Rouche’s theorem. Convergence of sequences, series, and infinite products of analytic functions. Entire functions, conformal mappings, Riemann mapping theorem, Riemann surfaces, gamma function, Riemann zeta function.
MATH 6450 Measure and Integration 3 cr.
Prerequisite: MATH 4102 or consent of department. MATH 6450 is prerequisite to MATH 6451. Measure theory, integration, types of convergence, absolute continuity, function spaces.
MATH 6451 Measure and Integration 3 cr.
Prerequisite: MATH 4102 or consent of department. MATH 6450 is prerequisite to MATH 6451. Measure theory integration types of convergence absolute continuity function spaces.
MATH 6490 Topics in Analysis 3 cr.
Prerequisite: consent of department.
MATH 6491 Topics in Analysis 3 cr.
Prerequisite: consent of department.
MATH 6492 Topics in Analysis 3 cr.
Prerequisite: consent of department.
MATH 6511 Algebra 3 cr.
Prerequisite: MATH 4512. Infinite Abelian groups, ordered groups, free groups, finite groups, rings, fields, field extensions, finite fields, Galois theory.
MATH 6590 Topics in Algebra 3 cr.
Prerequisite: consent of department.
MATH 6591 Topics in Algebra 3 cr.
Prerequisite: consent of department.
MATH 6592 Topics in Algebra 3 cr.
Prerequisite: consent of department.
MATH 6611 Topology 3 cr.
Prerequisite: MATH 4611. Homotopy, dimension theory, uniform spaces, compactification and other basic advanced topics.
MATH 6690 Topics in Topology 3 cr.
Prerequisite: MATH 6611 or consent of department.
MATH 6998 Advanced Readings in Mathematics 1-3 cr.
Prerequisite: consent of department. This course may be repeated to a total of six credits. The course consists of directed readings designed to meet the needs and interests of the individual student; regular conferences between the student and the instructor are required. The section number will correspond with credit to be earned.
MATH 7000 Thesis Research 1-9 cr.
To be repeated for credit until thesis is accepted. Section number will correspond with credit to be earned.
MATH 7040 Examination or Thesis Only 0 cr.
No credit. Open to students in a thesis program who have only (other than application for degree) the final typing and acceptance by the Graduate School of their thesis or dissertation or to students in a non-thesis program who have only (other than application for degree) to pass the final examination to complete graduation requirements.
