MATH g327 Vector Analysis 3 credits. Calculus of vector functions of several variables. Derivative matrix. Chain rule. Inverse function theorem. Multiple integration. Change of variables. Integrals over curves and surfaces. Green's, Stokes' and divergence theorems. Applications to physics. PREREQ: MATH 223.
MATH g330 Linear Algebra 3 credits. Fields, vector spaces, linear transformations and matrices, triangular and Jordan forms, eigenvalues, dual spaces and tensor products, bilinear forms, inner product spaces. PREREQ: MATH 222 AND MATH 230.
MATH g331-g332 Modern Algebra 3 credits each. Rings, fields, groups, algebras, and selected topics in abstract algebra. PREREQ: MATH 287 AND MATH 330.
MATH g343 Modern Geometry 3 credits. Projective, Euclidean, and non-Euclidean geometries from an axiomatic point of view. PREREQ: MATH 230 OR PERMISSION OF INSTRUCTOR.
MATH g352 General Statistics 3 credits. Probability, random variables, discrete and continuous distributions such as the Binomial, Poisson, Geometric, Hypergeometric, Normal, and Gamma, sampling distribution, point and interval estimation, hypothesis testing. PREREQ: MATH 120 OR MATH 222.
MATH g355 Operations Research I 3 credits. Deterministic problems in operations research oriented towards business. Includes linear programming, transportation problems, network analysis, PERT, dynamic programming, and elementary game theory. PREREQ: MATH 230, 250 OR PERMISSION OF INSTRUCTOR.
MATH g356 Operations Research II 3 credits. Probabilistic models oriented towards business. Selections from stochastic processes, Markov chains, queuing theory, inventory theory, reliability, decision analysis, and simulation. PREREQ: MATH 355.
MATH g360 Differential Equations 3 credits. Theory and applications of ordinary differential equations. PREREQ: MATH 222 AND MATH 230 OR PERMISSION OF INSTRUCTOR.
MATH g421 Advanced Engineering Mathematics I 3 credits. Cross-listed as ENGR g421. Analysis of complex linear and non-linear engineering systems using advanced techniques, including Laplace transforms, Fourier series and classical partial differential equations. PREREQ: MATH 360, ENGR 264.
MATH g422 Advanced Engineering Mathematics II 3 credits. Cross-listed as ENGR g422. Analysis of complex linear and non-linear engineering systems using advanced techniques, including probability and statistics, advanced numerical methods and variational calculus. PREREQ: ENGR 421 OR MATH 421.
MATH g423-g424 Introduction to Real Analysis 3 credits each. The real number system, limits, sequences, series, and convergence; metric spaces; completeness; and selected topics on measure and integration theory. PREREQ: MATH 287, MATH 326, MATH 330, AND MATH 360.
MATH g435 Elementary Number Theory 3 credits. Diophantine equations, prime number theorems, residue systems, theorems of Fermat and Wilson, and continued fractions. PREREQ: MATH 331.
MATH g441 Introduction to Numerical Analysis 3 credits. Designed to offer students in any applied science a reasonably broad introduction to standard numerical techniques for solving problems dealing with non-linear equations, systems of linear equations, differential equations, as well as techniques of interpolation, numerical integration, and differentiation. PREREQ: MATH 326 AND MATH 360 OR PERMISSION OF INSTRUCTOR.
MATH g442 Introduction to Numerical Analysis 3 credits. Extension of MATH 441 for students who wish to pursue more advanced techniques with emphasis on analysis. Typical topics covered include numerical methods applied to partial differential equations, integral equations, and in-depth treatment of topics covered in MATH 441. PREREQ: MATH 441.
MATH g450-g451 Mathematical Statistics 3 credits each. Probability, random variables, discrete and continuous distributions, order statistics, limit theorems, point and interval estimation, uniformly most powerful tests, likelihood ratio tests, chi-square and F tests, nonparametric tests. PREREQ: MATH 326.
MATH g462 Introduction to Complex Variables 3 credits. Introduction to the study of functions of a complex variable including analytic functions, power series, integral theorems, and applications. PREREQ: MATH 360 AND EITHER MATH 326 OR MATH 421.
MATH g465 Partial Differential Equations 3 credits. Equations of the first and second orders, methods of solution, Laplace's Equation, heat equation, and the wave equation. Emphasis on applications to problems in the physical sciences and engineering. PREREQ: MATH 360 AND EITHER MATH 326 OR MATH 421.
MATH g473 Introduction to Topology 3 credits. Metric spaces; convergence; notions of continuity; connected, separable and compact spaces. PREREQ: PERMISSION OF INSTRUCTOR.
MATH g481 Special Problems 1-3 credits. Reading and conference in an area not usually covered by a regular offering. Individual work under the supervision and guidance of a professor whose specialty includes the chosen area. Open to seniors and graduate students in good standing and with the consent of the instructor. May be repeated until 6 credits are earned.
MATH g491 Mathematics Seminar 1-3 credits. Advanced reading and discussion on selected topics in mathematics. May be taken for credit more than once. PREREQ: SENIOR STANDING OR EQUIVALENT.
MATH 597 Professional Education Development Topics. Variable credit. May be repeated. A course for practicing professionals aimed at the development and improvement of skills. May not be applied to graduate degrees. May be graded S/U.
MATH 625-626 Real Analysis 3 credits each. Structure of the Real number system, measures and measurable functions, the Lebesgue integral, other integrals, Lp spaces, differentiable functions, the Radon-Nikodym Theorem, Fubini's Theorem. PREREQ: MATH 424.
MATH 627-628 Complex Analysis 3 credits each. Classical theorems of Cauchy, Goursat, Mittag-Leffler, Weierstrass, Riemann, and Picard involving analytic functions, representation theorems, conformal mappings, entire and meromorphic functions, analytic continuation, and other topics. PREREQ: PERMISSION OF INSTRUCTOR.
MATH 631-632 Abstract Algebra 3 credits each. Categories, groups, rings and ideals, polynomials, and fields through Galois Theory, modules, lattices, advanced linear and multilinear algebra. PREREQ: MATH 332 AND 330 OR PERMISSION OF INSTRUCTOR.
MATH 633 Matrix Analysis 3 credits. Eigenvalues, special matrices, normal forms, matrix polynomials, matrix functions, matrix norms, Kronecker products, stability, matrix equations, generalized inverses, nonnegative matrices. PREREQ: MATH 330 AND MATH 424.
MATH 641-642 Numerical Analysis 3 credits each. Topics selected from approximation theory, optimization, numerical linear algebra, differential and integral equations, spline analysis, computer algorithms, and other areas of current research in numerical analysis. PREREQ: MATH 423 AND MATH 441.
MATH 650 Thesis (D.A.) 1-6 credits.
MATH 652 Stochastic Processes 3 credits. Topics from conditional probability and expectation, martingales, Kolmogorov's Theorem, Markov processes, random walks, Brownian motion, diffusions, dynamic programming, stochastic differential equations. Applications to modeling physical and/or social dynamical systems. PREREQ: MATH 450.
MATH 653 Advanced Topics in Probability and Statistics 3 credits. Topics such as experimental design, regression analysis, multivariate statistical analysis. PREREQ: MATH 352 AND MATH 230, OR PERMISSION OF INSTRUCTOR.
MATH 655-656 Combinatorics 3 credits each. Theory and applications of: choice and enumeration techniques, generating functions, partitions, designs and configurations, graph theory including digraphs, algebraic graph theory and extremal problems. PREREQ: PERMISSION OF INSTRUCTOR.
MATH 662-663 Differential Equations 3 credits each. Existence, uniqueness, and dependence of solutions upon initial conditions; linear equations; autonomous equations; dynamical systems and stability; partial differential equations of first and second order, with applications. PREREQ: MATH 326, MATH 327, AND MATH 360.
MATH 664-665 Applied Mathematics 3 credits each. Differential operators, variational formulations, transform theory, spectral theory, Green's functions, bifurcations, stability, integrability, perturbation methods, applications to physical problems stressing construction and analysis of ODE and PDE models. PREREQ: MATH 330 AND MATH 465.
MATH 667-668 Functional Analysis 3 credits each. Major results of functional analysis, such as the Hahn-Banach, open mapping, and closed graph theorems; study of Hilbert and Banach spaces; spectral analysis. PREREQ: MATH 423 OR MATH 625 OR PERMISSION OF INSTRUCTOR.
MATH 671-672 Topology 3 credits each. Fundamental theorems and examples from point-set topology; emphasis on general and metric topologies and continuous mappings; introduction to topology of manifolds, covering spaces, homotopy, homology, and cohomology. PREREQ: MATH 473 OR PERMISSION OF INSTRUCTOR.
MATH 681-682 Differential Geometry 3 credits each. Differentiable manifolds and mappings; bundles, connections, geodesics, and curvature; Lie groups; topics from Riemannian, Hermitian, or symplectic geometry. PREREQ: MATH 327 AND MATH 330.
MATH 691 Seminar 1-3 credits. Advanced readings, problems, and discussion on selected topics in mathematics. May be taken for credit more than once on distinct topics.
MATH 692 Doctor of Arts Seminar 2 credits. Topics include the nature and practice of mathematical research, grants, public speaking, professionally and classroom related software, information media, issues in mathematical pedagogy, standards, and curricula, university organization, history of mathematics. Graded S/U.
MATH 693 Mathematical Exposition 1 credit. Presentation of mathematics in a seminar setting. Small group practice in and critique of mathematical exposition. Requirements include presentation of a departmental colloquium on an assigned topic. Graded S/U.
MATH 699 Special Topics in Mathematics 1-3 credits. Each offering will deal with a topic selected from such fields of mathematics as algebra, analysis, geometry, number theory, topology, applied analysis, probability, and mathematical logic. May be taken for credit more then once. PREREQ: PERMISSION OF INSTRUCTOR.
MATH 700 Supervised Teaching Internship. Credit variable up to 9 credits. Graded S/U.