MATH 501 - Combinatorics I Credit Hours: 3.0 Prerequisites: MATH 301; MATH 360 or MATH 366 Description: Puzzles, numbers and counting, subsets, recurrence relations, generating functions, inversion, counting with symmetry, networks, matchings

 MATH 502 - Combinatorics II Credit Hours: 3.0 Prerequisites: MATH 501 Description: Graph algorithms, external set theory; partitions, Hadamard matrices, q-binomials, finite geometries, strongly regular graphs, triple systems, designs

 MATH 505 - Teaching Problem Solving in Mathematics K-12 Credit Hours: 3.0 Prerequisites: Teacher licensure. Offered as telecourse only. Description: Problem-solving strategies, cooperative learning, and manipulatives for K-12 classroom

 MATH 510 - Linear Programming and Network Flows Credit Hours: 3.0 Prerequisites: MATH 261 - Credit not allowed for both MATH 510 and ENGR 510 Description: Optimization methods; linear programming, simplex algorithm, duality, sensitivity analysis, minimal cost network flows, transportation problems

 MATH 517 - Introduction to Real Analysis Credit Hours: 3.0 Prerequisites: MATH 369; MATH 417. Description: Euclidean and metric spaces, compactness, continuity, sequences, series, multivariable differentiation, inverse and implicit function theorems

 MATH 519 - Complex Variables I Credit Hours: 3.0 Prerequisites: MATH 317. Description: Analytic functions, complex integration theory, singularities, elementary functions, and mapping

 MATH 520 - Nonlinear Programming Credit Hours: 3.0 Prerequisites: MATH 510/ENGR 510. Description: Theoretical, computational, practical aspects of nonlinear programming (NLP); unconstrained, constrained NLP; quadratic programming; large-scale NLP

 MATH 525 - Optimal Control Credit Hours: 3.0 Prerequisites: MATH 340 or MATH 345 Description: Theory and application of optimal control and optimal estimation theory; continuous and discrete time systems; Pontryagin maximum principle

 MATH 530 - Mathematics for Scientists and Engineers Credit Hours: 4.0 Prerequisites: MATH 340 or MATH 345 - Not for mathematics graduate students. Description: Credit not allowed for both MATH 530 and MATH 332. Proof-oriented linear algebra, ordinary and partial differential equations

 MATH 531 - Discrete Models of Physical Systems Credit Hours: 3.0 Prerequisites: MATH 340 or MATH 345 Description: Discrete models for physical systems; systems of ordinary differential equations, applied linear algebra; introduction to finite elements

 MATH 532 - Mathematical Modeling of Large Data Sets Credit Hours: 3.0 Prerequisites: MATH 369 or MATH 530; preparedness to do programming in a standard language. Description: Mathematical theory and algorithms for modeling large data sets. Application to real world problems. Emphasis on geometric ideas

 MATH 535 - Foundations of Applied Mathematics Credit Hours: 3.0 Prerequisites: MATH 340 or MATH 345 Description: Calculus of variations, peturbation methods, models of continuum, dimensional analysis, stochastic models, integral equations, diffusion

 MATH 540 - Dynamical Systems Credit Hours: 3.0 Prerequisites: MATH 369; MATH 417 Description: Linear and nonlinear systems, orbits, phase space, flows of vector fields, stability, bifurcation theory, chaos, strange attractors and applications

 MATH 545 - Partial Differential Equations I Credit Hours: 3.0 Prerequisites: MATH 340 or MATH 345 Description: Elliptic, parabolic, and hyperbolic partial differential equations with applications from various fields of engineering

 MATH 546 - Partial Differential Equations II Credit Hours: 3.0 Prerequisites: MATH 545 Description: Distribution theory, Green's functions, Sobolev spaces, elliptic and parabolic equations

 MATH 550 - Introduction to Numerical Methods for Partial Differential Equations Credit Hours: 3.0 Prerequisites: MATH 340 or MATH 345 or MATH 530 Description: Introduction to finite elements, finite differences, spectral methods, method of lines, conservation laws; stability and convergence analysis.

 MATH 560 - Linear Algebra Credit Hours: 3.0 Prerequisites: MATH 369 Description: Finite dimensional vector spaces, inner products, dual spaces, transformations, projections, adjoints, norms, eigenvalues, eigenvectors

 MATH 561 - Numerical Analysis I Credit Hours: 4.0 Prerequisites: CS 156 or CS 160 or CS 253 or MATH 151; MATH 560 Description: Numerical linear algebra, solving nonlinear systems, least squares, and minimization

 MATH 566 - Introduction to Abstract Algebra I Credit Hours: 3.0 Prerequisites: MATH 366 Description: Analysis of algebraic structures including groups, rings, fields, and vector spaces

 MATH 567 - Introduction to Abstract Algebra II Credit Hours: 3.0 Prerequisites: MATH 566 Description: Field theory, Galois theory, and advanced linear algebra

 MATH 570 - Topology I Credit Hours: 3.0 Prerequisites: MATH 417 or MATH 472 Description: Topologies on a set, continuity, product and quotient spaces, metrization, compactness, connectedness, introduction to covering spaces and the fundamental group

 MATH 571 - Topology II Credit Hours: 3.0 Prerequisites: MATH 566; MATH 570. Description: Homotopy, simplicial and singular homology, further topics in algebraic topology

 MATH 584 - Supervised College Teaching Credit Hours: 1.0 Prerequisites: Written consent of instructor

 MATH 592 - Seminar in Mathematics Credit Hours: 1.0 Prerequisites: Written consent of instructor Description: During the course of each semester a minimum of 10 one-hour seminar meetings selected from Green Slopes, the Mathematics Colloquium, or research seminars organized by mathematics faculty must be attended to satisfy the seminar requirement.

 MATH 601 - Advanced Combinatorics I Credit Hours: 3.0 Prerequisites: MATH 502; MATH 566 Description: Special numbers, mobius inversions, transversals, partial orders, different sets, codes, t-designs

 MATH 602 - Advanced Combinatorics II Credit Hours: 3.0 Prerequisites: MATH 601 Description: Hypergeometric functions, graph algorithms, hadamard matrices, strongly regular graphs, association schemes

 MATH 605A - Number Theory: Algebraic Number Theory Credit Hours: 3.0 Prerequisites: MATH 519 or concurrent registration; MATH 566; MATH 567 or concurrent registration. Description: A) Algebraic Number Theory. B) Arithmetic Geometry. C) Elliptic Curves

 MATH 605B - Number Theory: Arithmetic Geometry Credit Hours: 3.0 Prerequisites: MATH 519 or concurrent registration; MATH 566; MATH 567 or concurrent registration. Description: A) Algebraic Number Theory. B) Arithmetic Geometry. C) Elliptic Curves

 MATH 605C - Number Theory: Elliptic Curves Credit Hours: 3.0 Prerequisites: MATH 519 or concurrent registration; MATH 566; MATH 567 or concurrent registration. Description: A) Algebraic Number Theory. B) Arithmetic Geometry. C) Elliptic Curves

 MATH 617 - Integration and Measure Theory Credit Hours: 4.0 Prerequisites: MATH 517 Description: Riemann-Cauchy integration theory, sigma-algebras, Lebesgue theory of measure and integration, Fubini's Theorem, Radon-Nikodym theorem, L^p spaces

 MATH 618 - Advanced Real Analysis Credit Hours: 3.0 Prerequisites: MATH 560; MATH 617 Description: Normed linear spaces, Banach and Hilbert spaces, elements of functional analysis

 MATH 619 - Complex Variables II Credit Hours: 3.0 Prerequisites: MATH 519 519 Description: Infinite products, entire functions, analytic continuation, Reimann surfaces, other topics

 MATH 620 - Variational Methods and Optimization I Credit Hours: 3.0 Prerequisites: MATH 517; MATH 560 Description: Unconstrained and constrained infinite dimensional optimization, calculus of variations, applications

 MATH 621 - Variational Methods and Optimization II Credit Hours: 3.0 Prerequisites: MATH 620 Description: Unconstrained and constrained infinite dimensional optimization, variational inequalities, Lagrange multipliers, control, applications

 MATH 633 - Industrial and Applied Mathematics Credit Hours: 3.0 Prerequisites: MATH 530 or MATH 560 or MATH 561; preparedness to do programming in a standard language. Must register for lecture and laboratory Description: Team solution of problems arising in industrial and applied mathematics. Problem formulation, solution proposal, implementation and analysis

 MATH 640 - Ordinary Differential Equations I Credit Hours: 3.0 Prerequisites: MATH 340 or MATH 345 or MATH 530; MATH 369; MATH 517 Description: Existence and uniqueness, continuation, continuous dependence, linear systems, and stability

 MATH 641 - Ordinary Differential Equations II Credit Hours: 3.0 Prerequisites: MATH 640 Description: Topics selected from nonlinear boundary value problems, periodic phenomena, differential operators, and others

 MATH 645 - Advanced Partial Differential Equations I Credit Hours: 3.0 Prerequisites: MATH 546 Description: Abstract methods for linear partial differential equations

 MATH 646 - Advanced Partial Differential Equations II Credit Hours: 3.0 Prerequisites: MATH 645 Description: Problems in nonlinear partial differential equations

 MATH 651 - Numerical Analysis II Credit Hours: 4.0 Prerequisites: CS 156 or CS 160 or CS 253 or MATH 151; MATH 340 or MATH 345 or MATH 369 or MATH 530 Description: Interpolation, approximation, quadrature, initial and boundary value problems

 MATH 652 - Advanced Numerical Methods for PDEs Credit Hours: 3.0 Prerequisites: MATH 546 or MATH 560 or MATH 617 Description: Theory of numerical methods for solution of PDEs: convergence and stability properties; error estimation; approximation theory

 MATH 666 - Advanced Algebra I Credit Hours: 3.0 Prerequisites: MATH 567 Description: Theory of rings and algebras with applications

 MATH 667 - Advanced Algebra II Credit Hours: 3.0 Prerequisites: MATH 666 Description: Advanced topics from algebra: representation theory, Wedderburn theory, bilinear forms, multilinear and homological algebra

 MATH 670 - Introduction to Differential Manifolds Credit Hours: 3.0 Prerequisites: MATH 517 or MATH 570 Description: Finite-dimensional differential manifolds, submanifolds, vector fields and flows, Lie groups and algebras

 MATH 672 - Projective Geometry I Credit Hours: 3.0 Prerequisites: MATH 567 Description: Algebraic sets in projective space, the Nullstellensatz, rational maps and functions, coordinate rings, Hilbert functions, dimension, degree

 MATH 673 - Projective Geometry II Credit Hours: 3.0 Prerequisites: MATH 672 Description: Topics selected from curves and surfaces, sheaf theory, algebraic geometry, singularity theory, vector bundles

 MATH 676 - Topics in Mathematics Credit Hours: 3.0 - May be taken up to 5 times for credit Prerequisites: Determined by course instructor Description: Advanced study experiences which deal with established content areas in mathematics; for a list of recent topics click here.

 MATH 687 - Internship Credit Hours: Variable 1 - 9 Description: A work-learn experience integrating classroom theory with practical experience

 MATH 693 - Seminar in Mathematics Credit Hours: 3.0

 MATH 695 - Independent Study Credit Hours: Variable 1 - 18

 MATH 699 - Thesis Credit Hours: Variable 1 - 18

 MATH 717 - Functional Analysis I Credit Hours: 3.0 Prerequisites: MATH 618 Description: Topological vector spaces; Banach and Hilbert spaces

 MATH 718 - Functional Analysis II Credit Hours: 3.0 Prerequisites: MATH 717 Description: Spectral theory, operator theory, semigroups of transformations, and distribution theory

 MATH 750 - Numerical Methods and Models I Credit Hours: 3.0 Prerequisites: MATH 561 Description: Derivation of model equations, introduction to solution techniques and computing

 MATH 751 - Numerical Methods and Models II Credit Hours: 3.0 Prerequisites: MATH 561 Description: Convergence, stability, error estimates and computing

 MATH 793 - Seminar in Mathematics Credit Hours: Variable 1 - 18

 MATH 798 - Research Credit Hours: Variable 1 - 18

 MATH 799 - Dissertation Credit Hours: Variable 1 - 18