Graduate Courses....
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| 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: 3.0 |
| 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 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: 3.0 |
| 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 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: 3.0 |
| 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 |