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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: 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 |