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: 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