MTH 502: History of Mathematics, 3 credits.
The development of mathematics from its earliest beginnings through the first half of the twentieth century. Numeral systems, geometry, algebra, analysis and set theory.
Prerequisite: Two courses in mathematics at the 200 level or above.

MTH 504: Foundations of Geometry, 3 credits.
Axiom systems and models of Euclidean and Non-Euclidean geometry.
Prerequisite: MTH 230 or 309.

MTH 505: Theory of Numbers, 3 credits.
Divisibility, primes; congruences; quadratic resides and reciprocity; Diophantine equations. Applications to cryptography.
Prerequisite: MTH 210 or 504.

MTH 506: Logic, 3 credits.
Propositional and first-order logic: completeness. Computational logic: Robinson's resolution. Formalized theories: arithmetic, Gödel's incompleteness theorem, Tarski's theorem on undefinability of truth.
Prerequisite: MTH 230 or 309 or permission of theinstructor.

MTH 508: Survey of Modern Algebra, 3 credits.
Algebraic systems, equivalence classes, groups, rings, fields, unique factorization domains.
Prerequisite: MTH 210 and 230. Not open to students with credit in MTH 509 or 561.

MTH 509: Discrete Mathematics II, 3 credits.
Groups and combinatorics; applications of group theory to computer design and error correcting codes; semigroups and their applications to finite state machines; rings and fields; applications of Boolean algebra to computer design.
Prerequisite: MTH 210, 309.

MTH 510: Linear Algebra, 3 credits.
Abstract vector spaces, bases and dimensions, linear maps, eigen values and eigenvectors, inner product spaces, operators, spectral theorems, canonical forms.
Prerequisite: MTH 210; transition course in logical reasoning such as MTH 230 or 309 recommended but not required.

MTH 512: Elementary Complex Analysis, 3 credits.
Complex variables; conformal mapping, contour integration.
Prerequisite: MTH 211 or 310.

MTH 513: Partial Differential Equations I, 3 credits.
Derivation, well posedness, and qualitative properties of initial value and boundary value problems for the heat, wave and Laplace equations. Energy methods, causality, maximum principles, heat kernels, Fourier series, and potential theory.
Prerequisite: MTH 210, 311 and either MTH 310 or 312.

MTH 514: Partial Differential Equations II, 3 credits.
Continuation of MTH 513. Approximations of solutions, distributions and integral transform methods, spectral theory and scattering. Applications to physical problems. Nonlinear equations and phenomena.
Prerequisite: MTH 513 or permission of the instructor.

MTH 515: Ordinary Differential Equations, 3 credits.
Linear systems, equilibria and periodic solutions, stability analysis, bifurcation, phase plane analysis, boundary value problems, applications to engineering and physics.
Prerequisites: MTH 311 and either MTH 211 or 310.

MTH 516: Dynamics and Bifurcations, 3 credits.
Bifurcation of equilibria and periodic solutions, global theory of planar systems, planar maps, nonlinear vibrations, forced oscillations, chaotic solutions, Hamiltonian systems, applications to engineering and physics.
Prerequisites: MTH 515 or permission of the instructor.

MTH 517: Data Structures and Algorithm Analysis, 3 credits.
Data abstraction, formal specification, trees, B-trees, balanced binary trees, graphs, searching and sorting. Algorithm analysis. Memory management.
Prerequisite: MTH 112 and 309, and CSC 220.

MTH 520: Numerical Analysis I, 3 credits.
Numerical linear algebra including the algebraic eigenvalue problem.
Prerequisite: MTH 320 or permission of department chairman.

MTH 521: Numerical Analysis II, 3 credits.
Numerical solution of ordinary and partial differential equations.
Prerequisite: MTH 320 or 520 or permission of department chairman.

MTH 524: Introduction to Probability Theory, 3 credits.
Probability spaces, random variables, expectation, limit theorems.
Prerequisite: MTH 310 or permission of department chairman.

MTH 525: Introduction to Mathematical Statistics, 3 credits.
Probability distributions, theory of sampling and hypothesis testing.
Prerequisite: MTH 524.

MTH 527: Theory of Automata, 3 credits.
Finite-state automata, context-free grammars, pushdown automata, Turing machines and computability.
Prerequisite: MTH 309 or 508.

MTH 528: Combinatorics, 3 credits.
Permutations and combinations, generating functions, enumerative analysis.
Prerequisite: One of the following: MTH 508, 509 or 561.

MTH 531: Topology I, 3 credits.
Set theory, topological spaces, compactness, connectedness, separation properties, quotient spaces, Tychonoff Theorem, compactification, Urysohn Lemma and Tietze Extension Theorem, function spaces.
Prerequisite: Permission of department chairman.

MTH 532: Topology II, 3 credits.
Differential and topological manifolds, classical groups and associated manifolds, tangent and tensor bundles, vector fields, differential forms, transversality, Sard's theorem, Stokes' Theorem.
Prerequisite: MTH 210 and 531.

MTH 533: Introduction to Real Analysis I, 3 credits.
Numerical sequences and series; continuity; differentiation; integration; sequences and series of functions; Fourier series; functions of several variables; implicit and inverse function theorems.
Prerequisite: MTH 211 (or 310) and 230.

MTH 534: Introduction to Real Analysis II, 3 credits.
Continuation of MTH 533.
Prerequisite: MTH 533.

MTH 540: Algorithm Design and Analysis, 3 credits.
Design techniques include divide-and-conquer, greedy method, dynamic programming, backtracking. Time and space complexity. Sorting, searching, combinatorial and graph algorithms.
Prerequisite: MTH 517.

MTH 542: Statistical Analysis, 3 credits.
Statistical inference about one or two populations from interval, ordinal and categorical data; analysis of variance; simple and multiple linear regression; designing research studies.
Prerequisite: MTH 224, 310 (or 211 or 312).

MTH 551: Introduction to Differential Geometry, 3 credits.
Geometry of curves and surfaces in Euclidean space. Local space curve theory, intrinsic and extrinsic curvature of surfaces, geodesics, parallelism, and differential forms.
Prerequisite: MTH 210 and one of MTH 211, 310, 312, or permission of instructor.

MTH 561: Abstract Algebra I, 3 credits.
Groups, rings; linear algebra; modules.
Prerequisite: MTH 210 and permission of department chairman.

MTH 562: Abstract Algebra II, 3 credits.
Continuation of MTH 561.
Prerequisite: MTH 561.

MTH 591-594: Topics in Mathematics, 1-3 credits each.

MTH 609: Cryptography and Data Security, 3 credits.
Encryption algorithms; cryptographic techniques; access, information flow and inference controls.
Prerequisite: MTH 509.

MTH 611: Theory of Computation, 3 credits.
Recursive functions, Markov algorithms, Turing machines. Unsolvability.
Prerequisite: MTH 509 and at least one programming course.

MTH 612: Complexity Theory, 3 credits.
Models of computations, Blum's axioms, intractability, NP-completeness.
Prerequisite: MTH 611.

MTH 621: Mathematical Probability, 3 credits.
Development of the measure-theoretic approach probability. Random variables, central limit theory, laws of large numbers, martingales.
Prerequisite: Permission of department chairman.

MTH 625: Multivariate Analysis, 3 credits.
Sampling theory for multivariate normal populations. Component and factor analysis. Stochastic difference equations.
Prerequisite: MTH 525.

MTH 630, 631: Real Variables, 3 credits each.
Lebesgue measure and the Lebesgue Integral for R¹, Banach Spaces. General measure theory, topological groups and Haar Measure.
Prerequisite: MTH 532.

MTH 632, 633: Complex Variables, 3 credits each.
Complex numbers line or transformation, analytic function, conformality. Cauchy's Theorem, representation theorems, harmonic functions.
Prerequisite: MTH 531.

MTH 638: Stochastic Processes, 3 credits.
Prerequisite: MTH 631.

MTH 640, 641: Algebraic Topology, 3 credits.
Homotopy, covering space, Eilenberg-Steenrod axioms for (co) homology theories, Mayer-Vietoris sequences, Universal Coefficient theorem, Kunneth formula, computations and applications.
Prerequisite: MTH 532.

MTH 647: Computational Geometry, 3 credits.
Algorithms for solving geometric problems arising from application domains including raphics, robotics, and GIS.
Prerequisite: MTH 517 or permission of instructor.

MTH 651, 652: Differential Geometry, 3 credits each.

MTH 657: Lie Groups, 3 credits.

MTH 661, 662: Abstract Algebra, 3 credits each.
Prerequisite: MTH 562.

MTH 670: Directed Reading of Research, 2-4 credits.

MTH 680, 681: Topics in Analysis, 3 credits each.

MTH 682, 683: Topics in Topology, 3 credits each.

MTH 685: Topics in Algebra, 3 credits.

MTH 686, 687: Topics in Mathematics, 3 credits each.

MTH 690: Seminar for Beginning Graduate Students, 1-3 credits.
The selection of topics will be flexible but will be of interest to beginning graduate students.

MTH 692: Seminar, 1-2 credits.

MTH 710: Master's Thesis, 1-6 credits.
The student working on his/her master's thesis enrolls for the number of credits as determined by his/her advisor. Credit is not awarded until thesis has been accepted.

MTH 725: Continuous Registration-Master's Study, 0 credits.
To establish residence for non-thesis master's students who are preparing for major examinations. Credit not granted. Regarded as full time residence.

MTH 730: Doctoral Dissertation, 1-12 credits.
Required of all candidates for the Ph.D. The student will enroll for credit as determined by his/her advisor, but for not less than a total of 12 hours. Up to 12 hours may be taken in a regular semester, but not more than six in a summer session.

MTH 740: Research Project, 1-6 credits.
Required of all candidates for the Doctor of Arts degree. Student enrolls for credit as determined by advisor. Credit is not awarded until the doctoral project has been accepted. Total enrollment may not exceed six credits.

MTH 750: Research in Resident, 0 credits.
Used to establish research in residence for the Ph.D. and D.A., after the student has been enrolled for the permissible cumulative total in appropriate doctoral research. Credit not granted. May be regarded as full-time residence as determined by the Dean of the Graduate School.