MTH 502: History of Mathematics, 3 credits.
Fall Semester
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.
Fall Semester
Axiom systems and models of Euclidean and Non-Euclidean geometry.
Prerequisite: MTH 230 or 309.

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

MTH 506: Mathematical Logic, 3 credits.
Offered By Announcement Only
Logics, truth, proof, logical consequence, model theory, formalization, and computation. Meta-theory of first-order logic, computability theory, and Gödel's incompleteness theorems. Related results by Church, Turing, and Tarski. Discussion of their philosophical significance.
(co-listed with PHI 506 and CSC 506)
Prerequisite: MTH 230.

MTH 510: Linear Algebra, 3 credits.
Spring Semester
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.
Spring Semester
Complex variables; conformal mapping, contour integration.
Prerequisite: MTH 211 or 310.

MTH 513: Partial Differential Equations I, 3 credits.
Fall Semester
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, 310, and 311.

MTH 514: Partial Differential Equations II, 3 credits.
Spring Semester
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.
Fall Semester
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.
Spring Semester
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.
Offered By Announcement Only
Basic algorithmic analysis. Algorithmic strategies. Fundamental computing algorithms. Distributed algorithms. Cryptographic algorithms. Geometric algorithms.
(Colisted with CSC 517.)
Prerequisite: MTH 309 (or 230) and CSC 220.

MTH 520: Numerical Analysis I, 3 credits.
Fall Semester
Topics from numerical linear algebra including solving systems of equations, LU, QR, and SVD factorizations, eigenvalues and eigenvectors, iterative methods, and applications.
Prerequisite: MTH 320 or permission of department chair.

MTH 521: Numerical Analysis II, 3 credits.
Offered By Announcement Only
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.
Fall Semester
Probability spaces, random variables, expectation, limit theorems.
Prerequisite: MTH 224 and 310.

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

MTH 527: Theory of Computing, 3 credits.
Offered By Announcement Only
Sets, relations, and languages. Automata theory. Basic computability theory. Turing machines. The complexity classes P and NP.
(Colisted with CSC 527.)
Prerequisite: MTH 309 or 461.

MTH 528: Combinatorics, 3 credits.
Offered By Announcement Only
Permutations and combinations, generating functions, enumerative analysis.
Prerequisite: MTH 461 or 561.

MTH 531: Topology I, 3 credits.
Fall Semester
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.
Spring Semester
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.
Fall Semester
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.
Spring Semester
Continuation of MTH 533.
Prerequisite: MTH 533.

MTH 540: Algorithm Design and Analysis, 3 credits.
Offered By Announcement Only
Design techniques include divide-and-conquer, greedy method, dynamic programming, backtracking. Time and space complexity. Sorting, searching, combinatorial and graph algorithms.
(Colisted with CSC 540.)
Prerequisite: MTH 517 (or CSC 517).

MTH 542: Statistical Analysis, 3 credits.
Fall Semester
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 210, 224.

MTH 547: Introduction to Mathematical Finance, 3 credits.
Offered By Announcement Only
Models of financial markets. Derivative securities: European and American options. Tools of mathematical finance: binomial trees, martingales, stopping times. Concepts of arbitrage and hedging. Risk-neutral valuation of financial derivatives; the Black-Scholes formula and its applications.
Prerequisite: MTH 224.

MTH 551: Introduction to Differential Geometry, 3 credits.
Offered By Announcement Only
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 either MTH 211 or 310, or permission of instructor.

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

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

MTH 591-594: Topics in Mathematics, 1-3 credits each.
Offered By Announcement Only