Graduate Courses in Mathematics (MATH)

MATH 207 - Probability Theory

(Cross listed with Statistics 251.) Distributions of random variables and functions of random variables. Expectations, stochastic independence, sampling and limiting distributions (central limit theorems). Concepts of random number generation. Prerequisite: Math 121; Stat 151 or 153 recommended.

Credits: 3

MATH 221 - Deterministic Modls Oper Rsch

The linear programming problem. Simplex algorithm, dual problem, sensitivity analysis, goal programming. Dynamic programming and network problems. Prerequisites: MATH 124; MATH 121 desirable. Cross-listing: CSYS 221.

Credits: 3

MATH 222 - Stochastic Models in Oper Rsch

Development and solution of some typical stochastic models. Markov chains, queueing problems, inventory models, and dynamic programming under uncertainty. Prerequisite: 207 or Statistics 151, or instructor's permission.

Credits: 3

MATH 224 - Algorithm Design & Analysis

(Cross listed with CS 224.) Comprehensive analysis of common algorithmic paradigms including greedy algorithms, divide an conquer, dynamic programming, graph algorithms, and approximation algorithms. Complexity hierarchies. Prerequisites: CS 104 or 124, Math 173 recommended.

Credits: 3

MATH 230 - Ordinary Differential Equation

Solutions of linear ordinary differential equations, the Laplace transformation, and series solutions of differential equations. Prerequisite: 121. Corequisite: 124 or instructor's permission. Credit not granted for more than one of the courses Math. 230 or 271.

Credits: 3

MATH 235 - Mathematical Models & Analysis

Techniques of undergraduate calculus and linear algebra are applied for mathematical analysis of models of natural and human-created phenomena. Students are coached to give presentations. Prerequisites: MATH 121 and any of MATH 124, MATH 230, or MATH 271.

Credits: 3

MATH 236 - Calculus of Variations

Necessary conditions of Euler, Legendre, Weierstrass, and Jacobi for minimizing integrals. Sufficiency proofs. Variation and eigenvalue problems. Hamilton-Jacobi equations. Prerequisite: 230. Alternate years, 1997-98.

Credits: 3

MATH 237 - Intro to Numerical Analysis

Error analysis, root-finding, interpolation, least squares, quadrature, linear equations, numerical solution of ordinary differential equations. Prerequisites: 121; 124 or 271; knowledge of computer programming.

Credits: 3

MATH 238 - Applied Computational Methods

Direct and iterative methods for solving linear systems; numerical solution of ordinary and partial differential equations. Focus will be on application of numerical methods. Prerequisite: MATH 121, either MATH 124 or 271.

Credits: 3

MATH 240 - Fourier Series&Integral Trans

Fourier series, orthogonal functions, integral transforms and boundary value problems. Prerequisite: 230 or 271.

Credits: 3

MATH 241 - Anyl in Several Real Vars I

Properties of the real numbers, metric spaces, infinite sequences and series, continuity. Prerequisites: 52, 121, 124 or instructor's permission.

Credits: 3

MATH 242 - Anyl Several Real Variables II

Differentiation in Rn, Riemann-Stieltjes integral, uniform convergence of functions, Inverse and Implicit Function Theorems. Prerequisite: 241.

Credits: 3

MATH 251 - Abstract Algebra I

Basic theory of groups, rings, fields, homomorphisms, and isomorphisms. Prerequisites: 52, 124 or instructor's permission.

Credits: 3

MATH 252 - Abstract Algebra II

Modules, vector spaces, linear transformations, rational and Jordan canonical forms. Finite fields, field extensions, and Galois theory leading to the insolvability of quintic equations. Prerequisite: 251.

Credits: 3

MATH 255 - Elementary Number Theory

Divisibility, prime numbers, Diophantine equations, congruence of numbers, and methods of solving congruences. Prerequisite: 52 or 54.

Credits: 3

MATH 257 - Topics in Group Theory

Topics may include abstract group theory, representation theory, classical groups, Lie groups. Prerequisite: 251. Alternate years, 2000-01.

Credits: 3

MATH 260 - Foundations of Geometry

Geometry as an axiomatic science; various non-Euclidean geometries; relationships existing between Euclidean plane geometry and other geometries; invariant properties. Prerequisite: 52 or 54.

Credits: 3

MATH 264 - Vector Analysis

Gradient, curl and divergence, Green, Gauss, and Stokes Theorems, applications to physics, tensor analysis. Prerequisite: 121, 124 or 271.

Credits: 3

MATH 266 - Chaos,Fractals&Dynamical Syst

Discrete and continuous dynamical systems, Julia sets, the Mandelbrot set, period doubling, renormalization, Henon map, phase plane analysis and Lorenz equations. Corequisite: MATH 271 or MATH 230 or instructor's permission . Cross-listing: CSYS 266.

Credits: 3

MATH 268 - Mathematical Biology&Ecology

Mathematical modeling in the life sciences. Topics include population modeling, dynamics of infectious diseases, reaction kinetics, wave phenomena in biology, and biological pattern formation. Prerequisites: MATH 124, MATH 230; or instructor's permission. Cross-listing: CSYS 268.

Credits: 3

MATH 271 - Adv Engineering Mathematics

Differential equations and linear algebra, including linear ordinary differential equations, Laplace transforms, matrix theory, and systems of differential equations. Examples from engineering and physical sciences. Pre/co-requisites: Math 121 or Math 123.

Credits: 3

MATH 272 - Applied Analysis

Partial Differential Equations of Mathematical Physics, Calculus of Variations, Functions of a Complex Variable, Cauchy's Theorem, integral formula. Conformal mapping. Prerequisite: 230 or 271.

Credits: 3

MATH 273 - Combinatorial Graph Theory

Paths and trees, connectivity, Eulerian and Hamiltonian cycles, matchings, edge and vertex colorings, planar graphs, Euler's formula and the Four Color Theorem, networks. Prerequisite: 52 or 54 or instructor's permission.

Credits: 3

MATH 274 - Numerical Linear Algebra

Direct and iterative methods for solving linear equations, least square factorization methods, eigenvalue computations, ill-conditioning and stability. Prerequisite: 237.

Credits: 3

MATH 275 - Adv Engineering Analysis I

Analytical methods for the solution of partial differential equations in engineering mechanics and physics, including: eigenfunction expansions; Fourier series; Sturm-Liouville theory and special functions. Prerequisites: Graduate standing in engineering, mathematics, or physical sciences or permission. Not available for 300-level credit for Mathematics students. Cross-listed with CE 304 and ME 304.

Credits: 3

MATH 276 - Adv Engineering Analysis II

Advanced analytical techniques for problems in engineering mechanics and physics, including: integral transform methods, Green's functions, perturbation methods, and variational calculus. Prerequisites: ME 304 or equivalent. Not available for 300-level credit for Mathematics students. Cross-listed with CE 305 and ME 305.

Credits: 3

MATH 278 - Intro Wavelets & Filter Banks

Continuous and discrete-time signal processing. Continuous wavelet transform. Series expansion of continuous and discrete-time signals. Perfect reconstruction, orthogonal and biorthogonal filter banks. Wavelets from filter. Pre/co-requisites: 171, or instructor permission. Cross-listing: EE 274.

Credits: 3

MATH 295 - Special Topics

For advanced students in the indicated fields. Lectures, reports, and directed readings on advanced topics. Prerequisite: Instructor's permission. Credit as arranged. Offered as occasion warrants.

Credits: 1 to 18

MATH 300 - Principles of Complex Systems

Introduction to fundamental concepts of complex systems. Topics include: emergence, scaling phenomena, and mechanisms, multi-scale systems, failure, robustness, collective social phenomena, complex networks. Students from all disciplines welcomed. Pre/co-requisites: Calculus and statistics required. Linear Algebra, Differential Equations, and Computer programming recommended but not required. Cross-listing: CSYS 300.

Credits: 3

MATH 303 - Complex Networks

Detailed exploration of distribution, transportation, small-world, scale-free, social, biological, organizational networks; generative mechanisms; measurement and statistics of network properties; network dynamics; contagion processes. Students from all disciplines welcomed. Pre/co-requisites: Math 301/CSYS 301, Calculus, and Statistics required. Cross-listing: CSYS 303.

Credits: 3

MATH 330 - Adv Ordinary Diff Equations

Linear and nonlinear systems, approximate solutions, existence, uniqueness, dependence on initial conditions, stability, asymptotic behavior, singularities, self-adjoint problems. Prerequisite: 230.

Credits: 3

MATH 331 - Theory of Func of Complex Var

Differentiation, integration, Cauchy-Riemann equations, infinite series, properties of analytic continuation, Laurent series, calculus of residues, contour integration, meromorphic functions, conformal mappings, Riemann surfaces. Prerequisite: 242.

Credits: 4

MATH 332 - Approximation Theory

Interpolation and approximation by interpolation, uniform approximation in normed linear spaces, spline functions, orthogonal polynomials. Least square, and Chebychev approximations, rational functions. Prerequisites: 124, 237.

Credits: 3

MATH 333 - Thry Functions Real Variables

The theory of Lebesgue integration, Lebesgue measure, sequences of functions, absolute continuity, properties of LP-spaces. Prerequisite: 242.

Credits: 4

MATH 335 - Advanced Real Analysis

L2-spaces, LP-spaces; Hilbert, Banach spaces; linear functionals, linear operators; completely continuous operators (including symmetric); Fredholm alternative; Hilbert-Schmidt theory; unitary operators; Bochner's Theorem; Fourier-Plancherel, Watson transforms. Prerequisites: 333; 335 for 336.

Credits: 3

MATH 336 - Advanced Real Analysis

L2-spaces, LP-spaces; Hilbert, Banach spaces; linear functionals, linear operators; completely continuous operators (including symmetric); Fredholm alternative; Hilbert-Schmidt theory; unitary operators; Bochner's Theorem; Fourier-Plancherel, Watson transforms. Prerequisites: 333; 335 for 336.

Credits: 3

MATH 337 - Numerical Diff Equations

Numerical solution and analysis of differential equations: initial-value and boundary-value problems; finite difference and finite element methods. Prerequisites: MATH 237, either MATH 230 or 271 recommended.

Credits: 3

MATH 339 - Partial Differential Equations

Classification of equations, linear equations, first order equations, second order elliptic, parabolic, and hyperbolic equations, uniqueness and existence of solutions. Prerequisites: 230, 242.

Credits: 3

MATH 351 - Topics in Algebra

Topics will vary each semester and may include algebraic number theory, algebraic geometry, and the arithmetic of elliptic curves. Repeatable for credit with permission. Prerequisite: 252.

Credits: 3

MATH 353 - Point-Set Topology

Topological spaces, closed and open sets, closure operators, separation axioms, continuity, connectedness, compactness, metrization, uniform spaces. Prerequisite: 241.

Credits: 3

MATH 354 - Algebraic Topology

Homotopy, Seifert-van Kampen Theorem; simplicial, singular, and Cech homology. Prerequisite: 353.

Credits: 3

MATH 373 - Topics in Combinatorics

Topics will vary each semester and may include combinatorial designs, coding theory, topological graph theory, cryptography. Prerequisites: 251 or 273 or permission.

Credits: 3

MATH 382 - Seminar

Topical discussions with assigned reading. Required of M.S. degree candidates.

Credits: 1

MATH 391 - Master's Thesis Research

Credits: 1 to 18

MATH 395 - Special Topics

Subject will vary from year to year. May be repeated for credit.

Credits: 1 to 6

MATH 491 - Doctoral Dissertation Research

Credits: 1 to 18