Course Requirements

At least 48 quarter hours of graduate level work in mathematics and passing two comprehensive examinations in Algebra and Analysis.

Core Courses

Elective Classes

​With faculty advisor's written approval two of the elective courses can be substituted with graduate courses in allied fields, such as Computer Science, Physics, or Mathematical Education.

MAT 470

ADVANCED LINEAR ALGEBRA

Vector spaces, basis and dimension; matrix representation of linear transformations and change of basis; diagonalization of linear operators; inner product spaces; diagonalization of symmetric linear operators, principal-axis theorem, and applications. Cross-listed as MAT 370.
Prerequisites:
MAT 262 and (MAT 141 or MAT 215) are a prerequisite for this class.

MAT 471

GROUP THEORY

Course topics: Classes of groups; actions of groups on sets; Sylow theorems; decomposition of groups; structure of finite abelian groups.

MAT 472

FIELDS AND GALOIS THEORY

Course topics: Commutative rings and fields; irreducible polynomials and field extensions, adjunction of roots, algebraic extensions, splitting and normal fields, cyclic extensions, the Galois group, and the Fundamental theorem of Galois theory. Cross-listed with MAT 312.

MAT 473

RINGS AND MODULES

Course topics: Rings and Algebras; classes of unique factorization domains; modules and principal isomorphism theorems, classes of modules, decomposition of finitely generated modules; Jordan and rational canonical form of a matrix.

MAT 434

TOPOLOGY

An introduction to point-set topology: metric spaces, topological spaces, continuity, connectedness, and compactness.

MAT 435

MEASURE THEORY

This is a course in Lebesque integration; the study of measure spaces and measurable functions; the basic theorems of Lebesque integration; Egoroff's theorem, the monotone limit theorem, the Lebesgue dominated convergence theorem; an introduction to Lp spaces, Holder's inequality, Minkowski's inequality; Fubini's theorem.

MAT 436

FUNCTIONAL ANALYSIS

This course is an introduction to the basic theory of functional analysis. It covers linear operators and functionals on Hilbert and Banach Spaces, the Hahn Banach theorem, the uniform boundedness principle, and the open mapping theorem.

MAT 437

COMPLEX ANALYSIS

Course topics: Complex functions; complex differentiation and integration; series and sequences of complex functions. Cross-listed with MAT 337.

MAT 451

PROBABILITY AND STATISTICS I

The course covers elements of probability theory; distributions of random variables and linear functions of random variables; moment generating functions; and discrete and continuous probability models. COREQUISITE(S): MAT 260.
Prerequisites:
MAT 260 is a corequisite for this class.

MAT 452

PROBABILITY AND STATISTICS II

A continuation of MAT 451. More continuous probability model. Laws of large numbers and the central limit theorem. Sampling distributions of certain statistics. An introduction to the theory of estimation and principals of hypothesis testing. COREQUISITE: MAT 261.
Prerequisites:
MAT 451 is a prerequisite for this class and MAT 261 is a corequisite for this class.

MAT 453

PROBABILITY AND STATISTICS III

A continuation of MAT 452. More on hypothesis testing, most powerful, uniformly most powerful, and likelihood ratio tests. Introduction to the analysis of variance; linear regression; categorical data analysis, and nonparametric methods of inference.
Prerequisites:
MAT 452 is a prerequisite for this class.

MAT 481

FOURIER ANALYSIS AND SPECIAL FUNCTIONS

The course covers the basic principles of discrete and continuous Fourier analysis and its applications. Some of the topics covered are Fourier series, discrete Fourier transforms, fast Fourier transforms, and Fourier transforms.
Prerequisites:
MAT 262 is a prerequisite for this class.

MAT 484

MATHEMATICAL MODELING

Modeling of real world problems using mathematical methods. Includes a theory of modeling and a study of specific models, selected from deterministic stochastic, continuous and discrete models. Cross-listed as MAT 384.
Prerequisites:
(MAT 220 or MAT 262) and (MAT 451 or MAT 348) are a prerequisite for this class.

MAT 485

NUMERICAL ANALYSIS I

Use of a digital computer for numerical computation. Error analysis, Gaussian elimination and Gauss-Seidel method, solutions of linear and nonlinear equations, function evaluation, cubic splines, approximation of integrals and derivatives, Monte Carlo methods. Cross-listed with MAT 385.
Prerequisites:
MAT 220 or MAT 262 is a prerequisite for this class.

MAT 486

NUMERICAL ANALYSIS II

Theory and algorithms for efficient computation including the Fast Fourier Transform. Numerical solution of nonlinear systems of equations. Minimization of functions of several variables. Sparse systems of equations and eigenvalue problems. Cross-listed with CSC 386/486, MAT 386.
Prerequisites:
MAT 485 is a prerequisite for this class.

MAT 494

GRAPH THEORY AND NETWORK FLOWS

Directed and undirected graphs. Bipartite graphs. Hamiltonian cycles and Euler tours. Flows in capacity-constrained networks.

MAT 498

PROBLEM SOLVING IN MATHEMATICS

Course topics: problem solving in various topics from GRE Subject examination in Mathematics. Consult course schedule for current offerings. Course may be repeated for credit when title and content change.

MAT 596

ADVANCED TOPICS IN ALGEBRA

Consult course schedule for current offerings. Course may be repeated for credit when title and content change.

MAT 597

ADVANCED TOPICS IN ANALYSIS

Consult course schedule for current offerings. Course may be repeated for credit when title and content change.

MAT 598

ADVANCED PROBLEM SOLVING IN ALGEBRA AND ANALYSIS

Course topics: problem solving in various topics in Algebra and Analysis. Consult course schedule for current offerings. Course may be repeated for credit when title and content change.

MAT 595

GRADUATE THESIS RESEARCH

A thesis option is available to graduate students who wish to pursue an extended independent project. Students would work under the guidance of a faculty mentor. A total of 4 credits must be completed over the one or two quarters prior to the thesis submission.