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

Core Courses

- MAT 470 ADVANCED LINEAR ALGEBRA
- MAT 471 GROUP THEORY
- MAT 472 FIELDS AND GALOIS THEORY
- MAT 473 RINGS AND MODULES
- MAT 434 TOPOLOGY
- MAT 435 MEASURE THEORY
- MAT 436 FUNCTIONAL ANALYSIS
- MAT 437 COMPLEX ANALYSIS

Elective Classes

- Choose sixteen quarter hours from the following list:
- MAT 451 PROBABILITY AND STATISTICS I
- MAT 452 PROBABILITY AND STATISTICS II
- MAT 453 PROBABILITY AND STATISTICS III
- MAT 481 FOURIER ANALYSIS AND SPECIAL FUNCTIONS
- MAT 484 MATHEMATICAL MODELING
- MAT 485 NUMERICAL ANALYSIS I
- MAT 486 NUMERICAL ANALYSIS II
- MAT 494 GRAPH THEORY AND NETWORK FLOWS
- MAT 498 PROBLEM SOLVING IN MATHEMATICS
- MAT 596 ADVANCED TOPICS IN ALGEBRA
- MAT 597 ADVANCED TOPICS IN ANALYSIS
- MAT 598 ADVANCED PROBLEM SOLVING IN ALGEBRA AND ANALYSIS
- MAT 595 GRADUATE THESIS RESEARCH

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.

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.

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

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.

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.

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

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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

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.

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

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

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.

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.