Consent of Instructor. An advanced seminar in an active area of mathematical research. Content depends upon instructor's choice. Repeatable, may be taken two times, under different subtitles.

Prerequisite MATH 523 or equivalent. Groups and rings and their structure. Sylow theorems. Modules. History and applications.

Prerequisite MATH 709. Polynomial Noetherian rings and ideals. Fields and Galois theory. Structure of fields. History and applications.

Introduction to Representation Theory of various mathematical structures. Emphasis is on group representations.

Prerequisite: MATH 678. A broad yet deep survey of current topics in combinatorics and graph theory essential for teachers K-16, including applications to probability, coding theory, sorting and matching algorithms and optimization.

Prerequisite: A course in complex analysis. Analytic and meromorphic functions in the complex plane. Integration, conformal mapping and advanced topics.

Prerequisites: MATH 525; MATH 540 recommended. Analysis of functions of several variables, unifying and extending ideas from calculus and linear algebra. Includes the implicit function theorem and Stokes' Theorem.

Abstract spaces, Lebasque measure, continuity, integration and differentiation theorems, Baire category.

Prerequisite: MATH 735. Topics from real and functional analysis such as: measure theory, distributions, metric spaces and other topics of the instructor's choice.

Prerequisite: A course in Analysis. A course in the differential geometry of curves and surfaces. Both modern and classical aspects will be covered.

Applications of difference equations in problem solving and modeling, especially in the area of chaos.

The notion of proof, first order logic, set theory, ordinals, cardinals and an overview of the most important recent results in the field.

Prerequisite: MATH 732. A survey of topics in arithmetic and analytic number theory, such as Eulers' function, quadratic reciprocity, continued fractions and the distribution of prime numbers.

Topics from various fields of mathematics, for example, algebraic topology, functional analysis, Lie groups and algebras or nonlinear analysis. Repeatable, under different subtitles.

Required of all doctoral students. Four hours of credit for doctoral dissertation proposal research must be earned in partial fulfillment of requirements before admission to candidacy. Repeatable, maximum of four credits.

Required of all doctoral candidates. S/U graded. Repeatable, no limitations.