Explores role of structures in abstract algebra through an historical lens. Role of symmetry in the development of groups. Role of solving equations in the development of rings and fields
Polynomial Noetherian rings and ideals. Fields and Galois theory. Structure of fields. History and applications.
Survey of enumerative combinatorics motivated by discrete structures of historical and practical importance, including relations, functions, graphs, and groups. Explore connections between counting and the mathematical structure of finite sets.
Analytic and meromorphic functions in the complex plane. Integration, conformal mapping and advanced topics.
Analysis of functions of several variables, unifying and extending ideas from calculus and linear algebra. Includes the implicit function theorem and Stokes' Theorem.
Rigorous approach to real numbers and functions, with a historical perspective. Foundations of calculus and analytic geometry, including integration and measure. Elements of complex analysis and its applications.
Introduction to the process of mathematical modeling and, in particular, topics in modeling that have relevance to secondary school mathematics. This project-based course emphasizes development and communication of models.
Neutral, Euclidean, spherical, hyperbolic, and other geometries. Intuitive and axiomatic viewpoints. Connections to analysis, abstract algebra, and history of mathematics. Prepares students to research geometry education and teach undergraduate geometry.
The notion of proof, first order logic, set theory, ordinals, cardinals and an overview of the most important recent results in the field.
Surveys topics from fields of mathematics not included in existing courses, reflecting specific interests of students and instructors.
Four hours of credit for doctoral dissertation proposal research must be earned in partial fulfillment of requirements before admission to candidacy.
Doctoral Dissertation. S/U graded.