Graduate Program

Basic properties of discrete time dynamical systems, from a probabilisitc viewpoint. Recurrence, ergodic theorems, mixing, entropy. Minimality, unique ergodicity, topological entropy, variational principle. Applications to number theory, probability, and other areas of mathematics

Prerequisites: Measure theory. Some familiarity with probability would be useful, but not necessary

Location

(TR 12:30PM - 1:45PM)

Prerequisites: MATH 436 and 437. Undergrads must have permission of the Instructor.

Description: Number fields, rings of integers, factorization, class numbers. Frobenius and Dirichlet density theorems.

Location

(MW 2:00PM - 3:15PM)

Prerequisites: MATH 237 or equivalent. Undergrads must have permission of the Instructor.

Description: Rings and modules, group theory, fields and Galois theory.

Location

(MW 4:50PM - 6:05PM)

Prerequisites: Undergrads must have permission of the Instructor.

The first half of the course will study the general topological notions of topological space, metric spaces, quotient spaces, connectedness, compactness, manifolds and topological groups.  The second half of the course will be an introduction to the differential topology of smooth manifolds.  Topics include Sard’s theorem, transversality, intersection theory and applications such as the Jordan-Brouwer separation theorem, the Borsuk-Ulam theorem and the Poincare-Hopf theorem. This course will not cover the theory of differential forms, distributions or integration on manifolds which is usually covered in our spring graduate differentiable manifolds course instead.

Location

(MW 12:30PM - 1:45PM)

Prerequisites: MATH 436 and MATH 440. Undergrads must have permission of the instructor.

The combinatorial structure of complexes and the homology of polyhedra; applications of algebraic techniques in topology to classification of surfaces, fixed point theory, and analysis.

Location

(MW 2:00PM - 3:15PM)

Classical PDE's, including the heat and wave equations, with both quantitative and qualitative analysis.

Location

(TR 11:05AM - 12:20PM)

Prerequisites: Math 265H or equivalent. Undergrads must have permission of the instructor.

Description: measures, integration, differentiation, product measures, Banach spaces, L^p spaces.

Location

(MW 10:25AM - 11:40AM)

Prerequisites: Math 467 and 471. Undergrads must have permission of the instructor.

First-order partial differential equations, principles for higher-order equations, the wave equation, the Laplace equation, the heat equation, complex interpolation, Marcinkiewicz interpolation, Littlewood-Paley theory.

Location

(TR 9:40AM - 10:55AM)

Prerequisites: Open to first-year graduate students only.

Description: This course is a requirement for math Ph.D. students during their first fall in the Ph.D. program. The course will advise them on various aspects of their professional development. It will address:a) Research practices and development: Creating a CV, creating a professional webpage, milestones for grad school, grants and funding, conferences.b) Teaching: Responsibilities, techniques, etc.c) Community: Attendance of colloquia, seminars, meeting with faculty, etc.d) Other: Discussion of arXiv, math-sci net, latex, peer support network, etc.

Location

(M 2:00PM - 3:15PM)

Will cover the basics of discrete and continuous-time stochastic processes such as the theory of Martingales, Markov chains, and Brownian motion. Depending on the year, additional special topics in either discrete-time processes or continuous-time processes will be covered.

Location

(MW 12:30PM - 1:45PM)

Study of some physical models and mathematical analysis of scattering waves. Solvability of forward problems, and qualitative and quantitative properties of solutions. Formulation and solution of associated inverse problems, and discussion of open problems.

Location

(MW 10:25AM - 11:40AM)

This course is for PhD students that have made arrangements with a faculty member to complete readings and discussion in a particular subject in their field of study.

Location

( 7:00PM - 7:00PM)

This course is for PhD students that have made arrangements with a faculty member to complete readings and discussion in a particular subject in their field of study.

Location

( 7:00PM - 7:00PM)

This course is for PhD students that have made arrangements with a faculty member to complete readings and discussion in a particular subject in their field of study.

Location

( 7:00PM - 7:00PM)

This course is for PhD students that have made arrangements with a faculty member to complete readings and discussion in a particular subject in their field of study.

Location

( 7:00PM - 7:00PM)

This course is for PhD students that have made arrangements with a faculty member to complete readings and discussion in a particular subject in their field of study.

Location

( 7:00PM - 7:00PM)

This course is for PhD students that have made arrangements with a faculty member to complete readings and discussion in a particular subject in their field of study.

Location

( 7:00PM - 7:00PM)

This course is for PhD students that have made arrangements with a faculty member to complete readings and discussion in a particular subject in their field of study.

Location

( 7:00PM - 7:00PM)

This course is for PhD students that have made arrangements with a faculty member to complete readings and discussion in a particular subject in their field of study.

Location

( 7:00PM - 7:00PM)

This course is for PhD students that have made arrangements with a faculty member to complete readings and discussion in a particular subject in their field of study.

Location

( 7:00PM - 7:00PM)

This course is for PhD students that have made arrangements with a faculty member to complete readings and discussion in a particular subject in their field of study.

Location

( 7:00PM - 7:00PM)

This course is for PhD students that have made arrangements with a faculty member to complete readings and discussion in a particular subject in their field of study.

Location

( 7:00PM - 7:00PM)

This course is for PhD students that have made arrangements with a faculty member to complete readings and discussion in a particular subject in their field of study.

Location

( 7:00PM - 7:00PM)

This course is for PhD students that have made arrangements with a faculty member to complete readings and discussion in a particular subject in their field of study.

Location

( 7:00PM - 7:00PM)

This course is for PhD students that have made arrangements with a faculty member to complete readings and discussion in a particular subject in their field of study.

Location

( 7:00PM - 7:00PM)

This course is for PhD students that have made arrangements with a faculty member to complete readings and discussion in a particular subject in their field of study.

Location

( 7:00PM - 7:00PM)

This course is for PhD students that have made arrangements with a faculty member to complete readings and discussion in a particular subject in their field of study.

Location

( 7:00PM - 7:00PM)

This course is for PhD students that have made arrangements with a faculty member to complete readings and discussion in a particular subject in their field of study.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course is designed for master's degree students who have completed all required coursework but still need to finalize specific degree requirements under less than half-time enrollment.

Location

( 7:00PM - 7:00PM)

This course provides master's students who are currently completing their final required coursework, or with special circumstances like an approved reduced courseload, with the opportunity to work full-time on their degrees. Students will make significant progress toward completing their degrees.

Location

( 7:00PM - 7:00PM)

This course provides master’s students who have completed or are currently completing all course requirements with the opportunity to work full-time on their thesis. Students will make significant progress toward completing their degrees.

Location

( 7:00PM - 7:00PM)

A course specifically for full-time visiting students. It's a math course designed to accommodate students who are visiting the university from another institution. 

Location

( 7:00PM - 7:00PM)

This course is designed for PhD students who have completed all required coursework but still need to finalize specific degree requirements under less than half-time enrollment.

Location

( 7:00PM - 7:00PM)

This course provides PhD students who have completed or are currently completing 90 credits of coursework and have fulfilled all degree requirements (except for the dissertation) with the opportunity to work full-time on their dissertation. Students will make significant progress toward completing their degrees.

Location

( 7:00PM - 7:00PM)