Graduate Program

Fall Term Schedule

Fall 2025

Number	Title	Instructor	Time
MATH 404-01 Ergodic Theory & Dynamic Sys Juan Rivera Letelier TR 12:30PM - 1:45PM
Basic properties of discrete time dynamical systems, from a probabilistic 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)
MATH 430-1 Algebraic Number Theory Naomi Jochnowitz MW 2:00PM - 3:15PM
Number fields, rings of integers, factorization, class numbers. Frobenius and Dirichlet density theorems. Prerequisites: MATH 436 and 437. Undergrads must have permission of the Instructor. Location (MW 2:00PM - 3:15PM)
MATH 436-1 Algebra I Naomi Jochnowitz MW 4:50PM - 6:05PM
Rings and modules, group theory, fields and Galois theory. Undergrads must have permission of the Instructor. Location (MW 4:50PM - 6:05PM)
MATH 440-1 General Topology Jonathan Pakianathan MW 12:30PM - 1:45PM
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. Prerequisites: Undergrads must have permission of the Instructor. Location (MW 12:30PM - 1:45PM)
MATH 443-1 Algebraic Topology Douglas Ravenel MW 2:00PM - 3:15PM
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. Prerequisites: MATH 436 and MATH 440. Undergrads must have permission of the instructor. Location (MW 2:00PM - 3:15PM)
MATH 463-01 Partial Differential Equations Xuwen Chen TR 11:05AM - 12:20PM
Classical PDE's, including the heat and wave equations, with both quantitative and qualitative analysis. Location (TR 11:05AM - 12:20PM)
MATH 471-1 Analysis I Alex Iosevich MW 10:25AM - 11:40AM
Measures, integration, differentiation, product measures, Banach spaces, L^p spaces. Undergrads must have permission of the instructor. Location (MW 10:25AM - 11:40AM)
MATH 472-1 Analysis III Xuwen Chen TR 9:40AM - 10:55AM
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. Prerequisites: Math 467 and 471. Undergrads must have permission of the instructor. Location (TR 9:40AM - 10:55AM)
MATH 492-1 Grad Professional Seminar Sevak Mkrtchyan M 3:25PM - 4:40PM
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. Prerequisites: Open to first-year graduate students only. Location (M 3:25PM - 4:40PM)
MATH 504-1 Stochastic Processes (Discrete Time) Arjun Krishnan MW 12:30PM - 1:45PM
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. We will cover the basics of stochastic processes from Le Gall’s book on Measure Theory, Probability and Stochastic Processes and then we will focus on discrete time Markov chains and cover topics related to their mixing time from Levine and Peres’ book. Location (MW 12:30PM - 1:45PM)
MATH 589-01 Scattering Theory II (Topics in Inverse Problems) Allan Greenleaf MW 10:25AM - 11:40AM
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. An introduction to methods used to study inverse problems, with emphasis on mathematical foundations of techniques for noninvasive imaging, remote sensing and nondestructive material parameter identification. Problems studied will include those of X-ray imaging, seismic and radar imaging (based on the acoustic wave equation), quantum mechanical inverse scattering (based on Schroedinger’s equation), and electrical impedance tomography (based on the conductivity equation). Location (MW 10:25AM - 11:40AM)
MATH 591-01 PhD Readings Stephen Kleene 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)
MATH 591-02 PhD Readings Allan Greenleaf 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)
MATH 591-03 PhD Readings Alex Iosevich 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)
MATH 591-05 PhD Readings Naomi Jochnowitz 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)
MATH 591-06 PhD Readings Sevak Mkrtchyan 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)
MATH 591-07 PhD Readings Jonathan Pakianathan 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)
MATH 591-08 PhD Readings Juan Rivera Letelier 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)
MATH 591-09 PhD Readings Douglas Ravenel 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)
MATH 591-10 PhD Readings Sema Salur 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)
MATH 591-11 PhD Readings Thomas Tucker 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)
MATH 591-12 PhD Readings Arjun Krishnan 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)
MATH 591-13 PhD Readings Xuwen Chen 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)
MATH 591-14 PhD Readings Carl Mueller 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)
MATH 591-15 PhD Readings Dan Geba 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)
MATH 591-16 PhD Readings Dinesh Thakur 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)
MATH 591-18 PhD Readings Saul Lubkin 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)
MATH 591-19 PhD Readings Steven Gonek 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)
MATH 595-01 PhD Research Arjun Krishnan 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)
MATH 595-02 PhD Research Sevak Mkrtchyan 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)
MATH 595-03 PhD Research Stephen Kleene 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)
MATH 595-05 PhD Research Naomi Jochnowitz 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)
MATH 595-06 PhD Research Xuwen Chen 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)
MATH 595-07 PhD Research Alex Iosevich 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)
MATH 595-08 PhD Research Allan Greenleaf 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)
MATH 595-09 PhD Research Carl Mueller 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)
MATH 595-10 PhD Research Dan Geba 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)
MATH 595-11 PhD Research Dinesh Thakur 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)
MATH 595-12 PhD Research Douglas Ravenel 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)
MATH 595-14 PhD Research Jonathan Pakianathan 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)
MATH 595-15 PhD Research Juan Rivera Letelier 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)
MATH 595-17 PhD Research Saul Lubkin 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)
MATH 595-18 PhD Research Sema Salur 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)
MATH 595-19 PhD Research Steven Gonek 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)
MATH 595-20 PhD Research Thomas Tucker 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)
MATH 895-1 Continuation of Master’s Enrollment – 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)
MATH 897-1 Masters Dissertation Naomi Jochnowitz 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)
MATH 899-1 Masters Dissertation Naomi Jochnowitz 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)
MATH 986V-1 Full Time Visiting Student – 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)
MATH 995-1 Continuation of Doctoral Enrollment Sevak Mkrtchyan 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)
MATH 999-01 Doctoral Dissertation Sevak Mkrtchyan 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)

Number	Title	Instructor	Time
Monday
MATH 492-1 Grad Professional Seminar Sevak Mkrtchyan
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.
Monday and Wednesday
MATH 471-1 Analysis I Alex Iosevich
Measures, integration, differentiation, product measures, Banach spaces, L^p spaces.
MATH 589-01 Scattering Theory II (Topics in Inverse Problems) Allan Greenleaf
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.
MATH 440-1 General Topology Jonathan Pakianathan
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.
MATH 504-1 Stochastic Processes (Discrete Time) Arjun Krishnan
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.
MATH 430-1 Algebraic Number Theory Naomi Jochnowitz
Number fields, rings of integers, factorization, class numbers. Frobenius and Dirichlet density theorems.
MATH 443-1 Algebraic Topology Douglas Ravenel
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.
MATH 436-1 Algebra I Naomi Jochnowitz
Rings and modules, group theory, fields and Galois theory.
Monday, Wednesday, and Friday
Tuesday
Tuesday and Thursday
MATH 472-1 Analysis III Xuwen Chen
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.
MATH 463-01 Partial Differential Equations Xuwen Chen
Classical PDE's, including the heat and wave equations, with both quantitative and qualitative analysis.
MATH 404-01 Ergodic Theory & Dynamic Sys Juan Rivera Letelier
Basic properties of discrete time dynamical systems, from a probabilistic viewpoint. Recurrence, ergodic theorems, mixing, entropy. Minimality, unique ergodicity, topological entropy, variational principle. Applications to number theory, probability, and other areas of mathematics
Wednesday
Thursday
Friday