Graduate Program

Fall Term Schedule

Fall 2026

Number	Title	Instructor	Time
MATH 430-01 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 436-01 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 440-01 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 443-01 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 471-01 Analysis I Dan Geba 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 472-01 Analysis III Xuwen Chen TR 2:00PM - 3:15PM
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 2:00PM - 3:15PM)
MATH 492-01 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 504-01 Stochastic Processes (Continuous Time) Juan Rivera Letelier TR 3:25PM - 4:40PM
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. After the standard topics, this course will cover random dynamical systems. Location (TR 3:25PM - 4:40PM)
MATH 506-01 Topics in Probability (Probabilistic Techniques in Analysis and Quantum Walks) – TR 11:05AM - 12:20PM
The course will explore applications of algebraic methods to studying probabilistic models. We will discuss symmetric functions. Schur and Macdonald polynomials and their applications to the lozenge tiling, directed polymer and other models Prerequisites: Background in real analysis is recommended. Some familiarity with probability is helpful, although essential concepts will be reviewed as needed. This course introduces probabilistic methods in analysis, with a particular emphasis on heat kernel techniques and their applications. The central references are the monographs by Davar Khoshnevisan and Richard F. Bass, which develop deep connections between probability theory, partial differential equations, and harmonic analysis. We begin with Brownian motion and Markov processes, focusing on their role in representing solutions to classical analytical problems. Topics include transition densities, heat kernels, the Feynman–Kac formula, and connections to elliptic and parabolic PDEs. We then explore finer analytical properties such as Hoelder continuity, potential theory, and estimates for heat kernels on Euclidean spaces and more general structures. The course will also introduce quantum walks as discrete and unitary analogues of classical random walks. We discuss how probabilistic and spectral techniques extend to the quantum setting, highlighting similarities and differences between classical diffusion and quantum propagation. Applications to spectral theory, graphs, and fractal-type spaces will be emphasized. Throughout the course, students will develop both probabilistic intuition and analytical tools, with an emphasis on rigorous arguments and examples. Additional topics include Dirichlet forms, random walks on graphs, and heat kernel behavior on irregular spaces. Location (TR 11:05AM - 12:20PM)
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 – 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 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 492-01 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 471-01 Analysis I Dan Geba
Measures, integration, differentiation, product measures, Banach spaces, L^p spaces.
MATH 440-01 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 430-01 Algebraic Number Theory Naomi Jochnowitz
Number fields, rings of integers, factorization, class numbers. Frobenius and Dirichlet density theorems.
MATH 443-01 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 436-01 Algebra I Naomi Jochnowitz
Rings and modules, group theory, fields and Galois theory.
Monday, Wednesday, and Friday
Tuesday
Tuesday and Thursday
MATH 506-01 Topics in Probability (Probabilistic Techniques in Analysis and Quantum Walks) –
The course will explore applications of algebraic methods to studying probabilistic models. We will discuss symmetric functions. Schur and Macdonald polynomials and their applications to the lozenge tiling, directed polymer and other models
MATH 472-01 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 504-01 Stochastic Processes (Continuous Time) Juan Rivera Letelier
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.
Wednesday
Thursday
Friday