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MATH 430-01
Naomi Jochnowitz
MW 2:00PM - 3:15PM
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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)
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MATH 436-01
Naomi Jochnowitz
MW 4:50PM - 6:05PM
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Rings and modules, group theory, fields and Galois theory.
Undergrads must have permission of the Instructor.
- Location
- (MW 4:50PM - 6:05PM)
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MATH 440-01
Jonathan Pakianathan
MW 12:30PM - 1:45PM
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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)
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MATH 443-01
Douglas Ravenel
MW 2:00PM - 3:15PM
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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)
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MATH 471-01
Dan Geba
MW 10:25AM - 11:40AM
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Measures, integration, differentiation, product measures, Banach spaces, L^p spaces.
Undergrads must have permission of the instructor.
- Location
- (MW 10:25AM - 11:40AM)
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MATH 472-01
Xuwen Chen
TR 2:00PM - 3:15PM
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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)
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MATH 492-01
Sevak Mkrtchyan
M 3:25PM - 4:40PM
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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)
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MATH 504-01
Juan Rivera Letelier
TR 3:25PM - 4:40PM
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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)
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MATH 506-01
TR 11:05AM - 12:20PM
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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)
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MATH 591-01
Stephen Kleene
7:00PM - 7:00PM
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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)
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MATH 591-02
7:00PM - 7:00PM
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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)
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MATH 591-03
Alex Iosevich
7:00PM - 7:00PM
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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)
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MATH 591-05
Naomi Jochnowitz
7:00PM - 7:00PM
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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)
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MATH 591-06
Sevak Mkrtchyan
7:00PM - 7:00PM
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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)
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MATH 591-07
Jonathan Pakianathan
7:00PM - 7:00PM
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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)
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MATH 591-08
Juan Rivera Letelier
7:00PM - 7:00PM
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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)
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MATH 591-09
Douglas Ravenel
7:00PM - 7:00PM
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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)
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MATH 591-10
Sema Salur
7:00PM - 7:00PM
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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)
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MATH 591-11
Thomas Tucker
7:00PM - 7:00PM
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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)
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MATH 591-12
Arjun Krishnan
7:00PM - 7:00PM
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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)
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MATH 591-13
Xuwen Chen
7:00PM - 7:00PM
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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)
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MATH 591-14
Carl Mueller
7:00PM - 7:00PM
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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)
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MATH 591-15
Dan Geba
7:00PM - 7:00PM
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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)
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MATH 591-16
Dinesh Thakur
7:00PM - 7:00PM
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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)
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MATH 591-18
Saul Lubkin
7:00PM - 7:00PM
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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)
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MATH 591-19
Steven Gonek
7:00PM - 7:00PM
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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)
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MATH 595-01
Arjun Krishnan
7:00PM - 7:00PM
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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)
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MATH 595-02
Sevak Mkrtchyan
7:00PM - 7:00PM
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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)
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MATH 595-03
Stephen Kleene
7:00PM - 7:00PM
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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)
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MATH 595-05
Naomi Jochnowitz
7:00PM - 7:00PM
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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)
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MATH 595-06
Xuwen Chen
7:00PM - 7:00PM
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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)
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MATH 595-07
Alex Iosevich
7:00PM - 7:00PM
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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)
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MATH 595-08
Allan Greenleaf
7:00PM - 7:00PM
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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)
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MATH 595-09
Carl Mueller
7:00PM - 7:00PM
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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)
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MATH 595-10
Dan Geba
7:00PM - 7:00PM
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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)
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MATH 595-11
Dinesh Thakur
7:00PM - 7:00PM
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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)
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MATH 595-12
Douglas Ravenel
7:00PM - 7:00PM
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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)
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MATH 595-14
Jonathan Pakianathan
7:00PM - 7:00PM
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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)
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MATH 595-15
Juan Rivera Letelier
7:00PM - 7:00PM
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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)
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MATH 595-17
Saul Lubkin
7:00PM - 7:00PM
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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)
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MATH 595-18
Sema Salur
7:00PM - 7:00PM
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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)
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MATH 595-19
Steven Gonek
7:00PM - 7:00PM
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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)
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MATH 595-20
Thomas Tucker
7:00PM - 7:00PM
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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)
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MATH 999-01
Sevak Mkrtchyan
7:00PM - 7:00PM
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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)
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