MATH 436-1
Naomi Jochnowitz
MW 4:50PM - 6:05PM
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Prerequisites: MTH 237 or equivalent. Undergrads must have permission of Instructor. Description: Rings and modules, group theory, fields and Galois theory.
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- (MW 4:50PM - 6:05PM)
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MATH 440-1
Jonathan Pakianathan
MW 12:30PM - 1:45PM
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Prerequisites: MTH 265 or equivalent. Permission of instructor required for Undergraduates. Description: 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
- Gavett Hall Room 206 (MW 12:30PM - 1:45PM)
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MATH 443-1
Douglas Ravenel
MW 2:00PM - 3:15PM
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Prerequisites: MTH 436 and MTH 440. Permission of instructor required for Undergraduates. Description: 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.
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- (MW 2:00PM - 3:15PM)
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MATH 471-1
Dan Geba
TR 9:40AM - 10:55AM
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Prerequisites: MTH 265 or equivalent. Description: Lebesgue measure on the line; measure spaces; integration; convergence theorems; Radon-Nikodym theorem; differentiation; Fubini's theorem; function spaces.
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- Hylan Building Room 202 (TR 9:40AM - 10:55AM)
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MATH 472-1
Allan Greenleaf
MW 10:25AM - 11:40AM
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Banach spaces; dual spaces; Riesz representation theorem; Hilbert spaces; Fourier series; projective and unitary operators; spectral analysis of completely continuous self-adjoint operators. Applications.
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- (MW 10:25AM - 11:40AM)
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MATH 483-1
Alex Iosevich
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MATH 492-1
Doug Haessig
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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.
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MATH 493-1
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Prerequisites: Open to second year graduate students only. Description: Students will attend a selection of research talks and colloquia on current research in Mathematics. Required of math Ph.D. students during their 2nd fall in the Ph.D. program
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MATH 506-1
Carl Mueller
MW 3:25PM - 4:40PM
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Topics are related to recent research in the field.
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- (MW 3:25PM - 4:40PM)
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MATH 507-1
Arjun Krishnan
TR 9:40AM - 10:55AM
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First-Passage Percolation (FPP) is a simple shortest path problem on a graph: pick a graph; put some random weights on its edges to mimic the time to cross edges; pick any two vertices and _nd the shortest time (weight) path between them. The passage time between vertices is a random metric on the graph, and the shortest-time paths are geodesics for this metric. One usually studies the statistics of the passage time and the behavior of geodesics on Zd. This simple model has incredible connections to 1) the zeros of the zeta function 2) random matrix theory 3) representation theory and combinatorics 4) Hamilton-Jacobi PDEs. The model was proposed in the 60s, but the main questions in the _eld are almost entirely open. In this course, I will loosely follow the review \50 years of _rst-passage percolation", and then move on to the research level questions in towards the end of the course. Along the way, I intend to cover: (1) Shortest path and ow algorithms, (2) Geodesic dynamics through ergodic theory, and (3) Hamilton-Jacobi PDEs and nonlinear eigenvalue problems. The course will be mostly probabilistic and analytic. The prerequisites are the basic real analysis and probability courses: 471 and 406. However, I think you can easily manage if you've only taken one of these.
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- (TR 9:40AM - 10:55AM)
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MATH 531-1
Naomi Jochnowitz
MW 2:00PM - 3:15PM
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Valuations, ideal theory, divisors. Class number, unit theorem. Geometric applications.
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- (MW 2:00PM - 3:15PM)
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MATH 549-1
Frederick Cohen
MWF 11:50AM - 12:40PM
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The main direction of this subject is a development of topological spaces known as moment-angle complexes as well as toric manifolds. Moment-angle complexes are unions of products of circles, and 2-disks"indexed" by a finite simplicial complex. Moment-angle complexes admit actions of products of circles with orbit spaces frequently known as toric manifolds. These spaces and their properties are at the interface of topology, geometry, algebraic topology as well as combinatorics. The goal of the course is to develop some of the main structure theorems in the subject. There will be a strong emphasis on examples which will be developed in class.
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- (MWF 11:50AM - 12:40PM)
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MATH 591-01
Frederick Cohen
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MATH 591-02
Allan Greenleaf
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MATH 591-03
Alex Iosevich
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MATH 591-04
Stephen Kleene
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MATH 591-05
Naomi Jochnowitz
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MATH 591-06
Sevak Mkrtchyan
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MATH 591-07
Jonathan Pakianathan
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MATH 591-08
Juan Rivera Letelier
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MATH 591-09
Douglas Ravenel
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MATH 591-10
Sema Salur
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MATH 591-11
Thomas Tucker
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MATH 591-12
Arjun Krishnan
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MATH 591-13
Xuwen Chen
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MATH 591-14
Carl Mueller
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MATH 591-15
Dan Geba
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MATH 591-16
Dinesh Thakur
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MATH 591-17
Michael Gage
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MATH 591-18
Saul Lubkin
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MATH 591-19
Steven Gonek
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MATH 595-01
Arjun Krishnan
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MATH 595-02
Sevak Mkrtchyan
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MATH 595-03
Stephen Kleene
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MATH 595-04
Doug Haessig
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MATH 595-05
Naomi Jochnowitz
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MATH 595-06
Xuwen Chen
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MATH 595-07
Alex Iosevich
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MATH 595-08
Allan Greenleaf
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MATH 595-09
Carl Mueller
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MATH 595-10
Dan Geba
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MATH 595-11
Dinesh Thakur
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MATH 595-12
Douglas Ravenel
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MATH 595-13
Frederick Cohen
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MATH 595-14
Jonathan Pakianathan
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MATH 595-15
Juan Rivera Letelier
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MATH 595-16
Michael Gage
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MATH 595-17
Saul Lubkin
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MATH 595-18
Sema Salur
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MATH 595-19
Steven Gonek
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MATH 595-20
Thomas Tucker
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MATH 895-1
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MATH 897-1
Naomi Jochnowitz
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MATH 899-1
Naomi Jochnowitz
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MATH 995-1
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MATH 997-01
Arjun Krishnan
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MATH 997-02
Sevak Mkrtchyan
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MATH 997-03
Stephen Kleene
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MATH 997-04
Doug Haessig
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MATH 997-05
Naomi Jochnowitz
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MATH 997-06
Xuwen Chen
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MATH 997-07
Alex Iosevich
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MATH 997-08
Allan Greenleaf
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MATH 997-09
Carl Mueller
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MATH 997-10
Dan Geba
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MATH 997-11
Dinesh Thakur
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MATH 997-12
Douglas Ravenel
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MATH 997-13
Frederick Cohen
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MATH 997-14
Jonathan Pakianathan
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MATH 997-15
Juan Rivera Letelier
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MATH 997-16
Michael Gage
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MATH 997-17
Saul Lubkin
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MATH 997-18
Sema Salur
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MATH 997-19
Steven Gonek
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MATH 997-20
Thomas Tucker
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MATH 999-01
Stephen Kleene
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MATH 999-02
Arjun Krishnan
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MATH 999-03
Sevak Mkrtchyan
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MATH 999-04
Doug Haessig
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MATH 999-05
Naomi Jochnowitz
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MATH 999-06
Xuwen Chen
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MATH 999-07
Alex Iosevich
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MATH 999-08
Allan Greenleaf
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MATH 999-09
Carl Mueller
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MATH 999-10
Dan Geba
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MATH 999-11
Dinesh Thakur
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MATH 999-12
Douglas Ravenel
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MATH 999-13
Frederick Cohen
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MATH 999-14
Jonathan Pakianathan
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MATH 999-15
Juan Rivera Letelier
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MATH 999-16
Michael Gage
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MATH 999-17
Saul Lubkin
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MATH 999-18
Sema Salur
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MATH 999-19
Steven Gonek
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MATH 999-20
Thomas Tucker
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