MATH 4361
Naomi Jochnowitz
MW 4:50PM  6:05PM

Prerequisites: MTH 237 or equivalent. Undergrads must have permission of Instructor. Description: Rings and modules, group theory, fields and Galois theory.
 Location
 Hylan Building Room 206 (MW 4:50PM  6:05PM)

MATH 4401
Frederick Cohen
MWF 11:50AM  12:40PM

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 JordanBrouwer separation theorem, the BorsukUlam theorem and the PoincareHopf 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
 Hylan Building Room 1106A (MWF 11:50AM  12:40PM)

MATH 4431
Douglas Ravenel
MW 2:00PM  3:15PM

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.
 Location
 Hylan Building Room 206 (MW 2:00PM  3:15PM)

MATH 4711
Dan Geba
TR 9:40AM  10:55AM

Prerequisites: MTH 265 or equivalent. Description: Lebesgue measure on the line; measure spaces; integration; convergence theorems; RadonNikodym theorem; differentiation; Fubini's theorem; function spaces.
 Location
 Hylan Building Room 101 (TR 9:40AM  10:55AM)

MATH 4721
Xuwen Chen
MW 10:25AM  11:40AM

Banach spaces; dual spaces; Riesz representation theorem; Hilbert spaces; Fourier series; projective and unitary operators; spectral analysis of completely continuous selfadjoint operators. Applications.
 Location
 Hylan Building Room 206 (MW 10:25AM  11:40AM)

MATH 4831
Alex Iosevich
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MATH 4921
Allan Greenleaf
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Prerequisites: Open to firstyear 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, mathsci net, latex, peer support network, etc.

MATH 4931
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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

MATH 5041
Arjun Krishnan
TR 12:30PM  1:45PM

Discrete and continuous time Markov chains, Poisson processes, Brownian motion, stochastic calculus. One optional topic like branching processes, percolation, interacting particle systems, or potential theory.
 Location
 (TR 12:30PM  1:45PM)

MATH 5492
Jonathan Pakianathan
TR 2:00PM  3:15PM

Prerequisites: Familiarity with abstract algebra (either (MTH236H and MTH237) or (MTH436 and MTH437) or equivalent) and algebraic topology (MTH 443 or equivalent) is required. Description: The cohomology of groups is an area that lies at the intersection of topology, geometry, algebra and number theory. To every group, there is a unique classifying space (up to homotopy equivalence) that encodes the symmetries of the group and the cohomology of this space is called the cohomology of the group. This invariant is very useful in constraining the behaviour of group actions of that group on any object, whether the object is a space, a graph, a linear representation or a field extension in Galois theory. This course will study the basic properties of group cohomology and some of the fundamental computations. We will introduce the basic homological algebra, transfer and spectral sequence techniques needed to do the basic computations as well as the notion of equivariant cohomology to study questions related to group actions. We will also study a variant for finite groups called Tate cohomology. We will then apply this invariant to study some questions in topology, geometry and number theory.
 Location
 (TR 2:00PM  3:15PM)

MATH 59101
Frederick Cohen
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MATH 59102
Allan Greenleaf
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MATH 59103
Alex Iosevich
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MATH 59104
Stephen Kleene
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MATH 59105
Naomi Jochnowitz
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MATH 59106
Sevak Mkrtchyan
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MATH 59107
Jonathan Pakianathan
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MATH 59108
Juan Rivera Letelier
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MATH 59109
Douglas Ravenel
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MATH 59110
Sema Salur
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MATH 59111
Thomas Tucker
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MATH 59112
Arjun Krishnan
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MATH 59113
Xuwen Chen
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MATH 59114
Carl Mueller
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MATH 59115
Dan Geba
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MATH 59116
Dinesh Thakur
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MATH 59117
Michael Gage
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MATH 59118
Saul Lubkin
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MATH 59119
Steven Gonek
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MATH 59501
Arjun Krishnan
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MATH 59502
Sevak Mkrtchyan
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MATH 59503
Stephen Kleene
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MATH 59504
Doug Haessig
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MATH 59505
Naomi Jochnowitz
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MATH 59506
Xuwen Chen
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MATH 59507
Alex Iosevich
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MATH 59508
Allan Greenleaf
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MATH 59509
Carl Mueller
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MATH 59510
Dan Geba
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MATH 59511
Dinesh Thakur
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MATH 59512
Douglas Ravenel
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MATH 59513
Frederick Cohen
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MATH 59514
Jonathan Pakianathan
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MATH 59515
Juan Rivera Letelier
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MATH 59516
Michael Gage
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MATH 59517
Saul Lubkin
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MATH 59518
Sema Salur
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MATH 59519
Steven Gonek
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MATH 59520
Thomas Tucker
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MATH 8951
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MATH 8971
Naomi Jochnowitz
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MATH 8991
Naomi Jochnowitz
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MATH 9951
–
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MATH 99701
Arjun Krishnan
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MATH 99702
Sevak Mkrtchyan
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MATH 99703
Stephen Kleene
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MATH 99704
Doug Haessig
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MATH 99705
Naomi Jochnowitz
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MATH 99706
Xuwen Chen
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MATH 99707
Alex Iosevich
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MATH 99708
Allan Greenleaf
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MATH 99709
Carl Mueller
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MATH 99710
Dan Geba
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MATH 99711
Dinesh Thakur
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MATH 99712
Douglas Ravenel
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MATH 99713
Frederick Cohen
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MATH 99714
Jonathan Pakianathan
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MATH 99715
Juan Rivera Letelier
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MATH 99716
Michael Gage
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MATH 99717
Saul Lubkin
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MATH 99718
Sema Salur
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MATH 99719
Steven Gonek
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MATH 99720
Thomas Tucker
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MATH 99901
Stephen Kleene
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MATH 99902
Arjun Krishnan
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MATH 99903
Sevak Mkrtchyan
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MATH 99904
Doug Haessig
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MATH 99905
Naomi Jochnowitz
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MATH 99906
Xuwen Chen
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MATH 99907
Alex Iosevich
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MATH 99908
Allan Greenleaf
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MATH 99909
Carl Mueller
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MATH 99910
Dan Geba
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MATH 99911
Dinesh Thakur
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MATH 99912
Douglas Ravenel
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MATH 99913
Frederick Cohen
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MATH 99914
Jonathan Pakianathan
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MATH 99915
Juan Rivera Letelier
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MATH 99916
Michael Gage
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MATH 99917
Saul Lubkin
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MATH 99918
Sema Salur
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MATH 99919
Steven Gonek
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MATH 99920
Thomas Tucker
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