Graduate Program

Fall Term Schedule

Fall 2022

Number	Title	Instructor	Time
MATH 430-1 Number Theory Naomi Jochnowitz MW 4:50PM - 6:05PM
Prerequisites: 436, 437 Description: Number fields, rings of integers, factorization, class numbers. Frobenius and Dirichlet density theorems. Location Hylan Building Room 1101 (MW 4:50PM - 6:05PM)
MATH 436-1 Algebra I Naomi Jochnowitz MW 2:00PM - 3:15PM
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 1101 (MW 2:00PM - 3:15PM)
MATH 440-1 General Topology Juan Rivera Letelier MW 12:30PM - 1:45PM
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 Hylan Building Room 1106A (MW 12:30PM - 1:45PM)
MATH 443-1 Algebraic Topology 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 1104 (MW 2:00PM - 3:15PM)
MATH 471-1 Analysis I Allan Greenleaf MW 10:25AM - 11:40AM
Prerequisites: Math 265H or equivalent. Description: measures, integration, differentiation, product measures, Banach spaces, L^p spaces. Location Hylan Building Room 1106A (MW 10:25AM - 11:40AM)
MATH 472-1 Analysis III Dan Geba TR 9:40AM - 10:55AM
Prerequisites: Math 467 and 471. Description: 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. Location Hylan Building Room 1101 (TR 9:40AM - 10:55AM)
MATH 483-1 2nd Year Grad Orientation Alex Iosevich –
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MATH 488-1 Analytic Methods in Computer Science Kaave Hosseini MW 3:25PM - 4:40PM
Co-Located: CSC 288-1 (P), CSC 488-1, MATH 288-1, MATH 488-1 PLEASE NOTE: The meeting times for Fall 2022 - is MW 1525 - 1640 in Lechase Room 181 , (same as Math 288, CSC 288, CSC 488) Description: The purpose of this course is two-fold. First is to give a brief introduction to a number of areas in theoretical computer science such as coding theory, PAC learning, clustering, approximation algorithms, randomized algorithms, Ramsey theory, program/property checking, social choice theory, probabilistically checkable proofs, derandomization. Second is to look at each mentioned area through an analytic lens; That is, we introduce tools in spectral graph theory and Fourier analysis of boolean functions and use them to resolve major problems in each of those areas. Students are expected to have familiarity with undergraduate level discrete mathematics, graph theory, linear algebra, and probability. Location (MW 3:25PM - 4:40PM)
MATH 492-1 Grad Professional Seminar Allan Greenleaf –
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.
MATH 531-1 Algebraic Num Theory Dinesh Thakur MW 12:30PM - 1:45PM
Valuations, ideal theory, divisors. Class number, unit theorem. Geometric applications. Location Hylan Building Room 1101 (MW 12:30PM - 1:45PM)
MATH 537-1 Homology Saul Lubkin MW 2:00PM - 3:15PM
Projective and injective modules, complexes and resolutions, derived functors, including Ext and Tor, the homology and cohomology theory of groups and algebras, applications to the extension problem, etc. Location Hylan Building Room 1106A (MW 2:00PM - 3:15PM)
MATH 591-01 PhD Readings in Math – –
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MATH 591-02 PhD Readings in Math Allan Greenleaf –
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MATH 591-03 PhD Readings in Math Alex Iosevich –
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MATH 591-04 PhD Readings in Math Stephen Kleene –
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MATH 591-05 PhD Readings in Math Naomi Jochnowitz –
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MATH 591-06 PhD Readings in Math Sevak Mkrtchyan –
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MATH 591-07 PhD Readings in Math Jonathan Pakianathan –
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MATH 591-08 PhD Readings in Math Juan Rivera Letelier –
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MATH 591-09 PhD Readings in Math Douglas Ravenel –
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MATH 591-10 PhD Readings in Math Sema Salur –
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MATH 591-11 PhD Readings in Math Thomas Tucker –
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MATH 591-12 PhD Readings in Math Arjun Krishnan –
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MATH 591-13 PhD Readings in Math Xuwen Chen –
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MATH 591-14 PhD Readings in Math Carl Mueller –
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MATH 591-15 PhD Readings in Math Dan Geba –
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MATH 591-16 PhD Readings in Math Dinesh Thakur –
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MATH 591-17 PhD Readings in Math Sarada Rajeev –
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MATH 591-18 PhD Readings in Math Saul Lubkin –
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MATH 591-19 PhD Readings in Math Steven Gonek –
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MATH 594-1 Internship Alex Iosevich –
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MATH 595-01 PhD Research in Math Arjun Krishnan –
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MATH 595-02 PhD Research in Math Sevak Mkrtchyan –
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MATH 595-03 PhD Research in Math Stephen Kleene –
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MATH 595-04 PhD Research in Math Ivan Chio –
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MATH 595-05 PhD Research in Math Naomi Jochnowitz –
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MATH 595-06 PhD Research in Math Xuwen Chen –
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MATH 595-07 PhD Research in Math Alex Iosevich –
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MATH 595-08 PhD Research in Math Allan Greenleaf –
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MATH 595-09 PhD Research in Math Carl Mueller –
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MATH 595-10 PhD Research in Math Dan Geba –
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MATH 595-11 PhD Research in Math Dinesh Thakur –
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MATH 595-12 PhD Research in Math Douglas Ravenel –
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MATH 595-13 PhD Research in Math – –
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MATH 595-14 PhD Research in Math Jonathan Pakianathan –
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MATH 595-15 PhD Research in Math Juan Rivera Letelier –
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MATH 595-16 PhD Research in Math Michael Gage –
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MATH 595-17 PhD Research in Math Saul Lubkin –
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MATH 595-18 PhD Research in Math Sema Salur –
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MATH 595-19 PhD Research in Math Steven Gonek –
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MATH 595-20 PhD Research in Math Thomas Tucker –
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MATH 895-1 Cont of Master's Enrollment – –
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MATH 897-1 Master's Dissertation Naomi Jochnowitz –
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MATH 899-1 Master's Dissertation Naomi Jochnowitz –
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MATH 995-1 Cont of Doctoral Enrollment – –
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MATH 997-01 Doctoral Dissertation Arjun Krishnan –
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MATH 997-02 Doctoral Dissertation Sevak Mkrtchyan –
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MATH 997-03 Doctoral Dissertation Stephen Kleene –
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MATH 997-04 Doctoral Dissertation – –
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MATH 997-05 Doctoral Dissertation Naomi Jochnowitz –
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MATH 997-06 Doctoral Dissertation Xuwen Chen –
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MATH 997-07 Doctoral Dissertation Alex Iosevich –
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MATH 997-08 Doctoral Dissertation Allan Greenleaf –
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MATH 997-09 Doctoral Dissertation Carl Mueller –
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MATH 997-10 Doctoral Dissertation Dan Geba –
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MATH 997-11 Doctoral Dissertation Dinesh Thakur –
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MATH 997-12 Doctoral Dissertation Douglas Ravenel –
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MATH 997-13 Doctoral Dissertation – –
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MATH 997-14 Doctoral Dissertation Jonathan Pakianathan –
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MATH 997-15 Doctoral Dissertation Juan Rivera Letelier –
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MATH 997-16 Doctoral Dissertation Michael Gage –
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MATH 997-17 Doctoral Dissertation Saul Lubkin –
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MATH 997-18 Doctoral Dissertation Sema Salur –
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MATH 997-19 Doctoral Dissertation Steven Gonek –
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MATH 997-20 Doctoral Dissertation Thomas Tucker –
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MATH 999-01 Doctoral Dissertation Stephen Kleene –
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MATH 999-02 Doctoral Dissertation Arjun Krishnan –
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MATH 999-03 Doctoral Dissertation Sevak Mkrtchyan –
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MATH 999-04 Doctoral Dissertation – –
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MATH 999-05 Doctoral Dissertation Naomi Jochnowitz –
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MATH 999-06 Doctoral Dissertation Xuwen Chen –
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MATH 999-07 Doctoral Dissertation Alex Iosevich –
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MATH 999-08 Doctoral Dissertation Allan Greenleaf –
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MATH 999-09 Doctoral Dissertation Carl Mueller –
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MATH 999-10 Doctoral Dissertation Dan Geba –
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MATH 999-11 Doctoral Dissertation Dinesh Thakur –
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MATH 999-12 Doctoral Dissertation Douglas Ravenel –
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MATH 999-13 Doctoral Dissertation – –
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MATH 999-14 Doctoral Dissertation Jonathan Pakianathan –
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MATH 999-15 Doctoral Dissertation Juan Rivera Letelier –
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MATH 999-16 Doctoral Dissertation Michael Gage –
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MATH 999-17 Doctoral Dissertation Saul Lubkin –
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MATH 999-18 Doctoral Dissertation Sema Salur –
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MATH 999-19 Doctoral Dissertation Steven Gonek –
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MATH 999-20 Doctoral Dissertation Thomas Tucker –
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Number	Title	Instructor	Time
Monday
Monday and Wednesday
MATH 471-1 Analysis I Allan Greenleaf
Prerequisites: Math 265H or equivalent. Description: measures, integration, differentiation, product measures, Banach spaces, L^p spaces.
MATH 440-1 General Topology Juan Rivera Letelier
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.
MATH 531-1 Algebraic Num Theory Dinesh Thakur
Valuations, ideal theory, divisors. Class number, unit theorem. Geometric applications.
MATH 436-1 Algebra I Naomi Jochnowitz
Prerequisites: MTH 237 or equivalent. Undergrads must have permission of Instructor. Description: Rings and modules, group theory, fields and Galois theory.
MATH 443-1 Algebraic Topology Douglas Ravenel
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.
MATH 537-1 Homology Saul Lubkin
Projective and injective modules, complexes and resolutions, derived functors, including Ext and Tor, the homology and cohomology theory of groups and algebras, applications to the extension problem, etc.
MATH 488-1 Analytic Methods in Computer Science Kaave Hosseini
Co-Located: CSC 288-1 (P), CSC 488-1, MATH 288-1, MATH 488-1 PLEASE NOTE: The meeting times for Fall 2022 - is MW 1525 - 1640 in Lechase Room 181 , (same as Math 288, CSC 288, CSC 488) Description: The purpose of this course is two-fold. First is to give a brief introduction to a number of areas in theoretical computer science such as coding theory, PAC learning, clustering, approximation algorithms, randomized algorithms, Ramsey theory, program/property checking, social choice theory, probabilistically checkable proofs, derandomization. Second is to look at each mentioned area through an analytic lens; That is, we introduce tools in spectral graph theory and Fourier analysis of boolean functions and use them to resolve major problems in each of those areas. Students are expected to have familiarity with undergraduate level discrete mathematics, graph theory, linear algebra, and probability.
MATH 430-1 Number Theory Naomi Jochnowitz
Prerequisites: 436, 437 Description: Number fields, rings of integers, factorization, class numbers. Frobenius and Dirichlet density theorems.
Monday, Wednesday, and Friday
Tuesday
Tuesday and Thursday
MATH 472-1 Analysis III Dan Geba
Prerequisites: Math 467 and 471. Description: 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.
Wednesday
Thursday
Friday