Graduate Program

Term Schedule

Fall 2021

Number	Title	Instructor	Time
MATH 430-1 Number Theory Thomas Tucker MW 12:30PM - 1:45PM
Prerequisites: 436, 437 Description: Number fields, rings of integers, factorization, class numbers. Frobenius and Dirichlet density theorems. Location Hylan Building Room 1106 (MW 12:30PM - 1:45PM)
MATH 436-1 Algebra I 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 1101 (MW 4:50PM - 6:05PM)
MATH 440-1 General Topology Jonathan Pakianathan 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 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 (MWF 11:50AM - 12:40PM)
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 206 (MW 2:00PM - 3:15PM)
MATH 471-1 Real Analysis Dan Geba TR 9:40AM - 10:55AM
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. Location Hylan Building Room 101 (TR 9:40AM - 10:55AM)
MATH 472-1 Functional Analysis 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 self-adjoint operators. Applications. Location Hylan Building Room 206 (MW 10:25AM - 11:40AM)
MATH 483-1 2nd Year Grad Orientation Alex Iosevich –
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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 493-1 Current Topics in Math – –
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 504-1 Stochastic Process 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 Hylan Building Room 1106 (TR 12:30PM - 1:45PM)
MATH 549-2 Topics in Algebraic Topology: The Cohomology of Groups 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 Hylan Building Room 1106 (TR 2:00PM - 3:15PM)
MATH 591-01 PhD Readings in Math Frederick Cohen –
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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 Ivan Chio –
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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 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 Frederick Cohen –
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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 Doug Haessig –
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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 Frederick Cohen –
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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 Doug Haessig –
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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 Frederick Cohen –
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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 472-1 Functional Analysis Xuwen Chen
Banach spaces; dual spaces; Riesz representation theorem; Hilbert spaces; Fourier series; projective and unitary operators; spectral analysis of completely continuous self-adjoint operators. Applications.
MATH 430-1 Number Theory Thomas Tucker
Prerequisites: 436, 437 Description: Number fields, rings of integers, factorization, class numbers. Frobenius and Dirichlet density theorems.
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 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.
Monday, Wednesday, and Friday
MATH 440-1 General Topology Jonathan Pakianathan
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.
Tuesday
Tuesday and Thursday
MATH 471-1 Real Analysis Dan Geba
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.
MATH 504-1 Stochastic Process Arjun Krishnan
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.
MATH 549-2 Topics in Algebraic Topology: The Cohomology of Groups Jonathan Pakianathan
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.
Wednesday
Thursday
Friday