Graduate classes, Spring 2017, Mathematics

MATH 512: Analysis IICredits: 3− Description− Sections
Content: Topics will include: Measure and integration theory on the real line as well as on a general measure space, Bounded linear functionals on L^p spaces. If time permits, Sobolev spaces and Fourier transforms will be introduced.
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Prerequisites: Students are expected to have the background of Math 411-412 sequence or the equivalent.
000MSC: W303MW 8:30am - 9:45amDavid Borthwickmax 20
MATH 516: Numerical Analysis IICredits: 3− Description− Sections
Content: This course covers fundamental concepts of numerical analysis and scientific computing. Material includes numerical methods for curve fitting (interpolation, splines, least squares), differentiation, integration, and differential equations. It is assumed that students have a strong background in numerical linear algebra.
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Prerequisites: Math 515, undergraduate course work in multivariable calculus and ordinary differential equations. An undergraduate course in numerical analysis would help, but is not absolutely essential. Prerequisites: This is a "hands on" course and students will be required to demonstrate their understanding of the concepts through programming assignments in MATLAB/Octave (help will be given for the novice programmer).
000MSC: W303TuTh 11:30am - 12:45pmJames Nagymax 35
MATH 522: Algebra IICredits: 3− Description− Sections
Content: Continuation of 521. Topics: Modules, especially modules over a principal ideal domain, fields, Galois theory, representation of finite groups, Commutative algebra.
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Prerequisites: Math 521.
000MSC: E408TuTh 10:00am - 11:15amSuresh Venapallymax 16
MATH 536: Combinatorics IICredits: 3− Description− Sections
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000MSC: E406MW 2:30pm - 3:45pmHao Huangmax 16
MATH 558: Partial Differential EquationsCredits: 3− Description− Sections
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000MSC: E406TuTh 10:00am - 11:15amVladimir Olikermax 16
MATH 561: Matrix AnalysisCredits: 3− Description− Sections
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000MSC: W306TuTh 2:30pm - 3:45pmMichele Benzimax 25
MATH 577R: Seminar in CombinatoricsCredits: 3− Description− Sections
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000MSC: W303M 4:00pm - 5:00pmDwight Duffus
MATH 579R: Seminar in AnalysisCredits: 1 - 12− Description− Sections
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001Vladimir Oliker
002MSC: W301F 1:00pm - 2:00pmJames Nagy
MATH 590: Teaching SeminarCredits: 3− Description− Sections
Content: This seminar will concentrate on effective teaching techniques in mathematics. Topics included will include: General advice for new TA's. General advice for International TA's. Students will present several practice lectures over different levels of material. They will receive practice on quiz and test preparation. Syllabus information on courses most likely to be taught by new TA's will be supplied. General professional development information will also be included.
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000MSC: W306F 11:00am - 11:50amBree Ettinger / Steven La Fleurmax 16
MATH 597R: Directed StudyCredits: 1 - 9− Description− Sections
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MATH 599R: Master's Thesis ResearchCredits: 1 - 9− Description− Sections
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MATH 772: Numerical Partial Differential EquationsCredits: 3− Description− Sections
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000MSC: E406MW 1:00pm - 2:15pmAlessandro Veneziani
MATH 787R: Topics in CombinatoricsCredits: 3− Description− Sections
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000MSC: E408TuTh 11:30am - 12:45pmVojtech Rodl
MATH 788R: Topics in Algebra: Algebraic GroupsCredits: 3− Description− Sections
Content: The course will consist of the following distinct components : 1. Structure theory of reductive groups over algebraically closed fields : Overview of objects and notions such as tori, solvable groups, Lie algebras, Jordan decomposition. Conjugacy of Borel subgroups and maximal tori, root systems, Bruhat decomposition, representation and classification of semi simple groups in terms of root systems. 2. Galois cohomology of linear algebraic groups : Classical groups and algebras with involutions, Steinberg's theorem, dimension two fields and Serre's conjecture, cohomological invariants and a discussion on some open questions in this area.
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MATH 788R: Topics in Algebra: Representation TheoryCredits: 3− Description− Sections
Content: This is an introduction to representation theory. The first part of the course focuses on finite-dimensional characteristic zero representations of finite groups. The second part develops Lie algebra theory as a tool for studying representations of Lie groups. The last part introduces vertex operator algebras and the role they play in tying the finite and Lie theories together. Concrete examples are emphasized throughout.
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000MSC: E406MW 11:30am - 12:45pmJohn Duncan
MATH 797R: Directed StudyCredits: 1 - 9− Description− Sections
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MATH 799R: Dissertation ResearchCredits: 1 - 9− Description− Sections
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