Graduate classes, Spring 2014, 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: W302MW 10:00am - 11:15amDavid Borthwickmax 16
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: W302TuTh 11:30am - 12:45pmAlessandro Veneziani
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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Assessments: TBA
Prerequisites: Math 521.
000MSC: E406MW 1:00pm - 2:15pmRaman Parimalamax 16
MATH 532: Graph Theory IICredits: 3− Description− Sections
Content: Topics include: independence of vertices and edges (matchings), factorizations and decompositions, coloring (both vertices and edges), and classic external theory.
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Prerequisites: Mathematics 531.
000MSC: E408MW 11:30am - 12:45pmRon Gouldmax 16
MATH 544: Algebraic Topology IICredits: 3− Description− Sections
Content: Singular, simplicial and cellular homology, long exact sequences in homology, Mayer-Vietoris sequences, excision, Euler characteristic, degrees of maps, Borsuk-Ulam theorem, Lefschetz fixed point theorem, cohomology, universal coefficient theorem, the cup product, Poincare duality
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000MSC: E408TuTh 11:30am - 12:45pmDavid Zureick-Brown
MATH 546: Intro. to Differential Geometry IICredits: 3− Description− Sections
Content: An introduction to Riemannian geometry and global analysis. Topics to be covered: Manifolds, Riemannian metrics, Connections, Curvature; Geodesics, Convexity, Topics in Global Analysis.
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000MSC: E406TuTh 2:30pm - 3:45pmVladimir Olikermax 16
MATH 550: Functional AnalysisCredits: 3− Description− Sections
Content: An introduction to concepts and applications including: metric and normed spaces, Sobolev spaces, linear operators and functionals, compactness in metric and normed spaces, Fredholm's solvability theory, spectral theory, calculus in metric and normed spaces, selected applications.
Texts: Barbara D. MacCluer: "Elementary Functional Analysis", Graduate Texts in Mathematics, Springer, New York, 2008. Avner Friedman: "Foundations of Modern Analysis", Dover, New York, 2002.
Assessments: TBA
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000MSC: E406TuTh 10:00am - 11:15amMichele Benzi
MATH 577R: Seminar in CombinatoricsCredits: 3− Description− Sections
Content: The seminar in combinatorics is a research seminar for students and faculty. It runs weekly, and features speakers from outside Emory who come to talk about topics of interest to the Emory faculty.
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000MSC: W306M 4:00pm - 4:50pmDwight Duffusmax 20
MATH 578R: Seminar in AlgebraCredits: 3− Description− Sections
Content: Research topics in algebra of current interest to faculty and students.
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000MSC: W302Tu 4:00pm - 5:00pmDavid Zureick-Brown
RANTMSC: W304TuTh 2:30pm - 3:45pmKen Ono
MATH 579R: Seminar in AnalysisCredits: 3− Description− Sections
Content: Topics include: numerical methods for linear algebra, inverse problems and PDE's
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000MSC: W301TuTh 4:00pm - 5:00pmVladimir Olikermax 20
001MSC: W306W 12:50pm - 2:00pmAlessandro Veneziani
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: W306W 2:30pm - 3:20pmBree Ettingermax 25
MATH 597R: Directed StudyCredits: 1 - 9− Description− Sections
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MATH 787R: Topics in Combinatorics: Hypergraphs IICredits: 3− Description− Sections
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000MSC: E408Th 1:00pm - 2:15pm
F 9:00am - 12:00pm
Vojtech Rodlmax 16
MATH 788R: Topics in Algebra: Algebraic Geometry IICredits: 3− Description− Sections
Content: We will cover the topics: sheaves, schemes, cohomology of sheaves, Serre duality theorems and Riemann-Roch theorem for curves.
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000MSC: E406M 2:30pm - 3:45pm
W 11:30am - 12:45pm
Suresh Venapallymax 16
MATH 797R: Directed StudyCredits: 1 - 9− Description− Sections
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MATH 799R: Dissertation ResearchCredits: 1 - 9− Description− Sections
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