Graduate classes, Spring 2016, 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.
Texts: Real Analysis by Royden ISBN: 9780024041517
Assessments: TBA
Prerequisites: Students are expected to have the background of Math 411-412 sequence or the equivalent.
000MSC: E406MW 8:30am - 9:45amShanshuang Yangmax 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.
Texts: Numerical Mathematics by Quarteroni, Sacco and Saleri ISBN: 9783540346586
Assessments: TBA
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: W302MW 1:00pm - 2:15pmAlessandro Venezianimax 16
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.
Texts: Galois Theory by Stewart ISBN: 9781482245820
Assessments: TBA
Prerequisites: Math 521.
000MSC: E406MW 11:30am - 12:45pmSuresh Venapallymax 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
Texts: Algebraic Topology by Hatcher ISBN: 9780521795401
Assessments: TBA
Prerequisites: TBA
000MSC: E406TuTh 11:30am - 12:45pmDavid Zureick-Brownmax 16
MATH 545: Introduction to Differential Geometry ICredits: 3− Description− Sections
Content: TBA
Texts: Riemannian Manifolds: An Introduction to Curvature by Lee ISBN: 9780387983226
Assessments: TBA
Prerequisites: TBA
000MSC: W306MW 10:00am - 11:15amDavid Borthwickmax 20
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.
Texts: TBA
Assessments: TBA
Prerequisites: TBA
000MSC: W301M 4:00pm - 4:50pmDwight Duffusmax 30
MATH 578R: Seminar in AlgebraCredits: 3− Description− Sections
Content: Research topics in algebra of current interest to faculty and students.
Texts: TBA
Assessments: TBA
Prerequisites: TBA
000MSC: W304Tu 4:00pm - 4:50pmVictoria Powersmax 30
001MSC: W301W 4:00pm - 5:00pmDavid Zureick-Brownmax 20
MATH 579R: Seminar in AnalysisCredits: 1 - 9− Description− Sections
Content: Topics include: numerical methods for linear algebra, inverse problems and PDE's
Texts: TBA
Assessments: TBA
Prerequisites: TBA
000MSC: W306F 1:00pm - 1:50pmJames Nagymax 30
001MSC: W302Tu 4:00pm - 4:50pmVladimir Olikermax 20
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.
Texts: TBA
Assessments: TBA
Prerequisites: TBA
000MSC: E406F 2:00pm - 2:50pmBree Ettingermax 15
MATH 597R: Directed StudyCredits: 1 - 9− Description− Sections
Content: TBA
Texts: TBA
Assessments: TBA
Prerequisites: TBA
00PFaculty (TBA)max 999
MATH 599R: Master's Thesis ResearchCredits: 1 - 9− Description− Sections
Content: TBA
Texts: TBA
Assessments: TBA
Prerequisites: TBA
00PMSC: -----Faculty (TBA)
MATH 787R: Topics in CombinatoricsCredits: 3− Description− Sections
Content: TBA
Texts: TBA
Assessments: TBA
Prerequisites: TBA
000MSC: E408TuTh 10:00am - 11:15amVojtech Rodlmax 16
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.
Texts: TBA
Assessments: TBA
Prerequisites: TBA
000MSC: E408MW 1:00pm - 2:15pmRaman Parimalamax 16
MATH 789R: Topics in Analysis: Bayesian Inverse Problems and Uncertainty QualificationCredits: 3− Description− Sections
Content: This special topics course introduces basic concepts as well as more recent advances in Bayesian methods for solving inverse problems. Motivated by real-world applications, we will contrast the frequentists and the Bayesian approach to inverse problems and emphasize the role of regularization/priors. Also, we will explore sampling techniques used for uncertainty quantification.
Texts: Somersalo and Calvetti, An Introduction to Bayesian Scientific Computing, Springer, 2007 Kaipio and Somersalo, Statistical and Computational Inverse Problems, Springer 2004
Assessments: TBA
Prerequisites: TBA
000MSC: E406MW 3:00pm - 4:15pmLars Ruthottomax 16
MATH 797R: Directed StudyCredits: 1 - 9− Description− Sections
Content: TBA
Texts: TBA
Assessments: TBA
Prerequisites: TBA
00PFaculty (TBA)
MATH 799R: Dissertation ResearchCredits: 1 - 9− Description− Sections
Content: TBA
Texts: TBA
Assessments: TBA
Prerequisites: TBA
00PFaculty (TBA)