Graduate classes, Fall 2011, Mathematics

MATH 511: Analysis ICredits: 4− Description− Sections
Content: An introduction to fundamental analytic concepts including: The complex number system, geometry and topology of the complex plane, analytic functions, conformal mappings, complex integration, and singularities.
Texts: Function os one complex variable. John B.Conway. Springer-Verlag. 2nd edition. ISBN: 0-387-90328-3.
Assessments: TBA
Prerequisites: TBA
000MSC: E408MWF 10:40am - 11:30amDavid Borthwickmax 16
MATH 515: Numerical Analysis ICredits: 4− Description− Sections
Content: This course covers topics in numerical linear algebra, including: matrix factorizations such as LU, QR and SVD; direct and iterative methods for solving linear systems and least squares problems; numerical approaches to solving eigenvalue problems; problem sensitivity and algorithm stability. A solid theoretical background of algorithms will be balanced with practical implementation issues.
Texts: Numerical Linear Algebra and Applications, 2nd Edition. Datta, Biswa. SIAM. ISBN 978-0898716856
Assessments: TBA
Prerequisites: TBA
000MSC: E408TuTh 11:30am - 12:45pmMichele Benzimax 30
MATH 521: Algebra ICredits: 4− Description− Sections
Content: An introduction to fundamental algebraic concepts including: Groups, homomorphisms, the action of a group on a set, Sylow theorems, group representations and characters, rings, ring homomorphisms, and basics on commutative rings.
Texts: TBA
Assessments: TBA
Prerequisites: TBA
000MSC: E408TuTh 10:00am - 11:15amEric Brusselmax 16
MATH 523: Commutative Algebra and GeometryCredits: 4− Description− Sections
Content: This is an introductory course covering topics like affine and projective varieties, Hilbert's Nullstellensatz, morphism and rational maps of varieties, dimension, smoothness, algebraic curves, intersection multiplicity and Bezout's theorem. Topics from commutative algebra like integral extensions, Noether's normalisation lemma and primary decomposition will also be treated simultaneously.
Texts: TBA
Assessments: TBA
Prerequisites: TBA
000MSC: E406MW 11:35am - 12:50pmRaman Parimalamax 16
MATH 531: Graph Theory ICredits: 4− Description− Sections
Content: I will introduce basic graph-theoretical concepts, graphs, trees, networks, cycles, independence number, chromatic number, planarity and genus, paths and cycles, etc. I will emphasize "extremal" problems and counting techniques.
Texts: TBA
Assessments: Grades will be based on written assignments.
Prerequisites: TBA
000MSC: E408MWF 2:00pm - 2:50pmRon Gouldmax 16
MATH 543: Algebraic Topology ICredits: 4− Description− Sections
Content: TBA
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Assessments: TBA
Prerequisites: TBA
000MSC E306TuTh 1:00pm - 2:15pmEmily Hamiltonmax 6
MATH 557: Partial Differential Equations ICredits: 4− Description− Sections
Content: This course will introduce some of the basic techniques for studying and solving partial differential equations (PDE's) with special emphasis on applications. Included in the course are the following topics: 1. Basic concepts, sample problems, motivation 2. Maximum principles for elliptic and parabolic equations 3. Basic concepts of the theory of distributions 4. Method of fundamental solutions; Green's functions 5. Fourier transform 6. Variational methods, eigenvalues and eigenfunctions 7. Applications; Maxwell's equations, diffusion, geometric flows, image processing
Texts: TBA
Assessments: TBA
Prerequisites: TBA
000MSC: W304TuTh 2:30pm - 3:45pmVladimir Olikermax 30
MATH 577R: Seminar in CombinatoricsCredits: 4− 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: W306F 4:00pm - 5:00pmDwight Duffusmax 30
001MSC: OtherRon Gouldmax 30
MATH 577R: Seminar in Combinatorics: Network ScienceCredits: 1 - 4− Description− Sections
Content: TBA
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Assessments: TBA
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000MSC: W304W 3:00pm - 5:00pmRon Gould / Vicki Hertzbergmax 30
MATH 578R: Seminar in AlgebraCredits: 1 - 12− Description− Sections
Content: Research topics in algebra of current interest to faculty and students.
Texts: TBA
Assessments: TBA
Prerequisites: TBA
000MSC: E406Tu 3:00pm - 4:00pmVictoria Powersmax 16
MATH 579R: Seminar in AnalysisCredits: 4− Description− Sections
Content: Topics include: numerical methods for linear algebra, inverse problems and PDE's
Texts: TBA
Assessments: TBA
Prerequisites: TBA
000MSC: W306W 12:50pm - 1:40pmAlessandro Venezianimax 30
001MSC: W301Tu 4:00pm - 5:00pmVladimir Olikermax 30
MATH 597R: Directed StudyCredits: 1 - 12− Description− Sections
Content: TBA
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Assessments: TBA
Prerequisites: TBA
DUFFDwight Duffusmax 999
DUFFMSC: OtherKen Onomax 999
GOULMSC: OtherRon Gouldmax 999
NAGYJames Nagymax 999
VENEAlessandro Venezianimax 999
YANGShanshuang Yangmax 999
MATH 787R: Topics in Combinatorics: HypergraphsCredits: 4− Description− Sections
Content: TBA
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Assessments: TBA
Prerequisites: TBA
000MSC: E406TuTh 8:30am - 9:45amVojtech Rodlmax 16
MATH 788R: Topics in Algebra: Modular Forms/Elliptic CurvesCredits: 4− Description− Sections
Content: TBA
Texts: Introduction to Elliptic Curves and Modular Forms (Graduate Texts in Mathematics). Koblitz, N. Springer. ISBN: 0387979662. The web of modularity: arithmetic of the coefficients of modular forms and q-series. Ono, K. American Mathematical Society. ISBN: 0821833685.
Assessments: TBA
Prerequisites: TBA
000MSC: E406TuTh 11:30am - 12:45pmKen Onomax 16
MATH 789R: Topics in Analysis: Geometric Function Theory & PDECredits: 4− Description− Sections
Content: While conformal mappings are homeomorphic solutions of Cauchy-Riemann systems, quasiconformal mappings can be viewed as homeomorphic solutions of Beltrami systems. In this course we will study conformal and quasiconformal mappings in Euclidean spaces from a PDE perspective. A major focus of the course will be the presentation of the rigidity theory of 1-quasiconformal mappings, from the most elementary form in the complex plane to recent developments.
Texts: TBA
Assessments: TBA
Prerequisites: TBA
000E306TuTh 11:30am - 12:45pmShanshuang Yangmax 16
MATH 797R: Directed StudyCredits: 1 - 12− Description− Sections
Content: TBA
Texts: TBA
Assessments: TBA
Prerequisites: TBA
BENZMichele Benzimax 999
BORTDavid Borthwickmax 999
GARISkip Garibaldimax 999
NAGYJames Nagymax 999
RAMAMSC: OtherRaman Parimalamax 999
RODLVojtech Rodlmax 999
VENEAlessandro Venezianimax 999
MATH 799R: Dissertation ResearchCredits: 1 - 12− Description− Sections
Content: TBA
Texts: TBA
Assessments: TBA
Prerequisites: TBA
ABRAAaron Abramsmax 999
BENZMichele Benzimax 999
BORTDavid Borthwickmax 999
GOULRon Gouldmax 999
HAMIEmily Hamiltonmax 999
NAGYJames Nagymax 999
OLIKVladimir Olikermax 999
ONOKen Onomax 999
RAMARaman Parimalamax 999
RODLVojtech Rodlmax 999
VENEAlessandro Venezianimax 999
YANGShanshuang Yangmax 999