Graduate classes, Fall 2015, Mathematics

MATH 511: Analysis ICredits: 3− Description− Sections
Content: TBA
Texts: TBA
Assessments: TBA
Prerequisites: TBA
000MSC: E406MW 8:30am - 9:45amShanshuang Yangmax 16
MATH 515: Numerical Analysis ICredits: 3− Description− Sections
Content: Course will cover fundamental parts of numerical linear algebra including matrix factorizations, solution of linear systems and least-squares problems, the calculation of eigenvalues and eigenvectors, and basic notions on iterative methods for large-scale matrix problems. Issues pertaining to conditioning and numerical stability will be thoroughly analyzed. We will also point out and use links to other mathematical and computer science disciplines such as mathematical modelling, computer architectures and parallel computing.
Texts: A. Bjorck, Numerical Methods in Matrix Computations. Texts in Applied Mathematics 59, Springer, 2015.
Assessments: TBA
Prerequisites: Excellent background in linear algebra is assumed. Some knowledge of computer architectures, programming and elementary numerical analysis is highly desirable.
000MSC: E408TuTh 2:30pm - 3:45pmMichele Benzimax 16
MATH 521: Algebra ICredits: 3− Description− Sections
Content: Linear algebra, including canonical forms, infinite-dimensional vector spaces, tensor products, and multilinear algebra. Group theory including group actions and representations.
Texts: TBA
Assessments: TBA
000MSC: E406MW 10:00am - 11:15amSuresh Venapallymax 16
MATH 543: Algebraic Topology ICredits: 3− Description− Sections
Content: Homotopy theory, the fundamental group, free products of groups with amalgamation, Van Kampen's Theorem, covering spaces, classification of surfaces, classifying spaces, higher homotopy groups
Texts: TBA
Assessments: TBA
000MSC: E408MW 1:00pm - 2:15pmSuresh Venapallymax 16
MATH 550: Functional AnalysisCredits: 3− Description− Sections
Content: An introduction to concepts and applications including: metric and normed spaces, Hilbert and Banach 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, 1982.
Assessments: TBA
Prerequisites: Math 511, Math 512.
000MSC: E408TuTh 10:00am - 11:15amMichele Benzimax 16
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
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
000MSC: W304Tu 4:00pm - 4:50pmKen Onomax 30
MATH 579R: Seminar in AnalysisCredits: 1 - 9− Description− Sections
Content: TBA
Texts: TBA
Assessments: TBA
Prerequisites: TBA
000MSC: W302F 1:00pm - 1:50pmJames Nagymax 30
001MSC: W301Tu 4:00pm - 4:50pmVladimir Olikermax 30
MATH 597R: Directed StudyCredits: 1 - 9− Description− Sections
Texts: TBA
Assessments: TBA
00P- Faculty (TBA)max 999
BENZ Michele Benzimax 0
GOUL Ron Gouldmax 0
NAGY James Nagymax 999
ONO Ken Onomax 999
MATH 599R: ResearchCredits: 1 - 9− Description− Sections
Content: TBA
Texts: TBA
Assessments: TBA
Prerequisites: TBA
00P David Zureick-Brownmax 999
MATH 771: Numerical OptimizationCredits: 3− Description− Sections
Content: This course will provide students with an overview of state-of-the-art numerical methods for solving unconstrained, large-scale optimization problems. Algorithm development will be emphasized, including efficient and robust implementations. In addition, students will be exposed to state-of-the-art software that can be used to solve optimization problems.
Texts: TBA
Assessments: TBA
Prerequisites: Mathematics 511-512, 515-516.
000MSC: E406MW 1:00pm - 2:15pmLars Ruthottomax 16
MATH 787R: Topics in Combinatorics: HypergraphsCredits: 3− Description− Sections
Content: The course will have two components: (1) A series of lectures on the basics of order theory, including an introduction to finite and infinite partially ordered sets and lattices, topics from combinatorics/set systems such as Sperner theory, uses of ordering to study classes of graphs, digraphs and other relational systems. The length of time spent on this will depend upon the backgrounds and interests of participants. (2) Focus on topics from "Graphs and Homomorphisms" by Hell and Nesetril, particularly the lattice of graph types ordered by homomorphism. There will be time spent on recent papers motivated by the Hedetniemi Conjecture, diverse notions of chromatic number [fractional, circular], etc. A set of coherently organized papers will be made available to participants before the beginning of the seminar. The emphasis will be on several open problems [of varying degrees of accessibility].
Texts: TBA
Assessments: TBA
Prerequisites: The introductory sequence in combinatorics and basic knowledge of group theory and graph theory will be assumed.
000MSC: E406TuTh 10:00am - 11:15amVojtech Rodlmax 16
MATH 797R: Directed StudyCredits: 1 - 9− Description− Sections
Texts: TBA
Assessments: TBA
00P- Faculty (TBA)max 999
RAMA Raman Parimalamax 999
ZURE David Zureick-Brownmax 999
MATH 799R: Dissertation ResearchCredits: 1 - 9− Description− Sections
Texts: TBA
Assessments: TBA
00P- Michele Benzimax 999
NAGY James Nagymax 999
ONO Ken Onomax 999
RODL Vojtech Rodlmax 999
VENA Suresh Venapallymax 999
VENE Alessandro Venezianimax 999
ZURE David Zureick-Brownmax 999