Graduate classes, Fall 2015, Mathematics
MATH 511: Analysis I  Credits: 3  − Description  − Sections 
Content: TBA Texts: TBA Assessments: TBA Prerequisites: TBA  000  MSC: E406  MW 8:30am  9:45am  Shanshuang Yang  max 16  MATH 515: Numerical Analysis I  Credits: 3  − Description  − Sections 
Content: Course will cover fundamental parts of
numerical linear algebra including matrix factorizations,
solution of linear systems and leastsquares problems,
the calculation of eigenvalues and eigenvectors, and
basic notions on
iterative methods for largescale 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.  000  MSC: E408  TuTh 2:30pm  3:45pm  Michele Benzi  max 16  MATH 521: Algebra I  Credits: 3  − Description  − Sections 
Content: Linear algebra, including canonical forms, infinitedimensional vector spaces, tensor products, and multilinear algebra. Group theory including group actions and representations. Texts: TBA Assessments: TBA  000  MSC: E406  MW 10:00am  11:15am  Suresh Venapally  max 16  MATH 543: Algebraic Topology I  Credits: 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  000  MSC: E408  MW 1:00pm  2:15pm  Suresh Venapally  max 16  MATH 550: Functional Analysis  Credits: 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.  000  MSC: E408  TuTh 10:00am  11:15am  Michele Benzi  max 16  MATH 577R: Seminar in Combinatorics  Credits: 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  000  MSC: W301  M 4:00pm  4:50pm  Dwight Duffus  max 30  MATH 578R: Seminar in Algebra  Credits: 3  − Description  − Sections 
Content: Research topics in algebra of current interest to faculty and students. Texts: TBA Assessments: TBA  000  MSC: W304  Tu 4:00pm  4:50pm  Ken Ono  max 30  MATH 579R: Seminar in Analysis  Credits: 1  9  − Description  − Sections 
Content: TBA Texts: TBA Assessments: TBA Prerequisites: TBA  000  MSC: W302  F 1:00pm  1:50pm  James Nagy  max 30  001  MSC: W301  Tu 4:00pm  4:50pm  Vladimir Oliker  max 30  MATH 597R: Directed Study  Credits: 1  9  − Description  − Sections 
Texts: TBA Assessments: TBA  00P    Faculty (TBA)  max 999  BENZ    Michele Benzi  max 0  GOUL    Ron Gould  max 0  NAGY    James Nagy  max 999  ONO    Ken Ono  max 999  MATH 599R: Research  Credits: 1  9  − Description  − Sections 
Content: TBA Texts: TBA Assessments: TBA Prerequisites: TBA  00P    David ZureickBrown  max 999  MATH 771: Numerical Optimization  Credits: 3  − Description  − Sections 
Content: This course will provide students with an overview of stateoftheart numerical methods for solving unconstrained, largescale optimization problems. Algorithm development will be emphasized, including efficient and robust implementations. In addition, students will be exposed to stateoftheart software that can be used to solve optimization problems. Texts: TBA Assessments: TBA Prerequisites: Mathematics 511512, 515516.  000  MSC: E406  MW 1:00pm  2:15pm  Lars Ruthotto  max 16  MATH 787R: Topics in Combinatorics: Hypergraphs  Credits: 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.  000  MSC: E406  TuTh 10:00am  11:15am  Vojtech Rodl  max 16  MATH 797R: Directed Study  Credits: 1  9  − Description  − Sections 
Texts: TBA Assessments: TBA  00P    Faculty (TBA)  max 999  RAMA    Raman Parimala  max 999  ZURE    David ZureickBrown  max 999  MATH 799R: Dissertation Research  Credits: 1  9  − Description  − Sections 
Texts: TBA Assessments: TBA  00P    Michele Benzi  max 999  NAGY    James Nagy  max 999  ONO    Ken Ono  max 999  RODL    Vojtech Rodl  max 999  VENA    Suresh Venapally  max 999  VENE    Alessandro Veneziani  max 999  ZURE    David ZureickBrown  max 999 
