# Graduate classes, Spring 2010, Mathematics

 MATH 500: Probability Credits: 4 − Description − Sections
Content: This course will begin the development of fundamental topics in probability theory and its applications in combinatorics and algorithms. Included will be: events and their probabilities, random variables and their distributions, limit theorems, martingales, concentration of probability, random walks and Markov chains.
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000MSC: E406MWF 11:45am - 12:35pmPaul Hornmax 16
 MATH 512: Analysis II Credits: 4 − 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: W306MWF 10:40am - 11:30amDavid Borthwickmax 25
 MATH 516: Numerical Analysis II Credits: 4 − 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.
000MSC: W302TuTh 10:00am - 11:15amAlessandro Venezianimax 25
 MATH 522: Algebra II Credits: 4 − 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: A.W. Knapp, "Basic algebra", Birkhauser, 2006.
Assessments: TBA
Prerequisites: Math 521.
000MSC: E408TuTh 1:00pm - 2:15pmSkip Garibaldimax 16
 MATH 532: Graph Theory II Credits: 4 − 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: E406MW 12:50pm - 2:10pmRon Gouldmax 16
 MATH 550: Functional Analysis Credits: 4 − 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 application.
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000MSC: E408TuTh 11:30am - 12:45pmMichele Benzimax 16
 MATH 558: Partial Differential Equations Credits: 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
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000MSC: W302TuTh 2:30pm - 3:45pmVladimir Olikermax 25
 MATH 577R: Seminar in Combinatorics Credits: 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.
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000MSC: W306F 4:00pm - 5:00pmVojtech Rodlmax 15
 MATH 578R: Seminar in Algebra Credits: 1 - 12 − Description − Sections
Content: Research topics in algebra of current interest to faculty and students.
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000MSC: W303Tu 4:00pm - 5:00pmRaman Parimalamax 15
 MATH 579R: Seminar in Analysis Credits: 4 − Description − Sections
Content: Topics include: numerical methods for linear algebra, inverse problems and PDE's
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000MSC: W306W 12:50pm - 1:40pmMichele Benzimax 20
 MATH 590: Teaching Seminar Credits: 4 − 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 3:00pm - 3:50pmShanshuang Yangmax 20
 MATH 597R: Directed Study Credits: 1 - 12 − Description − Sections
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000MSC: -----Faculty (TBA)max 999
 MATH 599R: Master's Thesis Research Credits: 1 - 12 − Description − Sections
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000MSC: -----Faculty (TBA)max 999
 MATH 787R: Topics in Combinatorics: Probabilistic & Extremal Methods Credits: 4 − Description − Sections
Content: This course will develop discrete probabilistic aspects of topics begun in Math 535-536. We will discuss deletion method, The second-moment method, Lovasz-Local Lemma and its applications. Large deviation inequalities, Derandomization and The Regularity lemma and its applications.
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000MSC: E406TuTh 8:30am - 9:45amVojtech Rodlmax 16
 MATH 797R: Directed Study Credits: 1 - 12 − Description − Sections
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000MSC: -----Faculty (TBA)max 999
 MATH 799R: Dissertation Research Credits: 1 - 12 − Description − Sections
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000MSC: -----Faculty (TBA)max 999