Graduate classes, Spring 2009, Mathematics

MATH 512: Analysis IICredits: 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.
Prerequisites: Students are expected to have the background of Math 411-412 sequence or the equivalent.
000MSC: E406TuTh 11:30am - 12:45pmShanshuang Yangmax 16
MATH 516: Numerical Analysis IICredits: 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.
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: W304TuTh 2:30pm - 3:45pmJames Nagymax 16
MATH 522: Algebra IICredits: 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.
Prerequisites: Math 521.
000MSC: E408TuTh 1:00pm - 2:15pmVictoria Powersmax 16
MATH 536: Combinatorics IICredits: 4− Description− Sections
Content: This course is the second of the sequence of Math 535-536 and as such will continue to develop the topics from the first semester. Specific topics will include finite geometries, Hadermard matrices, Latin Squares, an introduction to design theory, extremal set theory and an introduction to combinatorial coding theory.
000MSC: E406MWF 12:50pm - 1:40pmRon Gouldmax 16
MATH 578R: Seminar in AlgebraCredits: 1 - 12− Description− Sections
Content: Research topics in algebra of current interest to faculty and students.
000MSC: W303Tu 4:00pm - 5:00pmEric Brusselmax 15
MATH 579R: Seminar in AnalysisCredits: 4− Description− Sections
Content: Topics include: numerical methods for linear algebra, inverse problems and PDE's
000MSC: W306W 12:50pm - 1:40pmEldad Habermax 20
MATH 590: Teaching SeminarCredits: 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.
000MSC: W306W 3:00pm - 3:50pmJames Nagymax 20
MATH 597R: Directed StudyCredits: 1 - 12− Description− Sections
000Faculty (TBA)max 0
MATH 599R: Master's Thesis ResearchCredits: 1 - 12− Description− Sections
000Faculty (TBA)max 0
MATH 787R: Topics in Combinatorics: Probabilistic & Extremal MethodsCredits: 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.
000MSC: W303TuTh 10:00am - 11:15amVojtech Rodlmax 16
MATH 788R: Topics in Algebra: Brauer Group and Related StructuresCredits: 4− Description− Sections
Content: We study the classical and cohomological Brauer group of a field, its role in algebraic geometry and number theory, and other applications. Topics include exponent and index of central simple algebras, splitting behavior, definition by descent, and Brauer Severi varieties.
000MSC: E408TuTh 10:00am - 11:15amEric Brusselmax 16
MATH 789R: Topics in Analysis: Computational Fluid DynamicsCredits: 4− Description− Sections
Content: The course provides an introduction to numerical methods for the partial differential equations in fluid dynamics. This is a dynamic research field, so attention will be given also to recent proposals. The course will cover mainly incompressible fluids, however a part will be devoted to compressible fluid dynamics. A part of the course will be given in the Computer Room.
000MSC: W302TuTh 11:30am - 12:45pmAlessandro Venezianimax 16
MATH 797R: Directed StudyCredits: 1 - 12− Description− Sections
000Faculty (TBA)max 0
MATH 799R: Dissertation ResearchCredits: 1 - 12− Description− Sections
000Faculty (TBA)max 0