Graduate classes, Spring 2008, Mathematics
|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.
Prerequisites: Students are expected to have the background of Math 411-412 sequence or the equivalent.
|000||MSC: W306||MWF 11:45am - 12:35pm||David Borthwick|
|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.
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.
|000||MSC: W304||TuTh 10:00am - 11:15am||Alessandro Veneziani|
|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.
Prerequisites: Math 521.
|000||MSC: E408||TuTh 11:30am - 12:45pm||Eric Brussel||max 15|
|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.
Prerequisites: Mathematics 531.
|000||MSC: E406||MWF 3:00pm - 3:50pm||Ron Gould||max 15|
|MATH 544: Algebraic Topology II||Credits: 4||− Description||− Sections|
Content: Singular, simplicial and cellular homology, long exact sequences in homology, Mayer-Vietoris sequences, excision, Euler characteristic, degrees of maps, Borsuk-Ulam theorem, Lefschetz fixed point theorem, cohomology, universal coefficient theorem, the cup product, Poincare duality
|000||MSC: W306||MWF 9:35am - 10:25am||Emily Hamilton||max 15|
|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.
|000||MSC: E406||TuTh 1:00pm - 2:15pm||Michele Benzi||max 15|
|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
|000||MSC: W301||TuTh 2:30pm - 3:45pm||Vladimir Oliker||max 15|
|MATH 578R: Seminar in Algebra||Credits: 1 - 12||− Description||− Sections|
Content: Research topics in algebra of current interest to faculty and students.
|000||MSC: W303||Tu 4:00pm - 5:00pm||Skip Garibaldi|
|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.
|000||MSC: W306||W 2:00pm - 2:50pm||James Nagy|
|MATH 597R: Directed Study||Credits: 1 - 12||− Description||− Sections|
|MATH 599R: Master's Thesis Research||Credits: 1 - 12||− Description||− Sections|
|MATH 741: Geometric Topology||Credits: 4||− Description||− Sections|
Content: In this course we will study discrete groups from a geometric perspective. (Discrete groups
are groups which are defned by generators and relations, such as free groups, free abelian
groups, braid groups, etc.) By treating groups as geometric objects, one can solve many
algebraic problems which are much more difficult without the geometry.
Introductory topics include:
Free groups, group presentations, Cayley graphs and Cayley complexes, Dehn's problems, fundamental groups, hyperbolic geometry, Eilenberg-MacLane spaces and some algebraic topology.
Advanced topics may include:
Coxeter and Artin groups, Bass-Serre theory (of groups acting on trees and other spaces), CAT(0) geometry, CAT(0) groups, hyperbolic groups, coarse geometry (quasi-isometries etc), ends of groups, boundaries of groups, Gromov's polynomial growth theorem.
|000||MSC: E408||TuTh 1:00pm - 2:15pm||Aaron Abrams||max 15|
|MATH 772: Numerical Partial Differential Equations||Credits: 4||− Description||− Sections|
Content: Examples and classification of PDE's, initial and boundary value problems, well-posed problems, the maximum principle, finite difference methods, variational formulations for elliptic PDE's, finite element methods, and iterative solution methods.
Prerequisites: Mathematics: 511-512, 515-516.
|000||MSC: E308A||TuTh 11:30am - 12:45pm||Eldad Haber||max 15|
|MATH 787R: Topics in Combinatorics: Extremal Combinatorics & Optimization||Credits: 4||− Description||− Sections|
|000||MSC: E406||TuTh 10:00am - 11:15am||Vojtech Rodl||max 15|
|MATH 787R: Topics in Combinatorics: Random Structures||Credits: 4||− Description||− Sections|
Content: The course will cover several advanced topics from the theory of random graphs, hypergraphs and other random structures, like random subsets of integers.
Prerequisites: No prerequisite is required, but some knowledge of probability, graph theory and combinatorics is anticipated
|000||MSC: W304||TuTh 8:30am - 9:45am||Andrzej Rucinski||max 15|
|MATH 788R: Topics in Algebra: Algebraic Geometry||Credits: 4||− Description||− Sections|
Content: After an introduction to affine and projective varieties, we shall cover the following topics on algebraic curves: Bezout's theorem, resolution of singularities for curves, Riemann Roch theorem. Necessary materials from commutative algebra will also be covered.
|000||MSC: E406||TuTh 11:30am - 12:45pm||Raman Parimala||max 15|
|MATH 797R: Directed Study||Credits: 1 - 12||− Description||− Sections|
|MATH 799R: Dissertation Research||Credits: 1 - 12||− Description||− Sections|