Fall 2004 COURSES

FALL 2004 COURSES

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Mathematics Course Descriptions:

MATH. 70100 - Functions of a Real Variable
M & W, 12:30-1:45 p.m., Rm. 5417, 4.5 credits, Prof. Randol, [47556]

MATH. 70300 - Functions of Complex Variable
T & R, 10:15-11:30 a.m., Rm. 6496, 4.5 credits, Prof. Keen, [47557]

MATH. 70500 - Algebra I
M & W, 2:00-3:15 p.m., Rm. 6417, 4.5 credits, Prof. Rocha, [47558]

MATH. 70700 - Topology I
T & R, 11:45 a.m.-1:00 p.m., Rm. 5417, 4.5 credits, Prof. Bendersky, [47559]

MATH. 70900 - Differential Geometry I
T & R, 2:00-3:15 p.m., Rm. 5417, 4.5 credits, Prof. Vasquez, [47560]

MATH. 71100 - Logic I
M & W, 4:15-5:30 p.m., Rm. 8405, 4.5 credits, Prof. Kossak, [47561]

MATH. 88500 - Discrete Geometry: Packing and Covering
W 4:15-6:15 pm, Rm. 8404, Prof. János Pach
How many objects of a given shape and size can be packed into a large box of fixed volume? Given a set system, what is the smallest number of elements with the property that every member of the system contains at least one of them? These questions raised by Gauss, Minkowski, Hilbert, Helly, Konig, and many others turned out to be centrally important in number theory, coding theory, discrepancy theory, mathematical statistics, combinatorial optimization, and many areas of computer science from bin packing to robotics. This course offers an introduction to this rapidly developing field, where combinatorial and probabilistic (counting) methods play a crucial role. Some familiarity with multivariate calculus and probability theory is required.
Topics: Geometry of numbers, Approximation of convex sets by polygons, Packing and covering with congruent convex discs, Lattice packing and lattice covering, The method of cell decomposition, Methods of Blichfeldt and Rogers, Efficient random arrangements, Epsilon-nets and transversals of hypergraphs, Geometric discrepancy, Bin packing.
Textbook: J. Pach and P. Agarwal: Combinatorial Geometry, Wiley, New York, 1995.

MATH. 82530 - Geom Appr to Alg Topology
T, 10:30 a.m.-12:30 p.m., Rm. 6417, 3 credits, Prof. Sullivan, [47565]

MATH. 83100 - Probability Theory
M & W, 2:00-3:15 p.m., Rm. 4419, 4.5 credits, Prof. Hueter, [47567]
The aims of this course are an introduction to the basic concepts in probability and stochastic processes and to convey how these techniques contribute in other fields and sciences. The core topics include: Laws of large numbers, central limit theorems, Stein-Chen method, random walks, martingales, Markov chains, and if time permits, Brownian motion and/or some special topics, for example, in stochastic geometry or random graphs. A real-analysis course or background is a prerequisite for the course. The textbook for the course will be ``Probability: Theory and Examples", by Richard Durrett, Second Edition, Duxbury Press, Belmont, CA, 1996.

MATH. 83530 - Algebra II
M, 4:15-6:15 p.m., Rm. 6417, 3 credits, Prof. Szpiro, [47563]

MATH. 86700 - Functional Analysis
M & W, 10:15-11:30 a.m., Rm. 5417, 4.5 credits, Prof. Kaplan, [47562]

MATH. 87300 - Tpcs in Alg Number Theory
R, 1:00-3:00 p.m., Rm. 4419, 3 credits, Prof. Kolyvagin, [47564]

MATH. 88500 - Discrete Geom: Packing/Covering
W, 4:15-6:15 p.m., Rm. 8404, 3 credits, Prof. Pach, [47568]

MATH. 88700 - Topics in Set Theory
T & R, 4:00-5:15 p.m., Rm. 4214.03 on Tu 6495 on Th, 4.5 credits, Prof. Hamkins, [47566]

MATH. 89901 - Ind Resch in Analysis
Rm. TBA, 1-12 credits, [47569]

MATH. 89902 - Ind Resch in Alg/Num Theory
Rm. TBA, 1-12 credits, [47570]

MATH. 89903 - Ind Resch in Geom/Topology
Rm. TBA, 1-12 credits, [47571]

MATH. 89904 - Ind Resch in Logic
Rm. TBA, 1-12 credits, [47572]

MATH. 89905 - Ind Resch in Applied Math
Rm. TBA, 1-12 credits, [47573]