Math 443

Differential Geometry II

Class meets Mon-Wed-Fri: 1:30-2:20 in Padelford C-401

Instructor:	Daniel Pollack
Office:	C-550 Padelford Hall
Phone:	206-543-1809
E-mail:	pollack@math.washington.edu
Web Page	http://www.math.washington.edu/~pollack/courses/spring00/M443.html

The Mathematics sequence Math 441/2/3 is being revised as of Autumn 1999. The sequence will began with Math 441, Topology. Math 442 is an Introduction to Differential Geometry, and Math 443 will continue with Topics in Geometry and Topology. The sequence as a whole will provide a solid introduction to a core area of modern mathematics. Topology and Differential Geometry form one of the most exciting areas of current mathematical research and play a major role in many other fields such as number theory, algebraic geometry, analysis and mathematical physics. In addition topology and geometry form the basis of numerous applications in fields outside of pure mathematics, such as physics, computer graphics, biology and engineering. Students who are considering pursuing a graduate degree in mathematics may find this course of particular interest.

Math 443 will be a continuation of Math 442: the study of the differential geometry of curves and surfaces in Euclidean three space. The text for this course will be Differential Geometry of Curves and Surfaces by Manfredo P. Do Carmo. The first (approximately) 2/3 of the course will focus on topics from chapters 4 and 5 of the book. (Chapters 1-3 were covered in Math 442.)

The last third of the course will consist of presentations by the students in the class on independent study topics. These topics will in general be related to the material presented in Math 441, 442 and the early portions of Math 443, however a great deal of latitude will be given to the students interests. A list of suggested topics will be available at the beginning of the quarter and students are welcome to suggest their own topics as well. Each student will have periodic meetings with the instructor regarding the independent study component of the course. Initially this will be to help focus the students choice of topic and identify appropriate references. Subsequently meetings will help understand the material and its relevance to the rest of the course. This will cumulate in each student giving 1 or 2 50-minute lectures to the class on their chosen topic and preparing a 5-10 page written report on their topic, to be handed in towards the end of the quarter.

I expect that this will be very exciting and allow each student to pursue, in a nontrivial way, a particular area in Geometry or Topology which is of interest to them. In hearing their fellow students lecture on a diverse selection of topics, it is hoped that the entire class will be exposed to a broader range of subjects than is usually found in a lecture class.