Office: LeConte 406
Phone: 7-5134
Email: nyikos@math.sc.edu
Office hours: MWF 10:00 - 11:30 and MW 2:30 - 3:30
Math 730 makes a natural follow-up to a basic real analysis course and is a highly desirable preparation for any course in functional analysis. It is also the foundation for additional courses in topology as well as a good introduction to the independence results of modern set theory. Since it is a small class, it is being tailored to a considerable extent to the needs of those taking it. So, besides the official textbook for this course, there will also be short excerpts from other books distributed in class from time to time.
The official texbook, Willard's General Topology, is not only at a bargain price but is, in my estimation, the only really good textbook of general topology for a beginning year of general topology. There are other excellent books for lower and higher levels, and some that include a great deal of extra material, but this one is unique in being tailored to a course at this level.
The course covers Chapters 1 through 5 in depth and some parts of the first three sections of Chapter 6 (Sections 17-19) and of Section 26 in Chapter 8.
There are no formal prerequisites, although a course in real analysis at either the undergraduate or graduate level would be very helpful, as would an undergraduate topology course. But students can still do well if they just have the sort of mathematical sophistication that comes from taking abstract algebra (Math 546 or Math 701) or graduate linear algebra (Math 700).
Students get several
opportunities to get homework problems right: they hand in what they can do
and I give hints for how to finish the problems they could not
finish. Points start getting deducted only on the third and subsequent
attempts. In the past, most students have gotten a big majority of the
problems right the second time around.
New Homework is collected once a week, usually on Monday.
Extra credit problems will be given from time to time; these only expire when some student has been handed back a completely correct solution, and there is no deduction of points for later attempts.
The grading is based on homework (55 percent) a midterm (15 percent) and a final exam (30 percent). In addition, class attendance and participation can make a difference in borderline cases.
Math 731 (General Topology II) is a follow-up to this course, offered in Fall 2007. Math 730 is certainly an adequate preparation but is not a prerequisite.
Students are not required to come up with proofs on the midterm nor the final exam in either of these courses, but only on homework; some memorization of proofs is expected, and students will be tested only for (some of the) proofs that have been talked about in class or gotten right by everyone on the homework, with plenty of opportunity for asking of questions.