Offered: Spring 1996 Instructor: David J. Eck Room: Eaton 110 Time: MWF 2:40 to 3:50 PM
As major areas of mathematics go, topology is relatively new, since it only emerged as a separate subject in the early part of the twentieth century. Topology studies abstract "spaces" called topological spaces. These are sets with just enough structure to make it possible to talk about "continuous functions" and a few other major topics such as connectedness and compactness.
There are actually several branches of topology. The basic study of topological spaces is known as point-set topology. This is what we will spend most of our time on this term. Towards the end of the course, though, I would like to spend a little time on algebraic topology, which combines ideas from topology and from abstract algebra. I would, at least, like to introduce the basic idea of the "fundamental group" of a topological space.
The text for the course if Foundations of Topology, by C. Wayne Patty. I have not developed a definite schedule of readings; we will cover as much of the book as time permits.
There will be weekly homework problem sets. Most or all of the problems will be assigned from the text. You can talk over the homework problems with other people in the class, but you should write up your own solutions. I will expect you to turn in homework problems on time.
There will be two tests. Each test will have an in-class part and a take-home part. The in-class part will cover definitions, statements of theorems, short essays, and some simple proofs. The take-home part will be given out in class on the day of the in-class part. It will consist mostly of more advanced proofs. You should not discuss problems on the take-home tests with anyone but me.
The tests are tentatively scheduled for Wednesday, April 24, with the take-home part due the following Monday, and for Wednesday, May 29, with the take-home part due on Monday, May 3 during the officially scheduled final exam period.
I will ask each person in the class to do several presentations. These might cover sections of the text, homework problems, or special topics. Ideally, I would prefer to devote one day a week to this, but we will have to see how things go.
Homework will count for 40% of the course grade. The in-class parts of the tests will count for 30% and the take-home part for another 30%. Your homework grade might include a component based on your class presentations.
My office is room 301 in Lansing Hall. I will announce regularly scheduled office hours as soon as my schedule is firm. But you will find that I am often in my office, and I encourage you to come by whenever you want to talk about the course or say hello.