Introduction to Topology
Announcements
Announcements will be posted here from time to time. Please check regularly. The most recent announcement(s) will always be in green.
Lecturer
Ken Brown, Malott 521, 5-3598, kbrown@cornell.edu, office hours Wednesdays and Fridays 4:00–5:00, and by appointment.
The class meets Tuesdays and Thursdays, 11:40–12:55, in Malott 203.
Teaching assistant
Andrew Marshall, alm@math.cornell.edu, office hours Mondays 2:00–3:00 in Malott 108. Andrew is willing to stay past 3:00, but please let him know in advance if you plan to arrive after 3:00 so that he can be sure to wait.
Course mailing list
Mail sent to math4530@math.cornell.edu will reach everyone in the class (including Andrew and me). We will use this for announcements, but students can also use it for questions of general interest, discussion, etc.
Course description
Approximately half of the course will cover general topology, also known as point-set topology (topological spaces, continuous maps, connectedness, compactness, etc.) This material is used in analysis and is also the foundation for more advanced work in topology. The second half of the course will be an introduction to algebraic topology.
Prerequisite
According to the catalogue, the prerequisite is sophomore linear algebra plus at least one math course numbered 3000 or higher. My interpretation of this is that the primary prerequisite is "mathematical maturity." What I have in mind here is that you should be able to read and write proofs, you should be willing to persevere on a hard problem, and you should be willing to learn things on your own once in a while.
Text
James R. Munkres, Topology, 2nd ed., Prentice Hall, 2000. We will cover most of Chapters 1–5 and a selection of topics from Part II (Chapters 9–14) as time permits.
Other references
I have placed the following book on reserve in the math library:
- R. Courant and H. Robbins, What is mathematics?, 2nd ed., Oxford University Press, 1996.
Chapter V is a nice introduction to topology. Another good source of introductory material is Wikipedia. The front page has an animation of a doughnut being transformed into a coffee cup.
Course requirements and grading
There will be weekly homework assignments due on Tuesdays at the beginning of class. I expect that most of your learning will take place while doing the homework, and it will count heavily toward your final grade (40%). The remaining 60% will be based on two prelims and a final (20% each). The first prelim will be in class on Tuesday, October 22. The second will be a take-home exam. The final is scheduled for Wednesday, December 18, 7:00–9:30pm. I am willing to consider a final project in lieu of a final exam. See me if this interests you.
I try very hard to design the homework to go along with what is happening in class. I might, for example, give you a problem due Tuesday that is intended to motivate a theorem I'll prove on that day. For this reason I will not accept late homework except in very unusual circumstances. I will, however, drop the lowest homework grade.
See the homework page for the assignments and some guidelines as to how I want your homework written.
Due to constraints on our resources, not all problems will be graded. If there is a problem you want feedback on, put a star by it and Andrew will look at it and make comments, whether or not it gets graded.
Working together
I have no objection in principle to collaboration on the homework, provided that it is done in a way that maximizes the benefit of the homework to all people involved. (One person simply telling another how to do a problem totally defeats the purpose of the problem.) It is my opinion that you get maximum benefit from a homework problem if you work hard on it alone before combining your ideas with someone else's. In any case, the paper that you turn in with your name on it should represent your own solutions, written in your own words, regardless of whether you arrived at some of those solutions in collaboration with others.
In particular, you may not simply copy someone else's homework and turn it in as your own. This will be treated as a violation of Cornell's Academic Integrity Code. Similarly, copying solutions that you might find on the internet or in some other source is illegal.
Academic integrity
I take academic integrity very seriously and will follow university procedures in all cases of suspected cheating. Details are spelled out in the Academic Integrity Handbook, cited above.