2008 March 15 / E-Mail Me

Carleton College Math 354, Winter 2008, Prof. Joshua R. Davis

This is a first course in topology. We will survey some essentials of point-set topology (topological spaces, continuity, compactness, connectedness) and of geometric/algebraic topology (homotopy, fundamental group, classification of surfaces). Topics are adjusted to match students' backgrounds and interests. You can expect to spend at least 10 hours per week on this course, outside class. The basic course materials are:

- Schedule, with reading assignments and homework exercises
*Topology*, 2nd edition, by James R. Munkres. The first edition is not acceptable, because it lacks much of the algebraic topology material.

Our class meets in CMC 319 during period 5A (MW 01:50PM-03:00PM, F 02:20PM-03:20PM). Here's how you get in contact with me:

Dr. Joshua R. Davis (call me Josh if you like)

E-mail: See here

Office: CMC 221, x4366

Office hours: Mon 11:00-12:00, Tue 3:00-4:00, Wed 3:00-4:00, Thu 8:30-9:30. You can also make an appointment; simply pick a free time from my weekly schedule and e-mail me. You can also talk to me after class.

Final grades (A, B, C, etc.) are assigned according to an approximate curving process. By this I mean that there are no predetermined percentages (90%, 80%, 70%, etc.) required for specific grades. The following elements contribute to the final grade. Notice that there is no final exam.

- Participation: Each class session covers one or two sections of the textbook, which
*you are expected to read before class*. Class will be conducted on the assumption that you have already read and thought about the sections. Attendance is mandatory; furthermore, you are expected to participate actively in group work, discussion, individual exercises, etc. Class participation influences final term grades in borderline cases. You are also required to attend office hours at least once before Exam 1. - Homework: Most of your learning in this course happens not in class but rather while doing homework. The problems are listed on the schedule. They are collected once per week. Depending on time constraints, perhaps only a subset of your submitted work is graded; in order to ensure full credit, do all of the assigned problems. Because we do not have a grader for this course, part of your homework responsibility is grading other students' problems. Altogether, homework counts for 25% of your grade.
- Exam 1: This in-class exam tests basic point-set topology. It takes place on Friday January 25 and is worth 25% of your grade.
- Exam 2: This take-home (unlimited time, open-book and -note) exam focuses primarily on the material covered since Exam 1. It takes place from Wednesday February 20 to Friday February 22 and is worth 25% of your grade.
- Exam 3: This take-home exam focuses primarily on the material covered since Exam 2. It is due on the last day of class and is worth 25% of your grade.

You are encouraged to work with others on all homework (but not on take-home exams). Work together to figure out the problems, but write them up separately. In particular, you may not copy someone else's work or allow them to copy yours.

Since Math 236: Structures is a prerequisite for this class, I assume that you know how to devise and write proofs. If you are having trouble, I am happy to help you. There is always a question of how much detail to show. The answer is simple: *Write up your work so that it can be understood by a fellow student.* By doing so, you show enough detail that your grader can ascertain whether you yourself understand the material. Your solutions should also be self-explanatory; the grader should not have to refer to the book, to determine whether your work is correct.

The problems should be answered in the order they were assigned, and clearly marked. If your paper is messy or disorganized from revisions or erasures, then you may need to recopy it. *Staple* each assignment or exam into a single packet to be graded.

During the term, you have one free pass to hand in homework (not take-home exams) late. To activate your free pass, e-mail me about it by the due date, and set a new due date in your e-mail. The new due date is usually within a few days of the old one. If it isn't, then you need to convince me of its necessity; otherwise, no explanation is necessary. Use your free pass wisely. In general I do not accept late papers except in extreme circumstances that are truly beyond the student's control.

If some medical condition affects your participation in class or your taking of exams, let me know in the first week of class, so that we can make arrangements. You may want to visit the dean's Disability Services/Resources page first.

- Vector Fields
- Connectedness
- Exam 1 (high 85, median 71; roughly speaking, above median means A, below means B)
- Exam 1 Answers
- Immersion Of RP
^{2} - Isotopy
- Groups
- Exam 2 (75th %tile = 77, 50th = 68.5, 25th = 61; for hours spent, 75th %tile = 19, 50th = 15, 25th = 9.5)
- Exam 2 Answers
- Exam 3