Math W4051: Topology

Fall 2007

Instructor: Ciprian Manolescu

E-mail: cm_at_math.columbia.edu
Office: Mathematics 601
Office hours: Mondays 2:30 - 3:30 pm and Tuesdays 3-4 pm, or by appointment

Teaching Assistant: Dmytro Karabash

E-mail: dk2204_at_columbia.edu
Office hours: Mondays 6-7 pm and Wednesdays 2-3 pm, in Math 406

Time and Place: 11:00 am - 12:15 am, Mondays and Wednesdays, 520 Mathematics Building

Web page: http://www.math.columbia.edu/~cm/top.html

Prerequisites: Familiarity with doing rigorous mathematical proofs, such as in Math V1208 (Honors Mathematics), Math W4041 (Modern Algebra), or W4061 (Analysis).

Topics to be covered: Metric spaces, continuity, compactness, quotient spaces. The fundamental group. Examples from knot theory and surfaces. Covering spaces.

Textbook: James R. Munkres, Topology, 2nd edition, Prentice Hall, Inc. It is available at the university bookstore. Keep in mind that we will not follow the book very closely, so it is important to attend the lectures or get the notes from another student. Some of the homework problems will be assigned from the book.

Grading: 40% homework, 40% final, 20% midterm.

Homework: Homework will be assigned every week and will be due the following Wednesday. The homework assignments will be handed out in class and will also be posted on the web page. You must hand in the homework in class each Wednesday. You are encouraged to talk about the problems with other students, but you should write up the solutions individually. You should acknowledge the assistance of any book, student or professor.
Late days: In case you cannot complete a homework assignment on time, you have a total of five late days that you can use throughout the semester. Once you use up these five days, no late homework will be accepted. The only exceptions are documented medical or family emergencies, which will not be subtracted from the late days. Note: Homeworks are due on Wednesdays by the end of class (12:15). Handing them on Wednesday afternoon or evening will count as a late day.
Exams: There will be one midterm given in class on Wednesday, October 24. The final exam is projected by the University to be on Monday, December 17 from 9am to noon. No make-up exams can be given, unless in case of an emergency.

Help: Help is available if you have trouble with the homework or the lecture material. If you are unable to come to my office hours, go to the Mathematics Help Room (406 Mathematics). This room is always staffed by at least one mathematics professor or graduate student Monday through Friday during business hours. You may drop by whenever the Help Room is open; no appointment is necessary.

Notes for the course, courtesy of Cayenne Boyer: 09/05, 09/10, 09/12, 09/17, 09/19, 09/24, 09/26, 10/01, 10/03, 10/15, 10/17, 10/22, 10/29, 10/31, 11/07, 11/12, 11/14, 11/19, 11/21, 11/26, 11/28, 12/03, 12/05, 12/10.

Problem Set 1 (due September 12), with solutions
Problem Set 2 (due September 19) with solutions
Problem Set 3 (due September 26) with solutions
Problem Set 4 (due October 3) with solutions
Problem Set 5 (due October 10) with solutions
Problem Set 6 (due October 17) with solutions and solution to Problem 3
Practice Midterm with some answers
Problem Set 7 (due November 7) with solutions
Problem Set 8 (due November 14) with solutions
Problem Set 9 (due November 21) with solutions
Problem Set 10 (due November 28) with solutions
Problem Set 11 (due December 5) with solutions
Practice Final with some answers