Basic Topology  -  Fall 2002 Syllabus

Prof. Ilya Kofman

Office:   607 Mathematics,  phone: 854-3210
Email:   ikofman@math.columbia.edu
Web site:   http://www.math.columbia.edu/~ikofman/
Visit the Topological Zoo

Course Time and Place:    1:10pm - 2:25pm  Monday and Wednesday,  520 Mathematics Building

Text:    Basic Topology  by M. A. Armstrong

Material Covered:    Topological spaces and continuous functions,  compactness and connectedness,  identification spaces  (Chapters 1-4),  Fundamental group and covering spaces  (Chapter 5, 10.4),  Classification of surfaces  (Conway's ZIP proof),  Simplicial homology  (Chapter 8),  and some interesting consequences  (Chapter 9).

Homework:  The homework assignments will be posted on this website, and any changes will be announced in class. Starred problems are extra credit. Incomplete work with good progress will be rewarded. Late homework will be penalized. I highly recommend working jointly on homework problems with fellow students, but in the end you must hand in your own work.

Grading:  The course grade is apportioned as follows:  homework 40%,  take-home midterm exam 30%,  final in-class presentation and written report 30%.

Help:  My office hours are right after class in my office 607 Mathematics.  The help room, 406 Mathematics, is open with people to answer questions all day long on weekdays, but some topics we cover require specialized knowledge.  You may also benefit from hiring a tutor.

Optimal Method of Study:  (1.) Read appropriate sections before coming to class.  (2.) Come to class.  (3.) Read the sections again after class.  (4.) Do the homework. Leave time to think--do not put homework off until it is due!  (5.) Come to office hours or the help room with any remaining questions.
 
Week Reading Homework Due
September 4 Sec. 1.1,  1.2,  1.3  1.4 Chapter 1:  1,2*,3,6,7,10,11,14,15,16,18,26*,27* Sep. 11
September 9 Sec. 2.1,  2.2,  2.3 Chapter 2:  2,3,5,7,11*,13,16,17,19*,20,22* Sep. 18
September 16 Sec. 3.1,  3.2,  3.3 Chapter 3:  1,4*,5,11,14,18,23,25 Sep. 25
September 23 Sec. 3.4,  3.5 Chapter 3:  30,31,32,34,37,41,43,44* Oct. 2
September 30 Sec. 3.6,  4.1,  4.2 Chapter 4:  1,2,3,5,6,7,8*,10,11*,12* Oct. 7
October 7 Sec. 4.3,  4.4 Chapter 4:  13,16,17,18*,19*,26,27,30,31,33*,34* Oct. 16
October 14 Review Take-home Midterm Exam Oct. 23
October 21 ZIP proof,  7.1,  7.5 Reading  
October 28 5.1,  5.2,  5.3 Chapter 5:  1,2,5,6,10,11,13,14 Nov. 6
November 6 5.4 Chapter 5:  17,27,28 Nov. 18
November 11 Sec. 6.4 (pp.137-140),  Appendix Chapter 6:  (p.140) 20,22 Nov. 18
November 18 Sec. 10.4 Section 10.4: (p.233) 20*,28* Dec. 2
November 25 5.5,  Chapter 8    
December 2 Presentations  In-class presentation and written report  
December 9 Presentations  In-class presentation and written report