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 |