This course is an introduction to the basic structures and concepts of point-set topology and beginning concepts of algebraic topology. This is a core course of the PhD program, and as such, the syllabus is relatively fixed. The list of topics to be covered is here.
Instructor: Michael Anderson
Office: 4-110 Math Tower
Email: anderson at math.sunysb.edu
Web site: http://www.math.sunysb.edu/~anderson
Office hours: MW 11:30-1:00 & by appointment in 4-110 Math Tower
Grader: Yuan Gao
Email: ygao at math. stonybrook dot edu
Office: Math Tower 2-106
Office hours: Mon 12-1 and 6-7 in MLC, Wed 4-5 in 2-106.
Lectures: MW 10:00-11:20am, ESS 181
Grading: Homework 30%, Midterm 30%, Final 40%
Topology, 2nd Edition, by James R. Munkres. Prentice-Hall 2000
Another useful text for the last third of the semester covering algebraic topology is:
Algebraic Topology by Alan Hatcher. This is available as PDF download on Hatcher's website: here.
There will be weekly homework assignments, generally due in class on (Wednesdays).
You may discuss homework problems with other students and consult other sources, but you and only you are responsible for writing the full solutions expressing your full understanding. Please also write clearly and legibly.
Late homework policy: In general, no late homework is accepted. Exceptions are at the discretion of the grader.
Check the course schedule below regularly for the assignments.
Wednesday, Oct 18, in lecture class
The material for the Midterm will be all following Sections, which you can ignore/skip: 14, 35, 38. There will be 6-8 problems, some easy, some harder, spread over all Chapters, but with a bit more emphasis on the later Chapters and Sections.
Tuesday, Dec 19, 2:15-5pm, in MAT 4-130
The problems on the Final Exam will mostly be on algebraic topology, but covers the following sections.
Chapter 7: 43, 45, 47. Chapter 9, all but 57. Chapter 11: 68-71, 73, Chapter 13: all.
Or the equivalent material in the Hatcher text. There will be 7-8 problems on the exam.
The best preparation is to practice doing problems, e.g. problems from the Hatcher text.
18: 2, 5, 13 19:6,7 20:4(a),8(a) 21:9
21:2, 8 22:3, 4 Suppl. Ex:4, 5 23:3, 5, 11
28, 29, 37
24:8. 25:4.26:1, 7, 8.. 27:2(a)(b). 28:7.
30:1a, 3, 4, 5a, 12. 31:2, 6, 8.
34, 36, 35
33:2, 4. 34:3, 4. 361,3.
35, 43, Midterm
43: 1, 2, 5, 7.45: 7ab.
45:2, 4(a), 5. 51: 1, 2, 3.
52:4, 5. 53:3, 4, 6b. 58:5,6.
54:1, 4, 5, 7, 8. 58:2(a)-(e). 59:2.
No HW - Tksgv. Break.
60:5 70:1, 71:2, 74:3, 4a, 79:2, 5 81:5
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