Math 730 Joel M. Cohen (Fall 2007)

This WEB page is http://www.math.umd.edu/~jmc/730.html, and was last updated: 9-7-07

Title:  Fundamental Concepts of Topology
Instructor: Professor Joel M. Cohen

Office: MTH 2313
Email: jmc@math.umd.edu
Telephone: (301)405-5109, Home phone: (202)546-1823.
Class Time: Tuesday-Thursday 11:00 a.m. - 12:15 p.m.
Location: Math B0429

Prerequisites: Math 403, 410, and 411 
Books: Topology and Geometry, G. Bredon,  Springer-Verlag, 1993
Algebraic Topology, A. Hatcher, Download Version
 

Office Hours: Tuesday-Thursday 1:00 - 2:00.  Occasionally, it may be necessary to change this time, so  let me know if you are planning to see me. Feel free to make an appointment for a different time with me, if you cannot see me during those hours. You can also send me email. I will answer queries as quickly as possible.
 

Course Contents:  Survey of basic point-set topology, fundamental group, covering spaces, Van Kampen's theorem, simplical complexes, simplicial homology, Euler characteristic, and the classification of surfaces.  We shall be covering most of the first three chapters of the book, starting with a brief survey of point-set topology.  It is not a complete course in point-set, but will give the student all the tools necessary for studying geometry and topology.
 

Web Posting:  If you have emailed me your permission to post your grades under an alias, you may check the grades by clicking here.
 
 

Grading: Each week there will be a graded homework assignment, due on Tuesday at the beginning of the class period.  Students may consult one another (consult, not copy) on homework assignments.  There will be a takehome exam due November 1 and a final exam on Thursday, December 13 at 8:00 a.m.  

The components of the final semester grade  are 30% Homework, 30% Midterm Exam, 40% Final Exam.
 

Additional Reading:
M.A. Armstrong, Basic Topology, Springer-Verlag, 1983
J. Munkres, Topology, Prentice-Hall,  1974
Singer and Thorpe, Lecture Notes on Elementary Geometry and Topology, Springer-Verlag.
W. Massey,  Algebraic Topology, Springer-Verlag.
Greenberg and Harper, Algebraic Topology, A First Course, Benjamin/Cummings,  1981.
S.E. Goodman, Beginning Topology, Brooks/Cole, 2005.
 
 

The following is an approximate schedule of sections to be covered, problems to be handed in, and suggested problems (in parentheses).  We will not necessarily cover all of each section.

Program
 

Week
 Sections
 Homework
 August 27
 I.1,2  p.3 - 1,2(3);p.7 - 1,4(2,5)
 September  3
 3,4,5 p.9 - 2,4,7 (1,3,6);p.12 - 1,4 (2,5);p.14 - 2,6(1,5,9)
                  10 7,8 p.21 - 2 (3);p.24 - 1,2,5,6
                  17 8,10,11,12 p. 31 - 1; p.39 - 1,2 
                  24 13 p.43 - 4,5 (6)
 October     1 14, II.2 p.50 - 1,6 (3,4,8); p.71 - 2,3
                   8 4,5 p.75 - 1 (2); p.80 - 1,2 
                  15 6 p.82 - 1,4 (2,3)
                  22 7 p.86 - 1,2,3 (4); 
                  29 8 p.88 - 1,3 (2)
November   5 9,10,11 p.89 - 1,3  (4); p.100 - 1,2
                  12 III.1 p.138 - 1,2,3
                  19 2,3,4 p.143 - 2,3,4;p.145 - 1
                  26 5,6,7 p.147 - 2 (1); p.150 - 1; p.154 - 1,3 (2)
December   3
 8,9, IV.21 p.158 - 1,2,5 (3,7); p.162 - 1,5,7 (3,8); p.250 -1
                  10 22,23,13 p.253 - 1; p.259 - 1,3;p.216 - 2