Math 730 Joel M. Cohen (Fall 2014)

This WEB page is http://www2.math.umd.edu/~jmc/730/ or simply jcohen730.org and was last updated: 10-11-14

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

Office: MTH 2313
Email: jcohen@umd.edu
Telephone: (301)405-5109, Home phone: (202)546-1823.
Class Time: T-TH 11:00  - 12:15
Location: Math 1308
Grader: Robert Maschal, Math 4202,  rmaschal@math.umd.ed

Prerequisites: Math 403, 410, and 411 

Books: Main text: Algebraic Topology, A. Hatcher, Downloadable
Reference: Topology and Geometry, G. Bredon,  Springer-Verlag, 1993
 
 

Office Hours: T-Th 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 fundamental group, covering spaces, Van Kampen's theorem, simplical complexes, simplicial homology, Euler characteristic, and the classification of surfaces. 

Grading: Each week there will be a graded homework assignment, due on Thursday at the beginning of the class period.  Students may consult one another (consult, not copy) on homework assignments.  There will be a take home exam (no consulting) due October 30, and a final exam on or due on Wednesday, December 17 at 8:00 a.m.  

The components of the final semester grade  are 30% Homework, 30% Midterm Exam, 40% Final Exam.
 
    Your participation in the evaluation of courses through CourseEvalUM is a responsibility you hold as a student member of our academic community. Your feedback is confidential and important to the improvement of teaching and learning at the University as well as to the tenure and promotion process. CourseEvalUM will be open for you to complete your evaluations for fall semester courses during the first two weeks of December. You can go directly to the website (www.courseevalum.umd.edu) to complete your evaluations approximately December 1. By completing all of your evaluations each semester, you will have the privilege of accessing the summary reports for thousands of courses online at Testudo.

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 (Hatcher)
 September  9
 Chapter 0

                  16 Chapter 0
 p. 18 – 4, 9, 11, 16, 18, 24
                  25 Chapter 1.1
 p.38 – 3, 5, 12, 16, 20
October      2
 Chapter 1.2
 p. 52 – 2, 7, 12, 13, 21
                   9
 Chapter 1.3
 p. 79 – 4, 7, 12, 14, 20
                  16 1.3, 2.1
 p.79 - 23, 25; p.86 - 6, 8
                  23

                  30

                  29

November   5

                  12

                  19

                  26

December   3

                  10