Math 730. Fundamental Concepts of Topology (Fall 1998)

Title: Fundamental Concepts of Topology
Meeting times: MWF.......9:00am-9:50am (MTH 0401)
Instructor: Professor Jonathan Rosenberg. His office is room 2114 of the Math Building, phone extension 55166, or you can contact him by email. His office hours are Thursdays 1-2 and Fridays 10-11, or by appointment. The course also has a half-time teaching assistant, Andrea Giacobbe, who will be grading most of the homework. You can find him in room 3304 of the Math Building, phone extension 55139, or you can contact him by email.
Text: Topology and Geometry, by Glen E. Bredon, Graduate Texts in Math., vol. 139, Springer-Verlag, Corrected 2nd Printing, 1995, ISBN 0-387-97926-3.
Prerequisite: Undergraduate-level advanced calculus and abstract algebra (MATH 410, MATH 411 and MATH 403)
Catalog description: Survey of basic point set topology, fundamental group, covering spaces, Van Kampen's theorem, simplicial complexes, simplicial homology, Euler characteristics and classification of surfaces.

Course Description:

Basically, we will cover Chapters I-III of Bredon, except for some of the "optional" sections. Classification of surfaces in Bredon is in the exercises at the end of Chapter III, and we will do this in a little more detail than is in the textbook.

Course Requirements and Grading Policy:

Homework will be assigned, collected, and graded, usually once a week. Assignments, and possibly partial solutions after the assignments are returned, will be posted here. In addition, there will be a mid-semester exam and a 2-hour final exam. This course is designed to prepare students for the first half of the graduate qualifying exam in Geometry/Topology. Thus grades will have the following meaning:

A. Knows the material thoroughly, at the level required to pass the Ph.D. qualifying exam.
B. Knows the material, but not as thoroughly -- roughly at the level required to pass the M.A. (but not the Ph.D.) qualifying exam.
C. Did some work in the course, but does not know the material even at the level required to pass the M.A. qualifying exam.
D, F. I hope these won't arise. Basically mean "did not expend any effort".

40% of the grade will be based on the final exam, 20% of the grade will be based on the mid-term exam, and 40% of the grade will be based on graded homework. Thus it is your responsibility to turn the homework in on time.

Tentative Schedule

Week of August 31	Bredon, Ch. I, sections 1-5
Week of September 7	No class 9/7 (Labor Day). Bredon, Ch. I, sections 6-8
Week of September 14	Bredon, Ch. I, sections 9-10
Week of September 21	No class 9/21 (Rosh Hashanah). Bredon, Ch. I, sections 11-12
Week of September 28	Bredon, Ch. I, sections 13-15. No class 9/30 (Yom Kippur).
Week of October 5	Bredon, Ch. I, section 17; Ch. II, sections 1-2
Week of October 12	Bredon, Ch. II, sections 3-5
Week of October 19	Bredon, Appendix C; Ch. II, section 6
Monday, October 26	Mid-term Exam on Ch. I, first part of Ch. II
Week of October 26	Bredon, Ch. II, sections 7-9
Week of November 2	Bredon, Ch. II, sections 10-12
Week of November 9	Bredon, Ch. III, sections 1-3
Week of November 16	Bredon, Ch. III, sections 4-5
Week of November 23	Bredon, Ch. III, sections 6-7. No class 11/27 (Thanksgiving).
Week of November 30	Bredon, Ch. III, sections 8-9
Week of December 7	Classification of Surfaces
Tuesday, December 15	Final Exam. (This site includes solutions to the exam.)