Math 445 - Spring 08

Instructor

Professor Shelly Harvey
Herman Brown 410
Phone: x3659
email: shelly at rice.edu

Course Information

Class meets: MWF from 2pm-2:50pm in HB 427
Office Hours: TBA
Webpage:   http://math.rice.edu/~shelly/445s08/
All homework and reading assignments can be found on Owlspace
Teaching Assistant: Andrew Elliot (email: elflord at rice.edu)

Required Textbook

James Munkres, Elements of Algebraic Topology, Perseus Books Publishing, Cambridge, Massachusetts, 1984. ISBN: 0-201-62728 (paperback)

Other useful textbooks

Allen Hatcher, Algebraic Topology; available free online at http://www.math.cornell.edu/~hatcher/AT/ATpage.html
M J Greenberg and J Harper, Algebraic Topology: a First Course (Benjamin/Cummings 1981)

Course Description

We will study the Homology and Cohomology of topological spaces. (Co)Homology is a way of associating a sequence of abelian groups to a topological space that are invariant under homeomorphism (and more generally homotopy equivalence). The homology groups of a space are in general easier to compute than the homotopy groups and hence they can be more useful in distinguishing some spaces. Some of the topics we will cover are Simplicial and Singular (Co)Homology, Relative (Co)Homology, the Eilenberg-Steenrod axioms, the Universal Coefficient Theorem, some basic Homological Algebra, Poincare Duality and the Cohomology ring. If time permits, we will cover some of the following topics: the Kunneth Formula, DeRham Cohomology and Cech Cohomology.

Prerequisite

Math 443 or equivalent and a course in Abstract Algebra.

Grades

Your grade in the class will be based on the following weights:

Homework:40%
Midterm: 25%
Final Exam:35%

Homework and Exams

Homeworks will be assigned every Wednesday and will be due the following Wednesday in class (or before class) unless otherwise stated; they will be posted on OWL-Space. Homework solutions must be legible. You must show all of your work for full credit. Late homework will receive at most 1/2 credit. There will be one midterm and a final exam. Good mathematical exposition will be counted on both exams and homework.

OWL-Space

OWL-Space is a is an open source software development effort to design, build and deploy a new Collaboration and Learning Environment (CLE) for higher education. I will post announcements, schedules, homeworks, reading assignments and a bulletin board where you can post comments and questions. You will also be able to see your current homework/exam grades on Owlspace. You should use your NETID as your login.

Disability Support

Any student with a documented disability needing academic adjustments or accommodations is requested to speak with me during the first week of class. All discussions will remain confidential. Students with disabilities need to also contact Disability Support Services in the Ley Student Center.
Please send comments to Shelly Harvey ( shelly at rice.edu).