Instructor
Shelly Harvey
Herman Brown 446
Phone: x3659
email: myfirstname at rice dot edu

Course Information
Class meets: MWF 2:00pm - 2:50pm in HB 453
Office Hours: TBA
Webpage: http://math.rice.edu/~shelly/540s12/
All homework and reading assignments can be found on Owlspace
Teaching Assistant: Chris Davis (cwd1 at rice dot edu)

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

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, De Rham Cohomology and Cech Cohomology.

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 Friday and will be due the following Friday in class (or before class) unless otherwise stated; they will be posted on OWL-Space (use your netid to log in). Homework solutions must be legible. You must show all of your work for full credit. Late homework will receive at most 1/2 credit. Your homework grade will consist of two scores: one for correctness and one for exposition.

Exams
There will be one midterm (the date to be determined) and a final exam. Both exams will be take home exams. Good mathematical exposition will be counted on both exams.

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.