### Course Meeting Times

Lectures: 2 sessions / week, 1 hour / session

### Prerequisites

*18.701 Algebra I* or *18.703 Modern Algebra*; and *18.901 Introduction to Topology*

Familiarity with topological spaces, covering spaces, and the fundamental group will be assumed, as well as comfort with the structure of finitely generated modules over a PID.

### Description

This is a course on the singular homology of topological spaces. Topics include: Singular homology, CW complexes, Homological algebra, Cohomology, and Poincare duality.

### Textbook

There are lots of textbooks that treat algebraic topology more or less at the level of this course.

Bredon, Glen E. *Topology and Geometry (Graduate Texts in Mathematics)*. Springer-Verlag Berlin and Heidelberg GmbH & Company, 1993. ISBN: 9783540979265. [Preview with Google Books] (Complete and geometric)

Davis, James F., and Paul Kirk. *Lecture Notes in Algebraic Topology (Graduate Studies in Mathematics, 35)*. American Mathematical Society, 2001. ISBN: 9780821821602. [Preview with Google Books] (Interesting selection of topics)

Dold, Albrecht. *Lectures on Algebraic Topology (Grundlehren Der Mathematischen Wissenschaften Series)*. Springer-Verlag, 1980. ISBN: 9780387103693. (Wonderful technique)

Hatcher, Allen. *Algebraic Topology*. Cambridge University Press, 2001. ISBN: 9780521791601. (Chatty)

May, J. Peter. *A Concise Course in Algebraic Topology (Chicago Lectures in Mathematics Series)*. University of Chicago Press, 1999. ISBN: 9780226511832. [Preview with Google Books] (Concise)

Munkres, James R. *Elements of Algebraic Topology*. Addison Wesley Publishing Company, 1984. ISBN: 9780201045864. (Meticulous)

Shastri, Anant R. *Basic Algebraic Topology*. Chapman and Hall / CRC, 2013. ISBN: 9781466562431. [Preview with Google Books] (Verbose)

Spanier, Edwin H. *Algebraic Topology*. Springer, 2008. ISBN: 9780387944265. [Preview with Google Books] (Encylopedic)

Vick, James W. *Homology Theory: An Introduction to Algebraic Topology*. Academic Press, 1973. ISBN: 9780127212500. [Preview with Google Books] (Efficient)

### Assignments and Exams

There will be 6 problems sets and a 40 minute oral exam during final exam week.

### Grading

The course grade will be based on homework assignments (75%) and a 40 minute oral exam (25%) during final exam week.