Textbook

As discussed in the course outline, the textbooks used in the course will be

• Elements of algebraic topology, by James Munkres, and
• Algebraic topology by Allen Hatcher.

These two books take a somewhat different approach. Hatcher's book tends to be better at giving some intuition. Munkres' book tends to be a little more careful and understandable with some of the definitions and foundational material. I'll try to indicate which one I think is better to read from each week.

Munkres also has an undergraduate book. This has a fair bit on the fundamental group (a somewhat different approach to algebraic topology than the homology we will discuss here), and a small amount on homology (only as far as H₁). This won't get you very far, but if you like this book, then you might like looking through these sections.

• Topology, by James Munkres, 2nd edition.

A lower-level book that does have a reasonably sophisticated treatment of homology (as well as of ideas such as simplicial complexes is the following.

• Basic topology, by Mark Armstrong.

Other sources

We will have a lively online discussion in the UP e-classroom system. Asking and answering questions of your peers will be of great benefit to your development.

Wikipedia has a number of articles on mathematical topics. They are mostly well-written and accurate, and many of the articles relevant to the content of Topology and homology theory should be fairly readable.