Students should know all relevant definitions, correct statements of the major theorems (including their hypotheses and limitations), and examples and non-examples of the various concepts. The students should be able to demonstrate their mastery by solving non-trivial problems related to these concepts, and by proving simple (but non-trivial) theorems about the concepts below, related to, but not identical to, statements proven by the text or instructor. For more detailed information visit the Math 677 Wiki page.

1. Category Theory
2. Abelian Categories
3. Spectral Sequences
4. Calculating Ext and Tor
5. Dimension
6. Group Homology/Cohomology