The Midterm Exam will be in the usual classroom on Thursday, March 12 during the regular class period. It has 50 points possible. As on any exam, it is wise to start with the problems that you feel confident that you know how to do, before moving on to others.

A significant portion will involve definitions and stating or checking basic facts. It will not be necessary to know complicated proofs of theorems (although working through their proofs is a good way to absorb the definitions and basic facts, as well as seeing some great ideas). If asked for a definition, try to give the one that we have used in this course (but any good one will do).

The following topics are likely to appear, although the exam is not limited to these topics:

1. The Excision Theorem, statement and not-too-difficult applications. and use.
2. The Hom functor, its behavior with respect to exactness.
3. Euler characteristic, basic properties, examples.
4. Degree, basic properties, examples.
5. Categories and functors, definitions and examples.
6. Cellular homology and calculations.
7. Free resolutions, basic properties.

The following topics do not appear, at least not explicitly: Mayer-Vietoris sequence, invariance of simplicial homology from the triangulation, applications of degree to vector fields, homology with coefficients, Eilenberg-Steenrod axioms, intuitive motivation of cohomology, Ext or anything after Ext.