The Final Exam will be in the usual classroom on Thursday, December 18, from 1:30-3:45 p. m. The exam has 75 points possible.

Some of the exam problems will be similar to homework problems, while others will draw upon the material presented in the lectures. 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. If asked for a definition, give the definition that we have used in this course.

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

1. Homotopy Extension Propery, statement and use.
2. van Kampen's Theorem, statement and applications.
3. Covering spaces, lifting theorems, the Lifting Criterion, covering transformations and groups of covering transformations.
4. Universal covering spaces.
5. Homology of Δ-complexes, definitions and computation.
6. Singular homology: definitions of singular simplices, singular chains, boundary homomorphism, chain complexes, chain maps, chain homotopy, relative homology.

The following topics do not appear, at least not explicitly: real and complex projective spaces, theory of CW-complexes, join construction, relative homotopy equivalence, free groups and group presentations, construction of surfaces as identification spaces.

There is no need to memorize long proofs of theorems, but familiarity with their basic ideas and key definitions is part of knowing the subject.

Exams I have written in other courses in recent years are available at the links that appear on my course pages page. The only graduate-level courses with exams were Math 5853 and 5863, but the latter course did contain some algebraic topology.