The format of the final exam will be similar to those of qualifying exams. (Note that old topology qualifying exams are posted on the web, so these will be a good practice exams.) There will be about 5 questions. All topics covered in this course can appear on the exam -- from point set topology to orientibility. Category theory, cellular homology, and Poincare duality won't be on the exam. At least one question will be from one of the problem sets for this course. It is possible that I will ask for proofs here and there. Usually, these should be rather short proofs, and in many cases they were presented in class. E.g. "state and prove Brouwer's fixed point theorem" might be a typical question. You will not be required to give lengthy proofs (such as homotopy invariance of homology or van Kampen's theorem), but you should be able to state all key theorems and definitions carefully. (E.g.: "Under what condition is H_n(X,A)=H_n(X/A) ?") You don't have to give proofs or justifications unless you are explicitly asked to do so. Thus, "state/describe..." really means that you just have to write down the answer, not give your calculation. "Disprove.." means that you have prove that the statement "..." is false. (Usually by giving a counterexample, you'd have to explain why it is a counterexample.) No tools will be allowed, in particular you may not consult your notes.
