Exam II will be in Room 809 PHSC on Wednesday, March 30, 2005, from 7:00-9:00 p. m. The exam is closed-book and closed-notes; that is, all you will need is something with which to write.

The exam will emphasize the fundamental group and use of the unique lifting properties of the map p: R --> S¹. The topics include (but are not limited to) the following:

1.	The change-of-basepoint homomorphism hγ.
2.	The definition of π1(X,x0) and of the induced homomorphism f#.
3.	The proof that π1(S1,s0) is isomorphic to Z.
4.	The fundamental group of the torus with one boundary circle.
5.	degree of maps from S1 to S1 (definition, basic idea, and basic results, but not the full details of the proofs).
6.	simply-connected spaces

The following topics will not appear on the exam:

1.	explicit formulas for path homotopies, such as in proving associativity in π1(X,x0)
2.	group theory review examples, conjugacy, etc.
3.	detailed proofs of the unique lifting for p: R --> S1.
4.	details of the proof that Sn is simply-connected
5.	proofs of No Retraction and Fixed-point Theorems
6.	[X,Y] and specific information about [Sm,Sn] (other than the case [S1,S1]).
7.	Fundamental Theorem of Algebra