Re: Hank's comment. I did not kick ass on the analysis exam, but I think it's conceivable that I passed. Here's one of the questions that just did not get answered at all:

8. a) Show that the set O(n) of all real orthogonal nxn matrices is compact.
b) Show that the tangent vector M to O(n) at the identity matrix is a skew-symmetric matrix; that is, it satisfies the contition M(transpose)=-M.

(note: I don't know what it means for a matrix to be orthogonal, because we never at all learned that in this class, and I'm sure my prof would have told me, but I like having an excuse not to have attempted this problem.)

Now that I look at the test some more, it actually seems quite likely that I failed. Fuck. (I can take it again in the fall with a much lower pass threshold.) Beth, who is going to Long Beach State next year, is on her way over to drink and watch House.