Math 3592H Honors Mathematics I Fall Semester 2008

Assignment 12 - Due Tuesday 12/2/2008. There will be no quiz on this day. The third midterm exam is on December 4. You will be tested on the material in Sections 2.1 - 2.6 which we have studied.

Read: Hubbard and Hubbard Section 2.6, 2.7.

Exercises (
Due Tuesday 12/2/2008):
Hand in only the exercises which have stars by them.

Section 2.6 (pages 221-222): 1, 2, 3, 4*, 5*, 6, 7*, 8*, 11*
(We have really done question 9 in class with subspaces of R^n, and the argument in abstract is the same. So far as I can see question 10 is pretty much the same as question 5, but maybe I am missing something.)
2.7 (pages 231-232): 1*

The following exercises are relevant for the material we do this week. I list them because they may be useful practice for the mid-term exam.
2.11 (pages 278-282); 8, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21

It is important to know about eigenvectors and eigenvalues, but the treatment in section 2.7 seems handicapped by not going far enough with the theory. In particular, they do not state the Cayley-Hamilton theorem which allows one to compute eigenvalues. I find the exercises from this section to be inadequate, and so I have only set one of them.