**Math 3593H Honors Mathematics II Spring Semester 2004
**

The first mid-term exam will be held on 1/19 in recitation. There will be no quiz. The questions on the exam will be about Sections 3.1 - 3.7 of the book. You may use a calculator. You may not use notes, the book or a computer.

Exercises:

Hint for 10: let v be an eigenvector and see what you can say about .

Extra question: A* Let be defined only on the unit disc . Show that on the unit disc this function takes its maximum value on the boundary. Calculate the maximum value and a point at which it takes it.

Hint: The equation has two roots, the larger of which is greater than 1. At the end of this question use a calculator.

I have spent quite some time trying to decide what to do about Section 3.8, which is about curvature. They get into some quite complicated formulas for computing curvature, and I do not think it helps one's understanding of curvature particularly to be fluent with this formulas. I would prefer a more rudimentary presentation with just the key facts. As it is, I think we should skip this section. This is a pity since only a few months ago it was determined with some accuracy that the universe we live in is flat, and not curved. It is nice to have some conception of what this means. If we have time at the end of the course (which, probably, we will not) we could come back to this.

The difference is that everyone can roast beef.