# Math 103 Assignment 6

## Common Homework

In section 8 of chapter 5 of Palka, do the problems 61, 62, 63, 70, 71, 73, 75, 76, 82, 83.

Read Chapter 5 sections 5, 6, and 7.

1. You should have proved Theorem 5.5 when you read the phrase "essentially verbatim." If you didn't, you should do it now or do it when you do.
2. Theorems 6.1 and 6.2 give the final word on some of the questions rasied in seminar. The corresponding questions about branches of pth root functions are addressed in problem 75.
3. For those of you who have seen the coboundary (derivative) operator acting on differential forms: Can you find a direct connection between the notions of "homologous to zero" and "exact (ie cohomologous to zero)?"
4. The problems which I did not assign which are related to section 7 are all of the sort where you are asked to prove something which is intuitively clear and which follows with little creativity from the definitions. Convince yourself that you can do these.
5. The proof of 7.1 is very clever. Don't take it for granted.
6. The converse to Corollary 7.2 is false. Can you find a counterexample?

## Presentations

• Dan: V.5.
• James: V.6 & V.7.

In both cases, be prepared--at least--to tell me what you think is the most important thing in your section when you come to speak to me Thursday. I will not give any further suggestions in public, but if either of you feel in need of direction, feel free to talk to me at any time.

## Food

Terrill will bring the food for break.

Student

Time

Sonya

10:30

James

1:30

Joan

2:00

Dan

2:30

Tim

1:00 Friday

Terrill

1:45 Friday