HOMEWORK
MTH 437/537 — Spring 2024

Ground Rules

Suggested Reading

It is to your advantage to skim suggested readings as soon as possible. However, do not expect to master this material the first time around. Don't worry; we'll cover it in class, after which the readings should make more sense. But be warned: we will not always cover the material the same way it is presented in the text. The bottom line is that you are only responsible for material covered in class.

Written Work

It is your job to explain your work to me clearly and completely. Here are some guidelines:

• Write legibly, or use a word processor;
• Do not use scratch paper;
• Explain at least briefly what you're trying to do, don't just do it;
• Use complete sentences;
• Equations should (mostly) be contained in sentences;
• Feel free to use technology when appropriate, but this must be clearly documented. If possible, attach a printout of your session, together with a brief explanation of what you did.

You may discuss homework problems with anyone you like, and you may use any reference materials you like. However, you must write up the solutions in your own words, and you must indicate what help you used. Late homework will be corrected as a courtesy to you, but can earn at most half credit.

Assignments
Assignments should be submitted via Gradescope before class on the due date.

Week 5

Suggested reading:

Chapter 4 of the text, as well as the first two sections of Chapter 5.

Assignment (HW #5 due 5/9/24):

Please complete the assignment sheet.

Week 4

Suggested reading:

Read the last four sections of Chapter 3 of the text.

Skim Chapter 4 of the text.

Assignment (HW #4 due 5/2/24):

Please complete the assignment sheet. (Problems §5.6:6–7 on pages 62–63 of the text.)

Week 3

Suggested reading:

Read §6.3 of the text.

Read the first seven sections of Chapter 3 of the text.

Assignment (HW #3 due 4/23/24 4/25/24):

Please complete the assignment sheet. (Problems §5.6:4–5 on page 62 of the text.)

Week 2

Suggested reading:

Review §6.1 of the text.

Read §19.1 and §19.3 of the text, then skim §19.4–§19.6, then read Chapter 2 of the text.

Skim §6.3 of the text.

Review Assignment (not to turn in):

Make sure you understand how to determine the connection 1-forms for polar coordinates.
It wouldn't hurt to compute the curvature 2-forms as well.

Assignment (HW #2 due 4/16/24):

Please complete the assignment sheet. (Problems §5.6:1–3 on pages 61–62 of the text.)
(You should be able to complete this assignment even though we have not yet discussed the Schwarzschild line element.)

Week 1

Suggested reading:

Chapters 4–6 of my book on special relativity, which are summarized in the first four sections of Chapter 1 of the text.

Assignment (HW #0 due 4/4/24):

Please send a short email message to me at tevian@math.oregonstate.edu.
Please include the following information:

• Your class (senior, 1st-year grad, etc.) and major(s) (math, physics, etc.).
• Did you take MTH 434/534 from me last term?
  If so, yes, this is the same assignment as last term, so please either remind me what you told me then or tell me something new (or both), and of course feel free to include comments about that class.
  If not, please tell me how you are planning to get up to speed with differential forms.

I will assume that email is a reliable way to reach you unless you tell me otherwise.

Assignment (HW #1 due 4/8/24 4/9/24):

Please complete the assignment sheet.