HOMEWORK
MTH 679 — Spring 2016

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 books.

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

(LG refers to Pollatsek's Lie group book; GO refers to our octonions book.)

Weeks 9 & 10

Suggested reading:

Read §6.7 of GO, and skim (the end of) §6.6. Also skim §11.5–11.6, §12.2, and §12.5.

(Later in the week, I will post lecture notes covering additional material.)

Assignment (due 6/1/16):

No assignment this week.

Week 8

Suggested reading:

Read §11.2–11.4 of GO, and skim §11.5.

Assignment (due 5/25/16):

No assignment this week.

Week 7

Suggested reading:

Reread §9.1 of GO. Also read §11.1 of GO, and skim §11.2–11.4.

Assignment (due 5/18/16):

Complete the assignment sheet.

Week 6

Suggested reading:

Read my notes on roots and their relevance to the classification of simple Lie algebras.
Also skim this article on the geometry of root diagrams.

(A local PDF version can be found here; you probably want to follow the last link.)

Assignment (due 5/11/16):

Complete the assignment sheet.

Week 5

Suggested reading:

Read §7.4 of GO.

(Later in the week, I will post lecture notes covering additional material.)

Assignment (due 5/4/16):

Complete the assignment sheet.

Week 4

Suggested reading:

Read §9.1 of GO, and skim the rest of §9. Read §10 of GO.

Assignment (due 4/27/16):

Complete the assignment sheet.

Week 3

Suggested reading:

Read §3, §4 and §5.1 of GO, and skim the rest of §5.

Assignment (due 4/20/16):

Complete the assignment sheet.

Week 2

Suggested reading:

Read §6.1–§6.3, §6.5–§6.6, and §7.1–7.3 of GO.

Skim §10.1–§10.2 and §12.1 of GO.

Assignment (due 4/13/16):

LG: §3.1: 11 (pp. 49–50), but for $\mathrm{SL}(2,\mathbb{C})$ rather than for $\mathrm{SL}(2,\mathbb{R})$.

You can also find a copy of this assignment here.
(You are again discouraged from using t as a parameter...)

Week 1

Suggested reading:

Skim Chapters 1 and 3 of LG.
Stop and read any bits that seem interesting, unfamiliar, or both, but don't try to master all the details.

Assignment (due 4/1/16):

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.).
• What is the most advanced algebra class you have taken?
  What is the most advanced geometry class you have taken?
  Feel free to include comments about these classes and/or your preparation in algebra and geometry.
• Why you are taking this class.

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

Assignment (due 4/6/16):

LG: §1.4: 16, 17 (p. 20), §3.1: 1b, 2b, 3ac (pp. 46–47)

You can also find a copy of this assignment here.
(You are strongly discouraged from using t as a parameter...)