# Math 337     Advanced Linear Algebra     Summer 2009

## Instructor: Sunil Chebolu

• Office: Stevenson 303B
• Email: szchebol@ilstu.eduz (with the two "z"'s removed)
• Office Hours: TTh 10:00 -- 11:00 in STV 303B or by appointment.
• Class meeting time: MTWTh 11:00 - 1:30 in WIH 111.
• Text:Abstract Algebra: Finite Dimensional vector spaces, by P.R. Halmos, Springer publication.

Announcements:

• (June 23) The first class test will be a take-home exam. I will give it on Thursday and it will be due next Monday.
• (June 19) We will go up to Section 20 of chapter 1, and then move on to Chapter 2. That is, we will skip section 21 - 31 of chapter 1. We may return to some of these skipped sections at a later stage if necessary.
• Welcome to the homepage of Math 337 -- an advanced course on Linear Algebra. I will post general announcements related to the course here. So please make sure you check this page frequently.

Other textbooks on linear algebra:

• Linear algebra: Kenneth Hoffman and Ray Kuntze
• Linear algebra: Tom Apostol
These are a couple of other good textbooks on linear algebra. But they are not necessary for this course, so you don't have to buy them. Just focus on Halmos, which is a treasure of knowledge, and has much more than what one can learn in 6 weeks! But if you want to take a look at a book on linear algebra with lots of problems, I recommend another book by Halmos: don't buy this, it is availble free on Google books: Linear algebra problem book -- Paul Halmos

## Homework Problems:

Week 5 (July 12 - July 18)

• Please read sections 46, 47, 49, 50, and 51 from the book (skip section 48)
• Section 47: 1, 2 (skip part d), 3, 4, 5.
• Section 49: 1, 2, 3, and 4.
• section 51: 1, 2, 3, 4, 7.

Week 4 (July 5 - July 11)

• Please read these sections from the book. [This is TERRIBLY IMPORTANT.]
• Section 40: Do all problems
• Section 43: Skip 1(b), 6(b), and do all the rest.

Week 3 (June 29 - July 4)

• Read section 37, 38, 39, 40, and 41 this week. Do the following problems.
• Section 38: 1, 2, 3a, 4, 5, 6, 9, 10, 11, 12, 13, 14, 16, 17,
• Section 40: Do all 4 problems.

Week 2 (June 22 - 28)

• Section 17: 1, 2, 3, 4 (How do you think of this subspace geomterically?), 6.
• Section 20: 1, 2, 3
• Section 33: 1 (a), 1 (b), 2, 3 (a), 3(b), 4, 5
• Section 35: 1 (do for n= 1, 2), 3, 4(a), 6(a)
• Section 36: 2, 3, 4, 6(a), 7.

Week 1 (June 15 - 21)

• Read the preface of the text book, and the syllabus.
• Read the first 15 sections of chapter 1. [This sounds a lot, but most of it, if not all, is part of the introductory course on linear algebra, so this is mostly review.]
• Section 1: 3, 5.
• Section 4: 5
• Section 7: 1, 3.
• Section 9: 1, 3, 4
• Section 12: 1, 3, 7(a), 8
• Section 14: 2, 5, 6.