Before Wednesday's class, BUY THE TEXTBOOK; READ pages 1-12 in the textbook. If you do not have the book, you can download these pages from the resource section of OWLSPACE for this class. This is mostly what I talked about in class, but in more detail. But read Theorems 1.1 and 1.2 which I may NOT discuss. Also, look at the Appendices, and at some point this week or next week, read over Appendices A, B and D.

9/4 Assignment #2

Friday lecture will cover pages 16-19; Look over Appendices A and B; Note that answers to SOME problems are in the back of the book. Suggested Problems(for extra practice): Section 1.2 #1,11,12,16; Section 1.3 #1; Required Problems Due next Wednesday 9/4 at the start of class: Section 1.2 #9 (omt Cor. 1 since it was done in class; use only Axioms, definitions, and Theorems already proved),18; Section 1.3 # 8b, 8d, 10,12 (try to use the A_ij notation introduced on pages 8-9),20 Suggested procedure for Homework this week: complete all the required reading as soon as possible. Arrange a time, say on Sunday, to get together with some other students to talk about how to approach the problems. TRY to do some of the problems BEFORE you meet with your group. Do you know how to start them? If you get stuck, use one the following resources. Resources: My office hours Tuesday 2:30-4:00. PLEASE COME if you are confused or uneasy or want to say Hi. Recitation Section Tuesday 4-5pm Hermann Brown 427, where Ms. Katherine Vance will work some problems similar to homework and answer questions. Students who have not had experience proving things SHOULD ATTEND. Possibly meet again with your group on Tuesday night. I expect that one third of the class will have trouble knowing how to START some of the problems, but after going to office hours or recitation, you will be surprised that it is not so hard. If you have limited or no experience with proofs and abstractions, it can be hard to get started and to know what should be the logical set-up. For another third of the class, this is very easy so far. Write your name on your papers. Write legibly. Write the assignment number and date due. Write using full sentences as much as possible. Use a minimum of mathematical abbreviations.

9/6 Reading Assignment #3

READ pages 24-29. You can start to do the HW that is due next Wednesday if you want. The written assignment is longer this week.

9/11 Assignment #4

Read pages 29-32, 39-40 and handout on logic; Suggested problems:Section 1.4 #1,2a,2c,3a,3c,4a, 7,8,11. Section 1.5 #1 (a must) Required problems: Section 1.4 # 2b, 3b, 10,13 Section 1.5 #2b,2f,5,12,20. These Required Problems will be due on Wednesday 9/11 at the beginning of class.

9/13 Reading Assignment #5

READ pages 42-45.

9/16 Reading Assignment #6

READ pages 45-51; You are not responsible for the statement of the replacement theorem, Lagrange Interpolation is optional; Section 1.7 is optional reading (but if you want to be a real math major you ought to read Section 1.7)

9/18 Assignment #7

Suggested problems: Section 1.6 #1a-l (a must-good test questions) Required problems: Section 1.6 # 4 (be clever and no computation is necessary),11 (just do first part),14,16,19,28 (find a basis with 2n elements-don't make the mistake of assuming that a vector has ``coordinates''); Extra Credit #24. These Required Problems will be due on Wednesday 9/18 at the beginning of class,

9/18 Reading Assignment #8

Monday's lecture covered pages 64-68 Read these pages. Note INDEX OF DEFINITIONS FOR CHAPTER ONE on page 62-63. This will be useful for TESTS.

9/25 Assignment #9

Read 68-74; Suggested problems:Section 2.1 #1 (a must) Required problems due on Wednesday 9/25 at the beginning of class Section 1.6 #32a,b (draw pretty colored pictures but also include complete verbal justification),#31a; Section 2.1 #3,#5 (expect a problem like #2 thru #5 on our exam), #13,#17 (this is an important result and not hard to prove), #14a (note that there are 2 implications to prove),14c. Problem #14 is logically demanding. Please attend recitation section if you have difficulty with this problem. FIRST MIDTERM EXAM IS IN-CLASS FRIDAY OCTOBER 4

9/27 Reading Assignment #10

Read pages 79-83.

10/2 Assignment #11

Read 86-90. Study for test using materials from class. Required problems due on Wednesday 10/2: Section 2.2 #2b,4,5c,8 (these easy problems are covered on midterm so they will be good practice); Extra credit: Section 2.2 #16 (THIS EXTRA CREDIT PROBLEM MUST BE HANDED IN ON A SEPARATE PIECE OF PAPER FROM YOUR HOMEWORK)

10/7 Reading Assignment #12

Read pages 90-93, Optional 94-95; Read Appendix B page 551-552,

10/9 Assignment #13

Read 99-102; Suggested problems: Section 2.3 #1 Required problems due on Wednesday 10/9: Section 2.3 #11 (T_0 is the zero transformation),12 (very importatnt result-just use definitions of one-to-one and onto and composition- these have nothing to do with being linear transformations-just functions), 13 (JUST do first part-use the actual summation notation definition of matrix multipolication); 2.4 # 4 (use definitions),5,6, 16 (one way is to guess the inverse and check it; don't assume A is invertible) Extra credit: Section 2.4 #9 (This is tricky. Hint:use Corollary 2 p.102 and Exercise 12a section 2.3)

10/11 Reading Assignment #14

Read 100-106; Appendix B page 551;By Monday READ 110-115

10/16 Assignment #15

Required problems due on Wednesday 10/16: Section 2.4 #14, Section 2.5 #2d, 3bd; Prove by mathematical induction: for each non-negative integer n, the sum 1+3+...+(2n+1) equals (n+1)-squared; 6b, 9, 10 (easy once you use the hint);

Read 147-154 Required problems due Wednesday 10/23: Section 2.6 #3a,8 (what is a "vector in (R^3)^* ?); Section 3.1 #5 (use the definition of elementary matrix- not some hand-waving),6 Section 3.2 #2d,f,4b,5bd; Extra Credit: Section 2.5 #8

Optional Reading Section 5.3; Suggested Problems: Section 5.1 #1 Required problems due Wednesday 11/20 Section 5.2 # 2f,3b,9a; Suppose A is a square matrix such that the sum of the entries in each row is 1. Prove that 1 is an eigenvalue of A and find a 1-eigenvector. Suppose B is a square matrix such that the sum of the entries in each column is 1. Prove that 1 is an eigenvalue of B. Section 5.3 2b,e (hint:diagonalize the matrices- you don't need to read section 5.3)

12/04 Assignment #26

Special Fun Extra credit Assignment due Wednesday after Thanksgiving-write up solution and explanation of your solution for 10 extra points on HomeworkPUZZLE #1.

11/24 Reading Assignment #27

Read 329-351

11/27 Assignment #28

Suggested Problems: Section 6.1 #1 Required problems due Wednesday 11/27 Section 6.1 #2 (but do not verify Cauchy-Schwarz and triangle), 8ac, 10(easy trick), 17(easy); Section 6.2 # 2a,9,11,22 (for part b see Example 10 page 351); Section 6.3 # 12a (Hint: There are 2 inclusions to prove. For one inclusion consider the inner product of Tx with itself)

11/30 Reading Assignment #29

Read the class hand-out concerning chapters 6.3-6.6, this is also available in the resource section of owlspace; Optional reading sections 6.3-6.6

12/6 Assignment #28

REMINDER of Fun Extra credit Assignment due 12/4-write up solution and explanation of your solution for 10 extra points on Homework score. This MUST BE HANDED IN SEPARATELY FROM YOUR HOMEWORK PUZZLE #1. Suggested Problem 6.5 #1 (omit1a); Required problems due Friday 12/6: Section 6.4 #2bd (just determine if it is self-adjoint); Extra problem #1. Prove that if $A$ is either an orthogonal matrix or a unitary matrix then its eigenvalues have length $1$.Extra problem # 2. Suppose that A is an n by n real matrix. Prove that A is symmetric if and only if A is orthogonally equivalent to a real diagonal matrix (one implication uses the spectral theorem). Extra problem #3. Let A be the matrix where A_11=1, A_12=2, A_21=2, A_22=4. Find the 4 subspaces associated to A as in the fundamental theorem of linear algebra, and draw pictures of these subspaces of R^2. Make sure that you have two 'graphs', one for the domain of L_A and one for the codomain.