Math 354 Assignments 2011

4 <\tr>
Due Date
Math 354 Assignments for Fall 2011
8/24 Reading Assignment #1
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 did NOT discuss. Also, look at the Appendices, and at some point this week or next, read over Appendices A, B and D.
8/26 Reading Assignment #2
Read pages 16-18 by Friday ; 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 8/31 at the start of class: Section 1.2 #9 (use only Axioms, definitions, and Theorems already proved),10 (you may quote results from calculus),18; Section 1.3 # 10,12 (try to use the A_ij notation),20,23a(extra credit); Section 1.4 # 2b,3b 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 Monday 3-3:30, 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. Bridget Franklin 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. The extra credit problem will not be difficult for you in a few weeks but some of you will find it hard to know how to proceed. Write your name on your papers. Write legibly. Write the assignment number and date due. Write using full sentences as much as possible.
9/2 Reading Assignment #3
READ pages 24-38. In class on Wednesday we covered pages 30-38. You can start to do the HW from Section 1.4 (see below) that is due next Wednesday if you want.
9/7 Assignment #4
Read pages 39-40 and 42-45 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 # 10,13 Section 1.5 #2b,5,9,12,20. These Required Problems will be due on Wednesday 9/7 at the beginning of class.
9/9 Reading Assignment #5
READ pages 42-45.
9/14 Assignment #6
Suggested problems: Section 1.6 #1a-i (a must-good test questions) Required problems: Section 1.6 # 4 (be clever and no computation is necessary),7 (show work),11 (just do first part),14,16,19,28 (find a basis with 2n elements); Extra Credit #24. These Required Problems will be due on Wednesday 9/14at the beginning of class,
9/16 Reading Assignment #7
Read pages 46-51 (Lagrange is optional;Section 1.7 optional); Read pages 64-70 Note INDEX OF DEFINITIONS on page 62-63. This will be useful for TESTS.
9/21 Assignment #8
Suggested problems:Section 2.1 #1 (a must) Required problems due on Wednesday 9/21 at the beginning of class Section 1.6 #32a,b (draw pretty colored pictures but also include verbal justification),#31 (for part b see top of page 22); Section 2.1 #3,#5 (expect a problem like #3 or #5 on the exam), #13, #14a (note that there are 2 implications to prove),14c, #17 (this is an important result).
9/21 Reading Assignment #9
Read pages 71-73 and 79-81. FIRST MIDTERM IS IN-CLASS FRIDAY SEPT. 30
9/23 Assignment #10
Read 79-83. Study for test using materials from class. Required problems due on Wednesday 9/28: Section 2.2 #2b,4,5c,8 (these problems are covered on midterm); Extra credit: Section 2.2 #16
9/26 Reading Assignment #11
10/2 Reading Assignment #12
Read pages 90-93, Optional 94-95; Read 99-100.
10/5 Assignment #13
Suggested problems: Section 2.3 #1 Required problems due on Wednesday 10/5: 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); 2.4 # 4 (use defintions),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 (Hint:use Corollary 2 p.102 and use Theorem 2.15 part e page 93 and Exercise 12a section 2.3)
10/7 Reading Assignment #14
Read 100-106; Appendix B page 551; Read 110-112 (stop at Thm 2.23)
10/12 Assignment #15
Read handout on proof by induction; Required problems due on Wednesday 10/12: Section 2.4 #13, 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 Extra Credit: Section 2.3 #16a
10/14 Reading Assignment #16
Read 112-115
10/17 Assignment #17
Read 119-121 (skip 122-123 and Section 2.7) Suggested Problems: Section 2.5 # 1,3ac Section 2.6 # 1a,b,c(for f.d. vector spaces),2 Required problems due Wednesday 10/19: Section 2.5 # 5, 6b, 8(you could do it by using a big diagram like mine from class),9,10(easy once you use the trick); Section 2.6 #3a,b (we wll do one example in class Monday),8 ; Extra Credit: Section 2.6 #10a,b
10/19 Reading Assignment #18
Read 147-150, 152-154. If you want to read beforehand what we will cover on Friday, Read 155-163
10/26 Assignment #19
Read:155-165; Suggested Problems: Section 3.2 #1 Required problems due Wednesday 10/26: Section 3.1 #6(you may use #5); Section 3.2 #2d,f,4b,5bd,6b 8,14a (use definitions, be logically precise, justify all steps, this problem will be graded on logical completeness) Extra Credit (not difficult): Section 3.2 #21
10/24 Reading Assignment #20
The material from Monday's lecture is pages 168-171. If you want to read beforehand what we will cover on Wednesday, Read 172-175
10/28 Reading Assignment #21
Skip 176-179, Read: 182--189 (this will be Friday's lecture)
11/2 Assignment #22
Suggested Problems: Section 3.3 #1, Section 4.1 #1abcd Required problems due Wednesday 11/2: Section 3.3 # 2b,2d,7a (show work-use Thm. 3.11),10; Section 3.4 #2b,f; Section 4.3 (just use basic properties of determinants from section 4.4-not the definition) #11,12,15
11/4 Reading Assignment #23
Read page 199; Skim Section 4.2, Read Section 4.4 (the rest of Chapter 4 is optional); REMINDER MIDTERM IS MONDAY IN CLASS
11/11 Assignment #24
Read 245-255; Suggested Problems:Section 4.1 #1abcd, Section 4.3 #1 Section 5.1 #1 Required problems due FRIDAY 11/11: Section 4.3 #13 (remember that the determinant will be a complex number in general) Section 4.4 #2d,3b,4d ; Section 5.1 3bc,4e,8a
11/13 Assignment #25
Special Fun Extra credit Assignment due Wednesday after Thanksgiving-write up solution and explanation of your solution for 10 extra points on HomeworkPUZZLE #1.
11/16 Assignment #26
Monday's lecture will be on pages 261-265; Suggested Problems: Section 5.1 #1 Required problems due Wednesday 11/16: Section 5.1 5,8c,9,12,14,15a,17a
11/18 Reading Assignment #27
11/23 Assignment #28
Suggested Problems: Section 6.1 #1 Required problems due Wednesday 11/23 Section 5.2 # 2f,3b,9a,10,11(easy-use 10) (Later we will see that if the characteristic polynomial splits over $\mathbb{F}$, then that matrix is always similar to an upper-triangular matrix so the trace is the sum of the eigenvalues and the det is the product of the eigenvalues !!); Section 6.1 #2 (but do not verify Cauchy-Schwarz and triangle), 3 (but do not verify Cauchy-Schwarz and triangle) 8ac, 10(easy trick),17(easy)
11/23 Reading Assignment #29
Read 341-348 (Monday's lecture)
11/25 Reading Assignment #30
Read 344-352 (Wednesday's lecture); Think about puzzle problem while eating turkey!! Let you r family members try to solve it without using math. This puzzle probem is extra credit and is due on Wednesday. You should write up your solution and answer all the questions asked. PUZZLE #1
12/1 Assignment #31
For all the following pages you would be much better to USE the class lecture notes that I will distribute Monday: 357-360 (you can skip Thm 6.8 and proof of 6.9 since I did it a different way), (optional pages recommended for computer scientists 360-363) Suggested Problem: Section 6.2 #1 Required problems due Friday 12/2 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 (hint: consider A-I). Can you find a 1-eigenvector? Section 6.2 # 2a,9,22 (for part b see Example 10 page 351); Section 6.3 # 3b (see example 2 page 359),12a (Hint: There are 2 inclusions to prove. For one inclusion consider the inner product of Tx with itself)