Math 354 Assignments 2012

Due Date
Math 354 Assignments for Fall 2012
8/22 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.
8/29 Reading 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 8/29 at the start of class: Section 1.2 #9 (use only Axioms, definitions, and Theorems already proved),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 3-3:40, 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. Aru Ray 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.
8/31 Reading Assignment #3
READ pages 24-38. You can start to do the HW that is due next Wednesday if you want.
9/5 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,2f,5,9,12,20. These Required Problems will be due on Wednesday 9/5 at the beginning of class.
9/7 Reading Assignment #5
READ pages 42-45.
9/10 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 (you might want to just read the theorems in Section 1.7)
9/12 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 9/12 at the beginning of class,
9/12 Reading Assignment #8
Monday's lecture covered pages 64-70. Note INDEX OF DEFINITIONS FOR CHAPTER ONE on page 62-63. This will be useful for TESTS.
9/19 Assignment #9
Read 71-72; Suggested problems:Section 2.1 #1 (a must) Required problems due on Wednesday 9/19 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 and not hard to prove). FIRST MIDTERM IS IN-CLASS FRIDAY SEPT. 28
9/21 Reading Assignment #10
Read pages 79-83.
9/24 Assignment #11
Read 86-90. Study for test using materials from class. Required problems due on Wednesday 9/26: 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
10/1 Reading Assignment #12
Read pages 90-93, Optional 94-95; Read 99-100.
10/3 Assignment #13
Suggested problems: Section 2.3 #1 Required problems due on Wednesday 10/3: 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 actual summation notation defintion of matrix multipolication); 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)
10/5 Reading Assignment #14
Read 100-106; Appendix B page 551; Read 110-115
10/10 Assignment #15
Required problems due on Wednesday 10/10: 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, 8(you could do it by using a big diagram like mine from class),9, 10 (easy once you use the hint);
10/12 Assignment #16
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
10/15 Assignment #17
Read 147-150 Required problems due Wednesday 10/17: Section 2.6 #3a,b (we wll do one example in class Monday),8 (what is a "vector in (R^3)^* ?); Section 3.1 #5 (use the definition of elementary matrix- not some hand-waving),6 Extra Credit: Section 2.6 #10a
10/19 Reading Assignment #18
Read 152-165 and pages 168-173
10/24 Assignment #19
Suggested Problems: Section 3.2 #1 Section 3.3 #1,Required problems due Wednesday 10/24: ; Section 3.2 #2d,f,4b,5bd,6b 8,14a, Section 3.3 # 2b,2d; Extra credit: Section 3.2 #21
10/24 Reading Assignment #20
Read 174-175; Skip 176-179, Read: 182--189 (this was Monday's lecture)
10/26 Reading Assignment #21
Read page 199; Skim Section 4.2, Read Section 4.4 (the rest of Chapter 4 is optional); REMINDER MIDTERM IS Friday Nov.9 IN CLASS
10/31 Assignment #22
Suggested Problems: Section 3.3 #1, Section 4.1 #1abcd Section 4.3 #1 Required problems due Wednesday 10/31: Section 3.3 # 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) #11,12,13(remember that the determinant will be a complex number in general),15 Section 4.4 #2d,3b,4d
11/9 Reading Assignment #23
Read 245-255; Read: 261-278 Optional: Section 5.3
11/13 Assignment #24
Suggested Problems: Section 5.1 #1 Required problems due Wednesday 11/13: Section 5.1 3bc,4e,8a,12,14,15a; Section 5.2 # 2f,3b,9a
11/28 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.
11/15 Reading Assignment #26
Read 329-347
11/22 Assignment #27
Suggested Problems: Section 6.1 #1 Required problems due Wednesday 11/22 Section 6.1 #2 (but do not verify Cauchy-Schwarz and triangle), 8ac, 10(easy trick), 17(easy); 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 # 12a (Hint: There are 2 inclusions to prove. For one inclusion consider the inner product of Tx with itself)
11/30 Assignment #28
For Sections 6.3 and 6.4, use class notes which were handed out this week rather than the textbook. REMINDER of Fun Extra credit Assignment due Wednesday after Thanksgiving-write up solution and explanation of your solution for 10 extra points on Homework PUZZLE #1. Required problems due FRIDAY 11/30: Section 6.4 #2bd (just determine if it is self-adjoint); Prove that if $A$ is either an orthogonal matrix or a unitary matrix then its eigenvalues have length $1$. Extra Credit:Section 6.2 # 18