Math 4433 Homework Assignments
Fall, 2009

Week 1:


Reading:
Wednesday 8/26 Friday 8/28
p. 1-34 (Ch. 1), p. 39-42 (Sec. 2.1), p. 52-55 (Def. 2.1 - Thm. 2.3)Read p. 55-57 (Def. 2.2 - Thm. 2.4), p. 62 (Def. 2.6)
Homework: Chapter 1, Exercises #3, 6, 10, 11, 14
Due date: Friday 8/28
Announcements: Most of Chapter 1 and a bit of Chapter 2 should be familiar from your Discrete Mathematics course. We will only touch on a few of these ideas in class, but you will be responsible for the material in these chapters except for Section 2.3 (the construction of the integers), p. 49-51 (the construction of the rationals), and Section 2.6 (complex numbers).
Homework will usually be due on Wednesdays. The next assignment is due on Wed. 9/2.
Challenge: (Challenge exercises are not required, but are encouraged for those planning to continue on in mathematics!)
Read the Appendix to Chapter 2 and prove the field axioms for the real numbers constructed by Dedekind cuts.

Week 2:


Reading:
Monday 8/31 Wednesday 9/2 Friday 9/4
p. 58-62 (Sec. 2.5) p. 75-78 (Sec. 3.1 up to Rmk. 3.1) 78-81 (to the end of Sec. 3.1, skip Cor. 3.1)
Homework: Chapter 2, # 2, 4, 21 (parts 4 and 5 of Theorem 2.3 only), 22 (part 2 of Theorem 2.4 only), 23, 34 (prove the triangle inequality from Definition 2.6), 36
Due date: Wednesday 9/2
Announcements: *** You do NOT have to do #33 in the homework. Sorry for the typo! It is the challenge exercise.
Challenge: Prove Ch.2, #33. Hint: By density here, we mean given any a,b in [0, λ] with a< b, show that there is some n such that a<φ(n)< b.

Week 3:


Reading:
Wednesday 9/9 Friday 9/11
none p. 81-2 (up to Thm. 3.2)
Homework: Chapter 3, # 4, 5, 24, and complete the problems on this handout. Also, check out the Math blog   and leave a comment on at least one post.
Due date: Wednesday 9/9
Announcements: No class on Monday, 9/7, due to the Labor Day Holiday. Have a nice weekend, everyone!
Challenge:

Week 4:


Reading:
Monday 9/14 Wednesday 9/16 Friday 9/18
p.82-84 (up to Ex. 3.4, skip Cor. 3.3) p.84-5 (to the end of Sec. 3.2) p. 85-88 (end of Prop. 3.7)
Homework: Chapter 3, # 23, 25, 27 and complete the problems on this handout.
Due date: extended until Thursday 9/17 at 5pm
Announcements: The first midterm exam will be on Wednesday September 23. The sections covered on the exam will be announced in class, but there will certainly be definitions and statements of theorems asked of you.
Challenge:

Week 5:


Reading:
Monday 9/21 Wednesday 9/23 Friday 9/25
none none p. 88-91 (Sec. 3.4)
Homework: Chapter 3, # 1(just the summation property for both limsup and liminf), 8 (This is Example 3.5, just do the first 3 examples), 12 (This is Proposition 3.8), 18, 19, 20
Due date: Friday 9/25
Announcements: The first midterm exam will be on Wednesday September 23. It will cover sections 2.1-2.5, 3.1-3.3 and anything covered in lecture which is not in the book.
The homework is extended until Friday, but it covers topics on the exam, so you should work on it early.
Challenge:



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