HW 1, due F 1/21: Read: P. 1-16. Do: Exercises 1-4 (p.6)

HW 2, Due 1/24. Read up to page 26. Do p9 5-7, p.26 1-4. (For #7, do V_3 only; skip V_4).
 

HW 3 Due 1/26. Page 33 questions 26,28,30, Page 26 Questions 5,6,7.

HW4 due 1/28 Page 26, 8,9,10 (10 is done in the appendix, but try to do it yourself) p33 29,31

HW5 Due 1/31 p 32 12,13,17,21,22 and 34.35 just for fun. You will need to look up the definition of relative complement of A in B.

HW6 due W 2/2: P. 32-34, 15,20,24,36,38

HW 7, due F 2/4: Do the following problems on Scorpling Flugs

There's an error on the solutions to HW 6, Scorpling flugs. 3b-- of course every set is a subset of itself!!

HW 8, due M 2/7: Read 36-38. Do p.38: 1, 2, 4.
 

HW 9, due W 2/9: Read p.39-41. Do: First do the "warm-up" problems listed below. Then do p.41: 6; p.38: 3, 5a. Hint for 5a (don't read this hint until after you've already tried your best to do the problem): Show if  then  . Second hint (try again to do the problem before reading this):  is a subset of  , so it's an element of ... .

HW 10, due F 2/11. Read p.42-44. Do: p.52: 11, 16, 18, 21.

HW 11, due M 2/14: Read p.45-47. Do: p.53: 19, 22ab, 23.

Midterm 1, W 2/16: Will cover HWs 1-10 and their corresponding sections. You should also know all definitions, as well as the following proofs that are in the book: prove that the sets defined in the definition on p. 44 are sets (inverse, composition, restriction, image); prove that dom R and ran R are sets. prove <x,y> is a set; prove <x,y> = <u,v> iff x=u & y=v; prove the laws and identities on p.28.
 

HW 12, due F 2/18: Read p.48. Do: p.53: 24, 25.

Midterm 1.1, W 2/23: Only one problem, to replace problem #4(b,c) of Midterm 1. Will cover HWs 1-10 and their corresponding sections.

HW 13, due 2/23: Make sure to read the book's formulation of Axiom of Choice on page 49 and try to see how it's related to our formulation given in class (see (4) on page 151). Do: p.53: 26, 29.

HW 14, Due F 2/25. P61: 33, 34 (prove or give a counterexample in each case), 35.

HW 15, Due Monday 2/28. P 61 37,38, and the following question:
Look at Theorem 3M on page 56. Then read the next paragraph.
Also note the definition of a “binary relation on A” on page 42.
Construct a relation R on the natural numbers that is symmetric and transitive on the natural numbers, an equivalence relation on the field of R, but is not an equivalence relation on the natural numbers.

HW 16: Due Wed 3/2. Page 62, 40, page 64, 43, 44.

HW17 Page 64: 45, Page 172: 1,2. Due Friday 3/4

HW 18 Pg 88: 30, 31, 32. Read "What Numbers Could Not Be" for Monday 3/12.

HW 19, due Friday 3/18: Read: p.70-73. Do: p.89: 33c; p.73: 2, 4, 6.
Also do the following problem (it may be better to do it before the above problems):
(i) Give three distinct transitive sets, each of which has exactly four elements.

HW 20, due Monday 3/21: Read p.73-78; may skip proof of Recursion Theorem. Do: p. 89: 38, 40; p. 78: 8. Check HW solutions folder for solutions.

HW 21, due Wednesday 3/23: Read p.79-82. Do: p.83: 13-15. Hints/suggestions: 13: Prove the contrapositive. 14: Prove by induction; use theorems in the book; and prove 1+1=2; 21=2.

HW 22, due F 3/25: Read p.83-85. Do: p.88: 18, 22, 23. Hint for 22 and 23 : Use induction.

HW 23, due M 3/28: Read: p.86-87. Do: 26, 37a. Also, give a detailed proof of Corollary 4Q (p.87).

Midterm 2, W 4/30. The midterm covers HWs 11-22.
 

HW 24, due F 4/1: p.88: Do: 24, 28, 37b. For 37b, just construct the desired bijection; no need to prove it is a bijection. Also, prove the theorem "Well Ordering of " without looking at the proof in the book.

HW25 Due Monday 4/4. Page 101, 4, page 133, 1 and 5. Also, using just the natural numbers (and set theoretic and associated notation), write the natural number 1, the integer 1 and the rational number 1.

HW26 1. a.Show that the open interval of reals, (0,1), is equinumerous to the positive reals, (0,infinity). Can you find a map that takes rationals to rationals.

b. Show that the set of all ordered triples <x,y,z> of natural numbers is equinumerous to the set of natural numbers.

c. Show that the set of finite strings from the English alphabet is equinumerous to the set of natural numbers.

P. 138, 6,7. One way to do 7 will involve the well ordering principle. Another way will use the axiom of choice. You get one piece of candy for using the axiom of choice, and two for using the well ordering principle (do it both ways and you get three!), unless your name is "Ramin", in which case you get no candy, but some goat cheese instead!

HW 28 Due Monday 4/11. Read pages 138-144
On Page 141-142 there are a number of facts about cardinal arithmetic. Prove that a) Aleph zero + Aleph zero = Aleph zero, b) 3.aleph zero = aleph zero (. here is cardinal multiplication), and c) That cardinal addition is associative.
Also do p.138, 8 and p.144, 13

HW 31, due M 4/18: Read p. 151, the bottom 6 lines on p.154, all of p.155, and the statement of Theorem 6N. (Zorn's Lemma is optional. Also, recommended but not required: read some of the proofs on p.152.) Do: P. 158: 18, 19, 24(sums only; no products).
 

HW 32, due W 4/20: Read p. 159. Learn the proof of Corollary 6P for the final exam. Do: p.161: 27. Also do these extra problems:
(i) Prove the function g in the proof of Corollary 6P is one-to-one.
(ii) Prove, without using Theorem 6Q, that if A and B are each equinumerous with , then their union is countable.
 

HW 33, due F 4/22: Read p.159, including the proof of Theorem 6Q. Do: p.161: 26, 28, 29.

HW 34, due M 4/25: Read p.162-165 (may skip proof of Lemma 6R). Do: p.165: 32, 34. (Optional: 35.)