Set Theory and Symbolic Logic

Spring 2017

syllabus  (important dates included)                 

 

Text work Problems to do Problems to Collect
1.7 1-3,10,11,12,17,21,23,24 10,24
 end Ch 2 ALL
 Back of Book  Ch 2 sets and proofs: 10,29,34,14,16,31

Ch 2 logic and proofs: 5,16,31,40,66,89,103,114,139,147

Ch 3 3,5,7,11,12

and also… 8,9,15,21 (8 and 21 will be collected)

    1-1 and Onto Problems

IS1: Prove that the function f:ℝ→ℝ given by
the cube root of x is both 1-1 and onto.

IS2: Prove that the function f:ℝ×ℝ→ℝ×ℝ given
by f((x,y))=(x²,4) is neither 1-1 nor onto.

IM1:  Let f:A→B be a function. Let X be a subset of A.
a. Prove X⊆f⁻¹(f(X)).
b. Give an example of f,X,A,B where X≠f⁻¹(f(X)).

Ch 4 All problems fair game 8,11,20,23
Ch 5 from 5.9: 1,4,6,7,10,14,17,18,19,20,23
CM1: Prove that a perfect square cannot be congruent to 3 mod 4.

CM2: Create a theorem that fully describes what a perfect square is congruent to mod 4. Prove it.

Ch 6 6.13: 1,5,6,8,22

end of book: 97,102,135,160

Schedule:  See below for what readings/problems are due each day:

Monday

 Wednesday

Friday

 Jan 30: Feb 1:  Read Sections 1.3-1.5 and do check yourself problems  Feb 3: Read sections 2.1-2.2.3 and write up proof from class on pigeonhole principle
 Feb 6: work on SC1 from handout. Probably due Wed. Work on some problems from end of Ch2. Try some of the problems in the back of the book too!  Feb 8: SC1 due AND read rest of Chapter 2 AND work on some Ch 2 problems and back of book problems  Feb 10:
 Feb 13: nothing due… but be working on the SC problems on the handwritten sheet (due Thursday by noon)- and the problems due Wednesday  Feb 15: Due today: problems

Ch 2: 10,16,18

back of book: 20,66,103,129,190

Due Thur by 1 pm: SCU and SCI

 Feb 17: Work on rewrites and, though not all collected, all the Ch 2 problems – fair game for the test next week
 Feb 20: negation worksheet collected, keep working on problems  Feb 22:  test 1 day Feb 24: reading due 3.1&3.2 and check yourself problems

rewrite of the following proofs deadline: Pigeonhole, SC1, SCU

 Feb 27: rewrite of SCI deadline  Mar 1: skeleton packet due, work on Ch 3 problems  Mar 3: IS1 and IS2 above due
 Spring Break
 Mar 13: Read 3.4-3.7 for today Note: 3.6 is the important section here… I want us to get isomorphisms down- graphs are an easy way to help us understand, but the main focus is on isoms!  Mar 15: worksheet from before spring break due (function problems)  Mar 17: read 4.1 and 4.2 and do check yourself problems

IM1 above due as well as problems 8 and 21 from Ch 3

 Mar 20: skeleton packet and IS1/IS2 deadline

work on the Induction chapter HW

 Mar 22: collect problems 11,20 from Ch 4 as redo problems  Mar 24: Read rest of Ch 4… someone will present/discuss flaw in the every duck is gray proof… work on Ch4 problems
 Mar 27: Ch 4 problems 8,23 due- not for redos Mar 29: deadline for IM problem Mar 31: TEST 2 date
 Apr 3:  for class, read 5.1-5.3

Tuesday: deadline for induction redos

 Apr 5: for class, work on the equiv relation worksheet emailed out

 

Apr 7:

Redo problem ER1 first attempt due today

 

 Apr 10: QUIZ on bookwork Ch 5 and equiv relations in general Apr 12:  collect Equiv Rel worksheet emailed out

 

Easter Break
Easter Break Apr 19: Read 6.1 and 6.2

Presentation due: The Axiom of Choice

start working on CM problems above

Apr 21: first attempt of CM problems due

 

Apr 24:

Essay due: The Axiom of Choice

ER1 redo deadline

Apr 26: work on Ch 6 problems listed above Apr 28:  Test 3 day
May 1:

CM redo deadline

May 3: work on Ch 15 problems May 5: work on Ch 15 problems
May 9: LAST DAY

 

 

 

From an old book… for my reference….

 Reading Questions  

Homework you do… collected…
1.1 1-7(do 3ish parts, you pick), 8  8
1.2 3,4,5,6,8,11a,12a,13c,16b D1,D4
1.3 4,5,10,15,16,17
1.4 5,6,8-11 17,18,20a,D4
2.1 1-4(do at least a couple parts),5,9,12,14,16,20bce,21 D1,14,16
2.2 1-6(do at least a couple parts of each),15,22a,23,26,27 23
2.3 1-7,12,14,16 a or b,17b,18,20,22,26 16,22
3.2 1-4,6-16,20,21
3.1 1,2,3(a couple parts),4ab,6,7,10,12,15-17,18(a couple parts),21,22 10,16, maybe more…
3.3 1,2,7,10 7 (do the part we did not do in class)
4.2 1-10,13,16,18 10a,18
5.2 1-4,10,23,24,39,40,42
6.1 1,4,6acfg,11,16