Math 240 Spring , '99
Introduction to Mathematical Thought 
Assignments

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TEXTS:  The Keys to Advanced Mathematics : Recurrent Themes in Abstract Reasoning by Daniel Solow ( Paperback,  Books Unlimited,1995 )
How to Solve It,  by G. Polya (Princeton U, ?)
Set Theory and related topics, 2nd Edition, by S. Lipshutz ( Schaum/ Mcgraw Hill,1998)

Assignments - (subject to change)
Problems are due on the class day for which they are listed.
Show all work and explain your reasoning (especially for SOS problems) 
Late homework is not accepted after 5 pm of the due day.
Week Monday Wednesday Friday
1 1/18 No Class: MLK DAY 1/20 Topic: Introduction and  general remarks.  1/22 Read :Polya Part I 
DS:1.1 
Problems:DS 1.1,3,5
 2 1/25Topic: Sets and set operations. 
Read: Finish Polya (all but dictionary) 
DS:1.2,1.3; 3.1-3.1.2 
SOS: ch 1, Solved problems 1-19 
ch 2, Solved problems 1-15 
Do: DS:1.7,1.9-1.14 
SOS: ch1: 41-45 		 1/27 Topic: Sets and set inclusion. Begin conditional statements. 
Read: DS:1.4,1.5 
Do: SOS: ch 2: 31,33, 38 		 1/29Topic: More on sets.What is a proof? 
Read : DS:1.6-(?) 
SOS: 
Do:
SOS: 
Proof w/o Words #1. 
3 2/1Read :Polya: Notation 
Polya: Definition 
Polya: Reductio ad absurdum and indirect proof. 
DS:1.6-1.6.2 

Do: DS:1.15,1.17,1.18,1.21-3;3.3.4 1.25,1.27 
SOS: Ch. 1: 45,56 

 2/3 Truth Tables 
Read : SOS: 10.1-10.4;10.8 
DS: 1.6-1.6.2; 1.6.4 
SOS Probs: 10.1-10.4 
Do: Proof Evaluation #1 		 2/5 
Read : 
 

SOS: 10.22-10.24 
DS: 1.27 (read sol'n), 1.28, 1.35 
Do: Proof w/o Words #2.

4 8 
Read : Polya:Problems to find...prove 
Decomposing and recombining. 
SOS:10.5,10.6,10.8,10.9, 10.10 
Problems: 10.5, 10.6, 10.12- 10.16 
Do: SOS: 10.25,10.26, 10.28 		 10 Read : Polya: Can you check the result? Can you derive the result differently? 
DS: 1.6.3,1.6.4;3.1.4(cartesian Product) 
SOS: 10.11; 3.1,3.2 
Solved Problems SOS: 3.1-3.3;10.17,10.18 
Do:SOS: 3.34,3.35,3.38,3.39; 
Proof Evaluation #2		 12Read 
SOS : 
Problems: Proof w/o Words #3. 
DO: SOS: 10.29 (a,b),10.32 
DS: 3.7 a,3.8a, 
5 15 Read: 
Polya:Signs of progress 
SOS: 2.1-2.5 (review on real numbers) 
problems 2.17-2.22 
DS: 1.6.3,1.6.4 (again!) 
Problems: 
SOS: 2.51, 2.64,2.66,2.67,2.71 
DW: 1.29, 1.30, 1.32,1.35		 17 Read: 
Polya:Working Backwards 
SOS: 1.9, 5.2,5.3 
solved prob 1.13,1.27, 1.28; 5.1,5.2 
D.S:1.67 
Problems: 
SOS:  1.51 (a,c), 1.64,1.65; 5.28 
Proof Evaluation #3
D.S.:1.36, 1.37		 19Read: 
Polya: "The intelligent problem solver" and "The intelligent reader." 
SOS: p41 "divisibility" Ex.2.7 
DS: 1.6.8, 1.6.9 
Problems: Proof w/o Words #4. 
DS:1.45-1.48
6 22Read: 
SOS: 4.1,4.2 (94-95 mid) 
solved probs:4.1,4.3,4.4, 4.6,4.8 
DS: 3.2.1 
Do: SOS :4.31, 4.32,4.35		 24Read: 
SOS: 4.3,4.4 
solved Probs: 4.11,4.12,4.14 
DS:3.2.3 
Do: Prove (i) C is a subset of  f -1(f(C)). 
(ii) f ( f -1(D)) is a subset of D 
Proof Evaluation #4		 26Read: 
SOS:  4.3,4.4 
solved Probs: 4.11,4.12,4.14,4.17,4.18(a,b), 4.21 
DS:3.2.3 
DO: 
Proof w/o Words #5. 
SOS:4.39,4.40, 4.41, 4.43(a,b)
7 3/1 Read: 
DS:3.2.3; 1.6.10(negation), 1.6.12(uniqueness) 
Do: SOS:4.48 (a,b) 
DS:3.25, 3.26		 3/3Read SOS: 4.4, 5,8; 5.3 through Ex.5.2 
solved probs:4.19, 4.20, 4.23;.5.13,5.14; 5.2, 5.3 
Do: Proof Evaluation #5 
SOS:4.45, 4.48 5.39,5.40; 5.30,5.31		 3/5 Read: SOS: 1.9; sp 1.29 
DS:1.6.10, 1.6.12 
DO:Proof w/o Words #6. 
DS: 1.43,.1.44, 1.50 
SOS:1.66,1.67
8 Exam #1 8 Read: DS:2.2.1 
DO: DS:2.7,2.8,2.9,2.10		 10 Read 
SOS 3.3, 3.4; 3.8 
solved probs 3.7(a,b), 3.16, 3.17 
DS: pages 118-121 
 Do: SOS: 3.55		 12 . Read 
SOS: 3.6 
solved probs 3.6(a,b),3.7(a,b) 
DO: 3.41(a,b),3.45(a,d), 3.46(a-c)
9Spring Break 15 No class. 17 No class. 19 No class.
10 22 Equivalence relations 

SOS: 
Do: 
SOS:

 24 Equivalence relations and Partitions: Integer Congruence 
Read 
SOS: 3.9 
Solved probs 3.22, 3.23, 3.26 
DS: pages121-123, 5.1.3 
DO: SOS: 3.59a, 360a 
DS: 5.2 
Proof Evaluation #6		 26 Proof w/o Words #7.
cardinal equivalence 
Read 
SOS:solved probs:3.24,3.25,3.27, 
DO: 
SOS:3.58, 3.59b, 3.60b
11 29More on congruence classes 
Countable and uncountable sets. 
Read SOS:1.8,6.1, 6.2, 6.3 
solved probs: 1.21-1.23,6.1, 6.2, 6.4 
DS:6.2.4 (this should cover several classes) 
DO: 
SOS:1.59-1.61, 6.31		 31Arithmetic and congruence I 
Read: SOS:6.3, 6.4 
solved probs:6.3,6.4, 
6.15 Method 1 
Do:DS:6.11 
SOS:6.33 
Proof Evaluation #7		 4/2 Read: 
SOS:6.3,6.4,6.5 
solved probs: 6.10,6.11 
Do:
12  4/5 Read: 

DO: 
SOS 

 4/7Read SOS: 6.5,2.7(start w/ Theorem 2.8 thru example 2.8) 
solved probs: 2.34,2.38 
DO :2.78,2.82		 4/9Read DS:5.1.1;5.1.2; 5.1.4 
SOS: Theorems 2.10 and 2.11 
solved probs:2.39-2.41,2.45 
Do:DS:5.1 
SOS:2.83,2.90
13Exam #2  12Read 
SOS: 2.8,2.9 
solved probs: 2.35,2.37,2.40,2.46 
Do: 2.79,2.80, 2.87		 14Review for Exam #2 
Proof Evaluation #8		 16 
14  19Read: 
DS: 1.6.5 (Induction) 
SOS:1.11 
Solved probs:1.34-1.36;2.29;2.36 
Do: SOS:1.73-1.75 
DS:1.33(b); 1.34(b)		 21Read: 
ch 8: 120-122, 
solved probs 15,16, 19-23, 25 
DO SOS:ch 8: 42,43, 39 		 23 Read DS: 5.2.1 
15Final Part I distributed  26 READ 
DS:p311-312(Symmetry Groups) 
handout on Pigeons&Counting 
DO: handout:10.1,10.2 		 28 READHandout on Pidgeon Hole Principle 
Do:DS:5.15, 5.16 		 30 Read: 
DO: Proof Evaluation  #9
Problems on Induction
Distribute Final I
16 
Last week of classes		 5/3Read: Handout on graphs, combinations.
DO: 4 induction problems on sheet		 5Read: SOS:2.1, Thrm 2.11 Polya:p114-121 induction 

DO:

 7
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