Math 240  Fall, '98
Introduction to Mathematical Thought 
Assignments

Back to Martin Flashman's Home Page :)

Last updated: 9/4/98 under construction.

TEXTS: Mathematical Thinking: Problem-Solving and Proofs by J. D'Angelo and D. West (Prentice Hall, 1997)
How to Solve It,  by G. Polya (Princeton U, ?)
Set Theory and related topics by S. Lipshutz ( Schaum/ Mcgraw Hill,1964)

Assignments - (subject to change) 8-18-98
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 8/24 
Topic: Introduction and  general remarks. 		 8/26 
Read :Polya 
D&W 
SOS 
Problems:  Proof w/o Words #1.		 8/28  Topic: Sets and set operations. 
Read: Finish Polya (all but dictionary) 
D&W Preface. 
ch 1 Sets p7-10. 
SOS: ch 1, Solved problems 1-19 
ch 2, Solved problems 1-15 
Problems:  D&W 1.7,1.10,1.15 
SOS: ch1: 41-45
 2 8/31 
Topic: Sets and set operations. 
Read:D&W ch.1 (remainder) 
ch 5 p.66 & bottom of 70. 
Problems:  D&W 1.16, 1.25, 
SOS: ch 2: 31,33, 38 		 9/2 Topic: More on sets.What is a proof? 
Read :  Polya: Definition 
D&W: p 17-21 
SOS: ch 5 probs 1-5, 7 
Problems:  Proof w/o Words #2.
SOS: ch 5. 21-24, 27		 9/4Read :Polya: Notation 
D&W:Sections 2.19-2.23 
Problems: 
D&W: 2.2-2.4, 2.8, 2.13
3 9/7 
No Class: LABOR DAY		 9 
Read :  Polya: Reductio ad absurdum and indirect proof. 
D&W: 2.27-2.28,2.30 
SOS : ch 2 prob 22,23,26 
Problems:Proof w/o Words #3.
SOS:  ch 2: 45 
D&W: 2.6, 2.7, 2.15,2.25		 11 
Read : 
Polya:Problems to find...prove 
D&W:2.29, 2.24-2.26 
SOS: ch.5 prob 6,8 
Problems: 
SOS: ch 5: 25, 28(prove) 
D&W: 2.27, 2.28
4 14Read : 
Polya: Decomposing and recombining. 
D&W:  Reread pp 11-12, 2.8-2.12 
SOS ch 3: pp 30-34,prob 8,9,22,24 
Problems: 
SOS: ch 3.:32,40,46 
D&W:2.10,2.11		 16 Read : 
Polya: Can you check the result? Can you derive the result differently? 
D&W:2.13-2.18 
SOS: ch14 pp 187-189, 191m-192m, probs1-4 
Problems:Proof Evaluation #1
SOS: ch14: 25, 26(odd), 27, 31		 18Read 
D&W:216-2.19 
SOS : ch 14 pp192-194 Probs  10-12 
Problems: 
SOS: ch 14: 33 
D&W: 2.21
5 21 Read: 
Polya:Signs of progress 
SOS: ch 4 pp 45-48 prob 1-7,12,13 
D&W: ch3  3.1-3.6, 3.12,3.13, 3.26-3.29 
Problems: 
SOS:ch 4: 45-51 
D&W: 3.2,3.3		 23 Read: 
Polya:Working Backwards 
SOS: ch 4: p 46-51 problems 14-20, 28-30 
D&W:3.40,3.41,3.44-3.45 
Problems: 
SOS: ch 4:59, 60, 65-67. 
D&W:3.9 
Proof Evaluation #2
Proof w/o Words #4. 		 25Read: 
Polya: "The inteliigent problem solver" and "The intelligent reader." 
SOS:ch 4: p47-51 probs 22-26,33-34 
D&W:3.46,3.47, 3.50 
Problems: 
SOS:ch4: 68,69,74 
D&W:3.22,3.25
6 28Read: 
SOS: ch4 : probs 8-11,37-39 
D&W: 3.26-3.31 
Do: SOS ch 4:52,53,54,57 
D&W:3.7(a,b),3.26		 30Read: 
SOS: ch 4 Probs 40-42 
D&W: 3.19-3.25, 3.30,3.31-3.34, 3.46-3.49, 3.51 
Do:SOS ch4:71,72,75 
D&W: 3.24, 3.27(a,b) 
Proof Evaluation #3
Proof w/o Words #5.		 10/2Read: 
SOS: ch 5 p67-68 
problems 10-3,16,19,20 
D&W: 3.12, 3.27 
DO: SOS:ch 5 29-31, 36 
D&W: 3.19, 3.27(c,d) 
7 10/5Read:: 
D&W:3.46-3.51 
Do: 
D&W:3.28,3.29,3.32		 10/7Read 
D&W: 3.46-3.51(again) 
Do: D&W:3.28,3.29,3.32(again) 
Proof Evaluation #4
Proof w/o Words #6.		 10/9 
Read: SOS:ch9: p134-135 prob 1,2 
ch 7 p106 prob 6-8
8  10/12 Read: SOS:ch9: p134-135 prob 1,2 
ch 7 p106 prob 6-8 
DO: SOS ch 7: 21-23 
ch 9: 21		 14 
Proof Evaluation #5 
Proof w/o Words #7.
Examination #1 between class10/14 to 10/16		 16 
9 19Read: 
SOS: ch 9:p135-136 prob 4,6,8, 10(method 1) 
ch 6: p81-86 prob 1-4,6,12,15,17,19,20,29-31
DO: SOS ch 9: 23, 24
ch6: 41,43,44,49 (omit c),55(omit c)		 21Read: D&W: 6.1,6.4,7.4-7.10
SOS:Repeat-ch 6: p81-86 prob 13, 18, 21,23,25,32,38
DO: SOS:ch 6: 42,50(1-5),53,63,64
D&W: 7.2, 7.5
Proof Evaluation #6 
Proof w/o Words #8.		 23Read 
D&W:p94 top-6.4
Repeat 7.4-7.10; 8.4
SOS: ch 9 prob 4
ch 7 p107-8 prob 12,14
DO: SOS: ch 7: 26, 28
D&W:7.1
10 26Read D&W: 7:11,7.13,7.14
SOS:ch 8: 120-122, prob 15,16
Do: D&W:7.7
SOS:ch 8: 42,43		 28Read D&W: 7.11,7.13-7.19
SOS:ch 7 prob 13
ch 8 prob 19-23, 25
DO: SOS: ch 8: 39
Proof Evaluation #7		 30Read D&W:7.12
DO:D&W:7.14
SOS:ch 8:44-46
11 11/2Read 
SOS: ch 8 p116 prob 1,2
DO:D&W: 6.1,6.2, 6.13
SOS ch 8: 26, 27		 11/4Read D&W: 6.4-6.6,6.7 (don't read the proof), 6.9, 6.13, 6.18
Do:6.26
Proof Evaluation #8		 11/6 Read:D&W p115
SOS ch 8 p118 prob 6,7,11
12 Examination #2
between class 11/11 to 11/13		 9 Read: D&W: 5.10-5.14, 5.19
SOS: ch 9 p137 prob 11,12
DO: D&W: 6.5,6.12
SOS ch 8: 30		 11Read D&W: 6.10-6.12
DO D&W:6.31(a,b)
Proof Evaluation #9		 13No assignment- exam#2
13 16Read D&W: 5.10-5.14, 5.19,5.20(?)
4.5-4.7
SOS: ch 9 p137-140 prob 14,15,17
28(solutions)
Do: D&W:5.8, 5.11, 5.18, 4.7		 18Read D&W: 3.35-3,37; 4.5-4.13
Do: D&W: 4.7, 4.5, 4.8, 4.15
Proof Evaluation #10		 20 No class
14 Fall Break 23No class 25No class 27No class
15Final Part I distributed 12/4- due 12/18. 30 READ D&W: 4.14-4.17, 4.20,4.22-4.25; 5.21-5.28
DO: D&W: 4.1-4.3,, 4.9, 4.10,4.24, 4.29, 4.33; 5.19,5.20		 12/2READ Polya:p114-121 induction
D&W: 4.18, 4.19;5.21-5.28

Proof Evaluation  #11

 12/4 Read: D&W:5.28-5.33
DO: D&W:5.26, 5.27
Distribute Final I
16 
Last week of classes		 12/7Read:
D&W: 11.1,11.5-11.13
DO: Induction Handout setups.		 9Read:
D&W: 4.9, 10.1-10.3, p163 middle-164.
DO: D&W: 10.2-10.4, 10.6, finish inductions (m-o)		 11

Back to Martin Flashman's Home Page :)