TEXTS: [SOL] The
Keys to Advanced Mathematics : Recurrent Themes in Abstract
Reasoning by Daniel Solow ( Paperback, BOOKMASTERS,1995
)ISBN:9780964451902
[FET] Proof in Geometry by A. I. Fetisov
(Dover).ISBN:9780486453545
[HOU] How to Think Like a Mathematician by Kevin Houston
(Cambridge University Press, 2009) ISBN:9780521719780
[SOS] Set Theory & Related Topics by Seymour Lipschutz
(McGrawHill,1998) ISBN:9780070381599
Week (Topics and readings) 
Tuesday  Thursday  

1 Introduction/ Reading Math /Start Sets SOL:1.1 HOU: Ch. 2 Polya: Summary on Problem Solving Introduction to Set Theory Representation of Set Equality, Subset, Etc 
117 Topic: Introduction and general remarks. 
119 Continue work on Class Problem #1
(Moodle) Optional online Exercises 1 Click here Start work on PS#1Problems: SOL 1.1,3,4,5 

2. HOU:Ch.1 and 3 SOL:1.2,1.3; 3.13.1.2 SOL: 1.4,1.5 Polya: Notation Polya: Definition Another Polya Summary Set Operations Optional online Exercises 2 Click here Properties of Set Operation Optional Exercises 3 Click here 
124 Topic: Sets and set operations. Topic: Sets and set inclusion. Begin conditional statements. PS#1Problems: SOL 1.1,3,4,5 
126 Topic: More on sets.What is a proof? Read : Do: Proof w/o Words #1. Do: PS#2.SOL:1.7,1.91.14 

3. HOU: Ch. 4 and 5 SOL:1.61.6.2; 3.1.1 3.1.4; 1.6.4 ; Problem1.27 sol'n 
131 Conditional Statements and Truth
Connected to Set Definitions of Union and Intersection. 
22 Truth Tables,and Universal Quantifiers Due: PS #3. SOL:1.15,1.17,1.18,1.21;3.13.4 Proof Evaluation #1 

4. HOU: Ch 6 and 7 [Note:
Be ware of TRUTH TABLES!] SOL 3.1 [Cont'd., Esp'ly 3.1.4(Cartesian Product) ],1.6.3, 1.6.4 
27 Conditional, Existential,
and Universal Statements. Forward and Backwards.
[Starting and Finishing] The importance of definitions. 
29 Due:PS #4. SOL: 1.25, 1.28,1.35 :Proof w/o Words #2 

5. HOU: Ch.8, 10, 12, 14,
15 SOL:1.6.7; SOL 3.1 [Cont'd., Esp'ly 3.1.4(Cartesian Product) ] Properties of Set Operation (PSO) 
214 Proofs about sets. Applications of definitions and direct arguments for conditional statements and universal quantifiers. Definition: Cartesian product of Sets.  216 Due: PS #5 SOL: 1.29, 1.30, 1.32; 3.9, 3.11, 3.12 plus (PSO): Write proofs in English (no logic symbolsonly set theory notation) for #7 

6. HOU: Ch 16, 17, 18 SOL: 3.1.4, 1.6.7 (again); SOS:1.11.7 Problem 1.12 
221 Definitions and Proof examples sets,
integers, rational numbers. Due: PS#6 SOL: 3.7, 3.8 
223 Complications with quantifiers. Proof Evaluation #2 

7 Indirect arguments,
Functions HOU: Reread Ch 1 (esp'lly pp 10,11) SOL: 1.6.8, 1.6.9 , 1.6.10; 3.2.1, 3.2.2 FET: Articles 121(pp. 128) [review with focus on geometry] Polya:Working Backwards ; Reductio... [on Moodle] 
228 Contrapositive. Reductio... Finite vs. infinite sets. Rational vs irrational real numbers. real vs nonreal complex numbers. Empty vs nonempty sets. Start Indirect Arguments. Due: PS #7 SOL: 1.36, 1.37, 1.43 
31 Contrapositive.
Reductio... When is something "Well defined"? Operations and Functions. Quiz #1 on line Moodle Due: PS #8 SOL : 3.13, 3.17 (b,d) [Changed 228] Proof w/o Words #3. 

8. Exam #1:
self scheduled: Wed. 37 Covers work through 31
Sign up on MOODLE. Functions! HOU: Ch 30 SOL:3.1.3, 3.2.3 pp 161166, 1.6.10 Polya: Problems to find...prove [on Moodle] 
36 Functions, Operations, and proofs! Due: PS #9: SOL:1.43 1.47 
38 Proof Evaluation #3  
Spring
Break: Start work on week 9 / Catch up on previous
reading! 
313  315 

9. HOU: Ch 11, 20, 23, 26 (some review), 30 (again!) Optional:Ch 28 SOL 1.6.12(uniqueness), 3.2.2 plus pp 166171 Optional: 5.1.1 SOS: 4.14.4 Exercises 4.14.3,4.8, 4.18 Much about functions. 
320 Due: PS 10 SOL: 3.14, 3.19, 3.25; [Ignoreassignment error HOU: Exercises 3.8 (ii, v, xii) 3102012] Optional :Much about functions Online Exercises (15 only) 
322 Proof
w/o Words #4. 

10 HOU: Ch 21, 27, 30 (again!) SOL:2.2.1; 3.2, 5.1.2, 6.24 
328 PS#11 [Download .pdf] plus SOL: 2.7(a,b),2.8,(a,b), 2.9, 2.10 Quiz # 2 online Moodle Due Wed. 
330 PS#12 [Download .pdf] Proof Evaluation #4 

11 Polya: Signs of progress
(on Moodle) SOL: 1.5.1; 1.6.11; 2.3.1 plus pp 117123. HOU: Ch 31 SOS: 3.3, 3.4, 3.6, 3.8, 3.9 Solved problem: 3.22 Online reading on relations, digraphs, and equivalence relations. 
43
PS #13 Online Exercises 1,2,5,6 
45 PS#14Partitions [Download .pdf] Proof w/o Words #5. 

12 SOL:6.2.4; 1.6.5,
pp9496 HOU: p6, pp224227 On a Property of the Class of all Real Algebraic Numbers. by G. Cantor (on Moodle) Pidgeon Hole Principle: I.[cuttheknot] and II [wikipedia] 
410 Continue Discussion of
Partitions and Relations Countable and uncountable sets. Distribute Partnership assignment 
412 Quiz #3 online Moodle
on functions, relations and partitions (by Monday!) The Real Numbers: Uncountable and countably infinite sets. Onto Functions and cardinal equivalence. 

13 Exam #2 Selfscheduled Wednesday 418. Sign up on Moodle. HOU Ch 28 esp.pp200303 SOL:5.1.4 The Tower of Hanoi, Cardinality Reading (on line) 
417Partnership assignment
due by 5 pm. Uniqueness in the FT of Arithmetic. Basic counting for Finite Sets. Applications of Counting: 
419 Proof w/o Words #6 Counting continued. Permutations, Combinations Start Discussion of uncountable infinite sets 

14 Final Part I distributed
on Thursday SOL: 1.5.1 pp2628; 1.6.5; 5.1.3 ; 5.3.1 HOU: Ch. 24; pp 224227 On line reading: The Fundamental Counting Principle Permutations Combinations A proof of the binomial theorem 
424 More Tower of Hanoi: Start Induction as a proof method. Counting the Power Sets, Binomial Theorem Integer Congruence Arithmetic and congruence Rings Zn, and ring homomorphisms: pi: Z > Zn. 
426 PS#15Counting
[Download .pdf] More on Induction Well Ordering Distribute Final I part I 

Below this line is not yet assigned!  
FET pp 2844. 
Proof Evaluation #5


15 Last week of classes 
51 
53PS #17
SOL:1.33(b); 1.34; 5.2 Proof Evaluation #6 

16 Final Examination Self
scheduled Review Session: Sunday 56 TBA 
58
FOR 107: 15001700 510 ARTA_027 08001000 511 FH 177: 10201220 FOR 107: 15001700 

, 1.50 Do: DS:3.25, 3.26 Problems: DS:3.2.3 DO: 
DS:1.6.10, 1.6.12 . DS: 1.43,.1.44, 1.50 


DS:6.11 

More on congruence classes Read DS:6.2.4 (this should cover several classes) DO: 
1025 Read: Do: Proof Evaluation #7 

Do:DS:5.1 

Read DS: 5.2.1 

READ DS:p311312(Symmetry Groups) handout on Pigeons&Counting DO: handout:10.1,10.2 
READ Handout on Do:DS:5.15, 5.16 Read: DO: Proof Evaluation #9 Problems on Induction Distribute Final I 

Read: Handout on graphs, combinations. DO: 4 induction problems on sheet 
Read:
DO: 