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
(McGraw-Hill,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 |
1-17 Topic: Introduction and general remarks. |
1-19 Continue work on Class Problem #1
(Moodle) Optional on-line Exercises 1 Click here Start work on PS#1-Problems: SOL 1.1,3,4,5 |
| 2. HOU:Ch.1 and 3 SOL:1.2,1.3; 3.1-3.1.2 SOL: 1.4,1.5 Polya: Notation Polya: Definition Another Polya Summary Set Operations Optional on-line Exercises 2 Click here Properties of Set Operation Optional Exercises 3 Click here |
1-24 Topic: Sets and set operations. Topic: Sets and set inclusion. Begin conditional statements. PS#1-Problems: SOL 1.1,3,4,5 |
1-26 Topic: More on sets.What is a proof? Read : Do: Proof w/o Words #1. Do: PS#2.SOL:1.7,1.9-1.14 |
| 3. HOU: Ch. 4 and 5 SOL:1.6-1.6.2; 3.1.1- 3.1.4; 1.6.4 ; Problem1.27 sol'n |
1-31 Conditional Statements and Truth
Connected to Set Definitions of Union and Intersection. |
2-2 Truth Tables,and Universal Quantifiers Due: PS #3. SOL:1.15,1.17,1.18,1.21;3.1-3.4 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 |
2-7 Conditional, Existential,
and Universal Statements. Forward and Backwards.
[Starting and Finishing] The importance of definitions. |
2-9 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) |
2-14 Proofs about sets. Applications of definitions and direct arguments for conditional statements and universal quantifiers. Definition: Cartesian product of Sets. | 2-16 Due: PS #5 SOL: 1.29, 1.30, 1.32; 3.9, 3.11, 3.12 plus (PSO): Write proofs in English (no logic symbols-only set theory notation) for #7 |
| 6. HOU: Ch 16, 17, 18 SOL: 3.1.4, 1.6.7 (again); SOS:1.1-1.7 Problem 1.12 |
2-21 Definitions and Proof
examples- sets, integers, rational numbers. Due: PS#6 SOL: 3.7, 3.8 |
2-23 Proof Evaluation #2 |
| Below this line is not yet assigned! | ||
| SOL: 1.6.8, 1.6.9 | 2-21 Read: DS: 1.6.8, 1.6.9, 1.6.10 PS #8 DS: 1.36, 1.37, 1.43 Read: DS: 3.2.1 |
9-27 Read: DS: 3.2.1 Polya:Working Backwards ; Reductio... [on Moodle] Proof w/o Words #3. PS #9 : 3.13,3.17 (a,b) |
| 7 |
2-28 Read 2.1.1,1.6.10(negation) Quiz #1 on -line Moodle |
10-4 :3.2.3 Read: 3.2.3, 1.6.10 Polya: Problems to find...prove [on Moodle] PS #10:DS:1.45-1.48 Proof Evaluation #3 |
| 8 Exam #1: TBA Covers work
through TBA |
3-7 Read:3.1.3; 3.2.3, pp
161-166 Quiz # 2 on-line Moodle |
10-11 Read:1.6.12(uniqueness) PS#11- [Download .pdf] Proof w/o Words #4. |
| Spring Break |
3-14 | |
| 9 |
3-21 Read DS: 1.6.12; 3.2.2 plus pp 166-171 PS #12. 3.25, 3.26 |
10-18 Read DS: 1.6.12 Much about functions. Optional On-line Exercises (1-5 only) PS#13- [Download .pdf] Proof Evaluation #4 |
| 10 |
3-28 Read: DS:2.2.1 PS #14. DS:2.7(a,b),2.8,(a,b)2.9,2.10 |
3-30 Read DS:2.3.1 plus pp 117-123. Quiz #3 on-line Moodle (by Monday!) Proof w/o Words #5. |
| 11 |
4-3 Read DS: 1.5.1; :2.3.1 plus pp 117-123. (again) PS#15-Partitions [Download .pdf] On-line reading on relations, digraphs, and equivalence relations.
|
4-5 Read: Notes on Equivalence Relation Example(.pdf). DS: 1.6.11 plus pp 117-123. (again) Continue readings on equivalence relations. Proof Evaluation #5 |
| 12 |
4-10 Countable and
uncountable sets. Cardinality Reading (on line) DistributePartnership assignment |
4-12 The Real Numbers: Uncountable and countably infinite sets. Onto Functions and cardinal equivalence. |
| 13 Exam #2 Self-scheduled Wednesday |
4-17 Partnership assignment due by 5 pm. Basic counting for Finite Sets. Applications of Counting: Permutations, Combinations, Counting the Power Sets, Binomial Theorem |
4-19 Proof w/o Words #6 On line reading: The Fundamental Counting Principle Permutations Combinations A proof of the binomial theorem DS: Read 1.5.1 pp26-28 Optional:Introduction to Trees The Division algorithm Proof in Geometry by Fetisov pp 7-44.
|
| 15Final Part I distributed | 4-24 DS: pages121-123, 5.1.3 Integer Congruence Arithmetic and congruence PS#16-Counting [Download .pdf] Read DS:5.1.1;5.1.2; 5.1.4 Rings- Zn, and ring homomorphisms: pi: Z -> Zn. Start Induction |
4-26 Read: DS: 1.6.5; 5.3.1 More on Induction- Well Ordering The Tower of Hanoi, Pidgeon Hole Principle: I.[cut-the-knot] and II [wikipedia] PS #17 DS:1.33(b); 1.34; 5.2 Proof Evaluation #6 Distribute Final I |
| 16 Last week of classes |
5-1 |
5-3 |
| , 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 |
|
| Polya:Signs of progress | DS:6.11 |
|
| More on congruence classes Read DS:6.2.4 (this should cover several classes) DO: |
10-25 Read: Do: Proof Evaluation #7 |
|
| Do:DS:5.1 |
||
| Read DS: 5.2.1 |
||
| READ DS:p311-312(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: |
|