TEXTS: The Keys to Advanced Mathematics : Recurrent Themes
in Abstract Reasoning by Daniel Solow ( Paperback, Books
Unlimited,1995
)
Proof in Geometry by A. I. Fetisov (Out of Print- Bookstore Reprint, D. C. Heath, Boston, 1963).
| Week | Monday | Wednesday | Friday |
|---|---|---|---|
| 1 | 8-21 Topic: Introduction and general remarks. |
8-23 Read :Polya: Summary on Problem Solving DS:1.1 Optional on-line exercises 1 PS#1.Problems:DS 1.1,3,4,5 |
8-25 Topic: Sets and set operations. Read: Another Polya Summary Optional on-line exercises 2 DS:1.2,1.3; 3.1-3.1.2 Do: PS#2.DS:1.7,1.9-1.14 |
| 2. |
8-28 Topic: Sets and set inclusion. Begin conditional statements. Properties of Set Operation Read: DS:1.4,1.5 |
8-30 Topic: More on sets.What is a proof? Read : DS:1.6-1.6.2; 3.1.3, 3.1.4 |
9-1 Read : Polya: Notation [new] Polya: Definition [new] DS:1.6-1.6.2 Do:Proof w/o Words #1. Do: PS #3. DS:1.15,1.17,1.18,1.21,1.22;3.1-3.4 |
| 3 | 9-4 Labor Day NO CLASS. |
9-6 Truth Tables, Conditional statements and Universal Quantifiers Connected to Set definitions of Inclusion and Equality. Read : DS: 1.6-1.6.2; 1.6.4 |
9-8 Read DS: Problem1.27 sol'n, Read : DS: 1.6-1.6.2; 1.6.4 Do: PS #4. DS: 1.25,1.27, 1.28,1.35 Do: Proof Evaluation #1 |
| 4 |
9-11 Read : Properties of Set Operation (PSO) DS:3.1 |
9-13 Read : DS: 1.6.3, 1.6.4 Do:PS #5 DS: 3.9,3.11, 3.12 plus (PSO): Write proofs in English (no logic symbols-only set theory notation) for #7 . [Changed sept. 11] |
9-15 "The Proof" Write 4 questions based on "the proof.". |
| 5 | 9-18 Read: DS: 1.6.3,1.6.4 (again!) 3.1.4(cartesian Product) DO:Proof w/o Words #2 |
9-20 Read: D.S:1.6.7 Problems: PS #6 DS: 1.29, 1.30, 1.32 |
9-22Read: DS: 1.6.8, 1.6.9 PS#7 DS: 3.7 a, 3.8a Proof Evaluation #2 |
| 6 | 9-25 Read: DS: 1.6.8, 1.6.9, 1.6.10 PS #8 DS: 1.36, 1.37, 1.43 |
9-27 Read:
DS: 3.2.1 Resubmit 3.12 and (PSO) #7 : Write proofs in English (no logic symbols-only set theory notation). also 1.32 |
9- 29Read:
DS: 3.2.1 Polya:Working Backwards ; Reductio... [on Moodle] Proof w/o Words #3. PS #9 : 3.13,3.17 (a,b) |
| 7 |
10-2 Read 2.1.1,1.6.10(negation) Quiz #1 on -line Moodle |
10-4 :3.2.3 |
10-6 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: Thursday 10-12. Covers work through PS #11. |
10-9
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] |
10-13 Proof w/o Words #4. |
| 9 |
10 -16 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] |
10-20 Proof Evaluation #4 |
| 10 |
10-23 Read: DS:2.2.1 PS #14. DS:2.7(a,b),2.8,(a,b)2.9,2.10 |
10-25 |
10-27 Read DS:2.3.1 plus pp 117-123. Quiz #3 on-line Moodle (by Monday!) Proof w/o Words #5. |
| 11 |
10-30 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.
|
11-1 Read: Notes on Equivalence Relation Example(.pdf). DS: 1.6.11 plus pp 117-123. (again) |
11-3 Continue readings on equivalence relations. Proof Evaluation #5 |
| 12 |
11-6
Countable and uncountable sets. Cardinality Reading (on line) DistributePartnership assignment |
11-8 The Real Numbers: Uncountable and countably infinite sets. Onto Functions and cardinal equivalence. |
11-10 No Class Holiday |
| 13 Exam #2 Self-scheduled Tuesday |
11-13 Partnership assignment due by 5 pm. Basic counting for Finite Sets. |
11-15 Applications of Counting: Permutations, Combinations, Counting the Power Sets, Binomial Theorem
|
11-17Proof
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 Reading assignment for 11-27: Proof in Geometry by Fetisov pp 7-44. |
| 14 Fall Break | 11-20 | 11-22 | 11-24 |
| 15Final Part I distributed | 11-27
DS: pages121-123, 5.1.3 Integer Congruence Arithmetic and congruence | 11-29
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 | 12-1Read: 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 | 12-4 | 12-6 | 12-8 |
| Below this line is not yet assigned! |
|||
| , 1.50 Do: DS:3.25, 3.26 Problems: DS:3.2.3 DO: |
9- 6 DS:1.6.10, 1.6.12 . DS: 1.43,.1.44, 1.50 |
||
| Polya:Signs of progress | 10-16 |
DO: |
DS:6.11 |
| 10 | 10-23 More on congruence classes Read DS:6.2.4 (this should cover several classes) DO: |
10-25 Read: Do: Proof Evaluation #7 |
|
| 11 | 11-3 Do:DS:5.1 |
||
| 12 |
11-10 No Class Holiday |
||
| 13 | 11-13 | 11-15 Read: DO |
11-17 Read DS: 5.2.1 |
| 15Final Part I distributed | 11-27 READ DS:p311-312(Symmetry Groups) handout on Pigeons&Counting DO: handout:10.1,10.2 |
11-29 READ Handout on Do:DS:5.15, 5.16 |
12-1 Read: DO: Proof Evaluation #9 Problems on Induction Distribute Final I |
| 16 Last week of classes |
12-4 Read: Handout on graphs, combinations. DO: 4 induction problems on sheet |
12-6 Read:
DO: |
12-8 |