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 |
| Below this line is not yet assigned! |
|||
| , 1.50 Do: DS:3.25, 3.26 Problems: DS:3.2.3 DO: |
Do: Proof Evaluation #5 Proof w/o Words #5. |
9- 6 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 |
|
| Read: DS:2.2.1 DO: DS:2.7,2.8,2.9,2.10 |
Read DS: pages 118-121 Do: |
|
|
| Polya: "The intelligent problem solver" and "The intelligent
reader." Polya: Decomposing and recombining. Polya: Can you check the result? Can you derive the result differently? Polya:Signs of progress |
10-16 Equivalence relations | 10-18 Equivalence relations and Partitions: Integer
Congruence Read DS: pages121-123, 5.1.3 DO: DS: 5.2 Proof Evaluation #6 |
10-20 cardinal equivalence Read DO: |
| 10 | 10-23 More on congruence classes Countable and uncountable sets. Read DS:6.2.4 (this should cover several classes) DO: |
10-25Arithmetic and congruence I Read: Do:DS:6.11 Proof Evaluation #7 |
10-27Read: Do: |
| 11 | 10-30Read:
DO: |
11-1 Read DO :2.78,2.82 |
11-3 Read DS:5.1.1;5.1.2; 5.1.4 Do:DS:5.1 |
| 12 Exam #2 |
11-6 Read Do: |
11-8Review for Exam #2 Proof Evaluation #8 |
11-10 No Class Holiday |
| 13 | 11-13Read: DS: 1.6.5 (Induction) Do: DS:1.33(b); 1.34(b) |
11-15 Read: DO |
11-17 Read DS: 5.2.1 |
| 14 Fall Break |
11-20 | 11-22 | 11-24 |
| 15Final Part I distributed | 11-27 READ DS:p311-312(Symmetry Groups) handout on Pigeons&Counting DO: handout:10.1,10.2 |
11-29 READHandout on Pidgeon Hole Principle 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 |