| Wk | Date | Lec | Topic |
Reading |
Hws |
Collected |
|---|---|---|---|---|---|---|
| 1 | 1/19 |
1 |
Introduction Logical form and statements |
2.1: 5, 8, 13, 17, 35, 37, 46, 52 | ||
1/21 |
2 |
Conditional statements Valid and invalid arguments |
2.2: 10, 15, 21, 35, 43, 50 2.3: 10, 13, 23, 28, 29, 32, 40 |
|||
| 2 | 1/26 |
3 |
Digital Logic Circuits Number Systems and Circuits for Addition |
2.4: 2, 6, 10, 21, 31 2.5: 5, 11, 21, 26, 34, 37, 45, 47 |
2.1, 2.2, 2.3 |
|
1/28 |
4 |
Predicates and quantified statements |
3.1: 4c, 5b, 15, 16b, 20, 29 3.2: 2, 4b, 4d, 8, 14, 25c, 44 |
|||
| 3 | 2/2 |
5 |
Statements containing multiple quantifiers Arguments with quantified statements |
3.3: 4c, 11e, 38, 40b, 43, 61 3.4: 14, 15, 19, 22, 27, 32, 34 |
2.4, 2.5, 3.1, 3.2 | |
2/4 |
6 |
Direct proof and counterexample |
4.1: 28, 37, 41, 56 4.2: 10, 17, 25, 32 4.3: 16, 20, 39, 43, 49 4.4: 25, 52 |
|||
| 4 | 2/9 |
- |
No class, I am out of town |
|||
2/11 |
7 |
Indirect argument: contradiction and contraposition Two classical theorems |
4.6: 4, 7, 12, 22, 28, 35 4.7: 4, 8, 15, 17, 24 |
3.3, 3.4, 4.1, 4.2, 4.3, 4.4 | ||
| 5 | 2/16 |
8 |
Algorithms Sequences |
4.8: 8b, 16, 20, 24, 28 5.1: 7, 15, 17, 28, 50, 79 |
||
2/18 |
9 |
Induction |
5.2: 7, 11, 14, 23, 36 5.3: 10, 17, 23, 29, 35, 37 |
4.6, 4.7, 4.8, 5.1 | ||
6 |
2/23 |
- |
No class, Commnunity Day of Learning |
|||
2/25 |
10 |
Strong mathematical induction and the well-ordering principle |
5.4 14.pdf |
5.4: 2, 15, 18, 19, 21, 25 | ||
| 7 | 3/1 |
11 |
Correctness of Algorithm |
5.5 15.pdf |
5.5: 2, 7, 9, 12 | 5.2, 5.3, 5.4 |
3/3 |
- |
Midterm 1 |
||||
8 |
- |
Spring Break! |
||||
| 9 | 3/15 |
12 |
Recursively defined sequences Solving recurrence relations by iteration |
5.6-5.7 16.pdf |
5.6: 8, 14, 20, 32, 40 5.7: 11, 36, 44, 52 |
|
3/17 |
13 |
Recursion |
5.8: 10, 14, 24 5.9: 8, 11, 14, 16, 18, 20 |
5.5, 5.6, 5.7 | ||
| 10 | 3/22 |
14 |
Basic definitions and properties of sets Set identities, proofs, Russell's paradox and the halting problem |
6.1: 12, 25, 30, 33c, 35c-d 6.2: 14, 22, 31, 41 6.3: 7, 20, 26, 37 6.4: 23, 25 |
||
3/24 |
15 |
Introduction to counting Possibility trees and multiplication rule |
9.1: 6, 13b, 19, 22, 33 9.2: 2, 14c, 15, 29, 30, 33 |
5.8, 5.9, 6.1, 6.2, 6.3, 6.4 | ||
11 |
3/29 |
16 |
Counting elements of disjoint sets: the addition rule |
9.3: 2, 10, 17, 20, 21, 22, 30, 49 9.4: 11, 16, 19, 30, 32, 36 9.5: 7, 11, 16, 20, 28 |
||
3/31 |
17 |
r-combinations with repetition allowed The Binomial Theorem Combinatorial proofs |
9.6: 4, 6, 15, 18 9.7: 7, 16, 39, 42 |
9.1, 9.2, 9.3, 9.4 | ||
| 12 | 4/5 |
18 |
Gambling and Probabilities |
9.8 27.pdf |
9.8: 5, 15, 18, 20, 21, 23 | |
4/7 |
19 |
Conditional probability, Bayes' Formula and independent events |
9.9: 15, 24, 28, 29, 30, 33 | 9.5, 9.6, 9.7 | ||
13 |
4/12 |
- |
Midterm 2 |
|||
4/14 |
20 |
Graphs Trails, Paths and Circuits |
10.1: 20, 28, 30, 33, 44, 48 10.2: 2, 8, 11, 35, 48, 49 |
9.8, 9.9 | ||
14 |
4/19 |
21 |
Matrix Representation of Graphs |
10.3-10.4 |
10.3: 4, 5, 6, 7, 21, 23 | |
4/21 |
22 |
Trees Rooted Trees |
10.5: 3, 6, 23, 26 10.6: 3, 14, 17, 20 |
10.1, 10.2, 10.3 | ||
15 |
4/26 |
23 |
Review |
10.5, 10.6 | ||
4/28 |
24 |
No class, I am out of town |