| Wk | Date | Lec | Topic |
Reading |
Hws |
Collected |
|---|---|---|---|---|---|---|
| 1 | 1/17 |
1 |
Introduction Logical form and statements |
2.1: 5, 8, 13, 17, 35, 37, 46, 52 | ||
1/19 |
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 | 1/24 |
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 | |
1/26 |
4 |
Predicates and quantified statements |
3.1: 4c, 5b, 15, 16b, 20, 29 3.2: 2, 4b, 4d, 8, 14, 25c, 44 |
|||
| 3 | 1/31 |
5 |
Statements containing multiple quantifiers Arguments with quantified statements |
3.3-3.4 07.pdf |
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 |
2/2 |
6 |
Direct proof and counterexample |
4.1-4.5
08.pdf |
4.1: 28, 37, 41, 56 4.2: 10, 17, 25, 32 4.3: 16, 20, 39, 43, 49 4.4: 25, 52 |
||
| 4 | 2/7 |
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 | |
2/9 |
8 |
Class cancelled due to snow |
- |
- | ||
| 5 | 2/14 |
9 |
Algorithms Sequences |
4.8: 8b, 16, 20, 24, 28 5.1: 7, 15, 17, 28, 50, 79 |
4.6, 4.7 | |
2/16 |
10 |
Induction |
5.2-5.3 13.pdf |
5.2: 7, 11, 14, 23, 36 5.3: 10, 17, 23, 29, 35, 37 |
||
6 |
2/21 |
11 |
Strong mathematical induction and the well-ordering principle |
5.4: 2, 15, 18, 19, 21, 25 | 4.8, 5.1, 5.2 | |
2/23 |
- |
Midterm 1 |
||||
| 7 | 2/28 |
12 |
Correctness of Algorithm |
5.5
15.pdf |
5.5: 2, 7, 9, 12 | 5.3, 5.4 |
3/2 |
13 |
Recursively defined sequences Solving recurrence relations by iteration |
5.6: 8, 14, 20, 32, 40 5.7: 11, 36, 44, 52 |
|||
8 |
- |
Spring Break! |
||||
| 9 | 3/14 |
14 |
Class cancelled due to snow |
|||
3/16 |
15 |
Recursion and structral induction |
5.8: 10, 14, 24 5.9: 8, 11, 14, 16, 18, 20 |
5.5, 5.6, 5.7 | ||
| 10 | 3/21 |
16 |
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 |
||
3/23 |
17 |
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 | ||
11 |
3/28 |
- |
No class, I am out of town |
|||
3/30 |
- |
Midterm 2 |
||||
| 12 | 4/4 |
18 |
Counting elements of disjoint sets: the addition rule Application: the pigeonhole principle Counting subsets of a set: combinations |
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 |
6.3, 6.4, 9.1, 9.2 | |
4/6 |
19 |
r-combinations with repetition allowed The Binomial Theorem Combinatorial proofs |
9.6: 4, 6, 15, 18 9.7: 7, 16, 39, 42 |
|||
13 |
4/11 |
20 |
Gambling and Probabilities |
9.8 27.pdf |
9.8: 5, 15, 18, 20, 21, 23 | 9.3, 9.4, 9.5, 9.6 |
4/13 |
21 |
Conditional probability, Bayes' Formula and independent events |
9.9 28.pdf |
9.9: 15, 24, 28, 29, 30, 33 | ||
14 |
4/18 |
22 |
Graphs Trails, Paths and Circuits |
10.1: 20, 28, 30, 33, 44, 48 10.2: 2, 8, 11, 35, 48, 49 |
9.7, 9.8, 9.9 | |
4/20 |
23 |
Matrix Representation of Graphs |
10.3: 4, 5, 6, 7, 21, 23 | |||
15 |
4/25 |
23 |
Trees
Rooted Trees |
10.5: 3, 6, 23, 26 10.6: 3, 14, 17, 20 |
10.1, 10.2, 10.3 | |
4/27 |
24 |
Review |