Syllabus

 

Wk Date Lec
Topic
Reading
Hws
 Collected
1
       
 
9/5
1
Introduction
1.1-1.3
notes
9/7
2
Logical form and statements
Conditional statements
2.1-2.2
notes
2.1: 5, 8, 13, 17, 35, 37, 46, 52
2.2: 10, 15, 21, 35, 43, 50
 
2
9/10
3
Valid and invalid arguments
2.3
notes
10, 13, 23, 28, 29, 32, 40
2.1, 2.2
9/12
4
Digital Logic Circuits
2.4
notes
2, 6, 10, 21, 31
  
9/14
5
Number Systems and Circuits for Addition

2.5
notes
5, 11, 21, 26, 34, 37, 45, 47
  
3
9/17
6
Predicates and quantified statements
3.1-3.2
notes
3.1: 4c, 5b, 15, 16b, 20, 29
3.2: 2, 4b, 4d, 8, 14, 25c, 44
2.3, 2.4, 2.5
9/19
7
Statements containing multiple quantifiers
3.3
notes
4c, 11e, 38, 40b, 43, 61
  
9/21
8
Direct proof and counterexample
4.1
notes
5, 13, 28, 37, 41, 50
  
4
9/24
9
Direct proof and counterexample
4.2: 10, 17, 22, 25, 32
4.3: 5, 16, 20, 43, 49
4.4: 25, 52
3.1, 3.2, 3.3, 4.1
9/26
10
Indirect argument: countradiction and contraposition
Two classical theorems
4.6-4.7
notes
4.6: 4, 7, 12, 22, 28, 35
4.7: 4, 8, 15, 17, 24
9/28
11
Algorithms
8b, 16, 20, 28
5
10/1
12
Sequences
5.1
notes
4, 7, 13, 17, 22, 28, 50, 79
4.2, 4.3, 4.4, 4.6, 4.7, 4.8
10/3
13
Induction I
(covered by Prof. Eaton)
5.2
notes
4, 7, 11, 14, 23, 36
10/5
-
Midterm 1
 

6
10/8
14
Induction II
5.3
notes
7, 10, 17, 23, 29, 35, 37
5.1, 5.2
10/10
15
Strong mathematical induction and the well-ordering principle
5.4
notes
2, 15, 18, 19, 21, 25
10/12
16
Correctness of algorithm
5.5
notes
2, 7, 9, 12
7
-
Fall Break!
 
8
10/22
17
Recursively defined sequences
5.6
notes
8, 14, 20, 32, 40
5.3, 5.4, 5.5
10/24
18
Solving recurrence relations by iteration
5.7-5.8
notes
5.7: 11, 36, 44, 52
5.8: 10, 14, 24
10/26
19
Recursion
5.9
notes
8, 11, 14, 16, 18, 20

9
10/29
20
Class cancelled due to hurricane

10/31
21
Basic definitions of set theory
6.1
notes
12, 25, 30, 33, 35
5.6-5.9
11/2
22
Properties of sets
6.2-6.4
notes
Chapter 7
6.2: 14, 22, 31, 41
6.3: 7, 16, 20, 37
6.4: 23, 25
10
11/5
23
Introduction to counting
9.1
notes
6, 13b, 19, 22, 33
6.1-6.4
11/7
24
Possibility trees and multiplication rule
9.2
notes
2, 14c, 15, 29, 30, 33
11/9
25
Counting elements of disjoint sets: the addition rule
2, 10, 17, 20, 21, 22, 30, 32
11
11/12
26
Application: the pigeonhole principle
9.4
notes
11, 16, 19, 30, 32, 36
9.1, 9.2, 9.3
11/14
27
Counting subsets of a set: combinations
r-combinations with repetition allowed
9.5: 7, 11, 16, 20, 28
9.6: 4, 6, 12, 18
11/16
28
The Binomial Theorem
9.7
notes
9.7: 7, 16, 39, 42
12
11/19
-
Midterm 2
 
9.4-9.7
11/21
29
Gambling and Probabilities
9.8
notes
5, 15, 18, 20, 21, 23
11/23
-
Happy Thanksgiving!
 
13
11/26
30
Midterm 2, Combinatorial proofs and Conditional Probability
 
9.8
11/28
31
Conditional probability, Bayes' Formula and independent events
9.9
notes
15, 24, 28, 29, 30, 33
11/30
32
Graphs
10.1
notes
20, 25, 28, 30, 33, 48
14
12/3
33
Trails, Paths and Circuits
10.2
notes
2, 8, 11, 35, 48, 49
9.9, 10.1
12/5
34
Matrix Representation of Graphs
(covered by Prof. Eaton)
10.3
10.3: 4, 5, 6, 7, 21, 23
12/7
35
Graph Representation
Trees
10.3-10.5
notes
notes
10.5: 3, 6, 23, 26
15
12/10
36
Trees and Rooted Trees
10.6
notes
10.6: 3, 14, 17, 20
10.2-10.5
12/12
37
Review
  
10.6