Syllabus

Wk Date Lec
Topic
Reading
Hws
1
       
9/3
1
Introduction
  
9/5
2
Logical form and statements
1.1
5, 8, 15, 20, 36, 49
2
9/8
3
Conditional statements
1.2
6, 8, 13, 21, 39, 46
9/10
4
Valid and invalid arguments
1.3
9, 11, 13, 23, 29, 32
9/12
5
Introduction to Python
Write a python function that calculates the factorial of n. (not collected)
3
9/15
6
Application: Digital Logic Circuits
2, 6, 10, 21, 31
9/17
7
Application: Number Systems and Circuits for Addition
9/19
8
Predicates and quantified statements
4c, 6b, 15, 16b, 27
4
9/22
9
Predicates and quantified statements II
2, 4b, 4d, 8, 12, 43
9/24
10
Statements containing multiple quantifiers
4c, 12e, 39b, 59
9/26
11
Direct proof and counterexample
3.1
3, 5, 12, 13, 27, 32
5
9/29
12
Direct proof and counterexample
3.2-3.5
3.2: 5, 10, 15, 21, 24, 32
3.3: 5, 11, 16, 20, 37
10/1
13
Indirect argument: countradiction and contraposition
Two classical theorems
3.6 and 3.7
3.6: 4, 6, 11, 20, 22, 26
3.7: 4, 8, 15, 17
10/3
14
Application: Algorithms
6
10/6
-
Midterm 1
10/8
15
Sequences
4.1
2, 4, 6, 13, 15, 22, 28, 37
10/10
16
Induction I
4.2
4, 7, 9, 12, 20
7
-
Fall Break!
8
10/20
17
Induction II
7, 9, 17, 29, 32
10/22
18
Strong mathematical induction and the well-ordering principle
2, 13, 16, 17, 19
10/24
19
Application: Correctness of algorithm
9
10/27
20
Basic definitions of set theory
5.1
11, 15, 19, 22, 27, 29
optional practice quiz
10/29
21
Properties of sets
5.2
4, 9, 13, 14, 20, 29
10/31
22
Disproofs, algebraic proofs and Bolean algebras
Russell's paradox
5.3 and 5.4
5.3: 7, 10, 16, 27, 30
5.4: 3, 6, 10
10
11/3
23
Introduction to counting
6, 13b, 19, 22
11/5
24
Possibility trees and multiplication rule
2, 14c, 15, 30, 36d
11/7
25
Counting elements of disjoint sets: the addition rule
2, 10, 15, 22, 27
11
11/10
26
Counting subsets of a set: combinations
6.4
7, 12, 13b, 16, 20a
11/12
27
r-combinations with repetition allowed
6.5: 2, 6, 12, 13
11/14
28
Gambling and Probabilities
6.8 and 6.9
lecture notes
6.8: 15, 21
12
11/17
29
Review
11/19
-
Midterm 2
11/21
30
Function defined on general sets
7.1
6, 12, 14, 25, 32, 41
13
11/24
31
One-to-one and onto, inverse functions
7.2
7, 13, 18, 23
11/26
-
Happy Thanksgiving!
    
-
Happy Thanksgiving!
14
12/1
32
Application: the pigeonhole principle
11, 14, 19, 30, 33
12/3
33
Composition of functions
7.4
2, 4, 6, 10, 17
12/5
34
Recursively defined sequences
8.1
2, 6, 12, 14
15
12/8
35
Solving recurrence relations by iteration
11, 23, 27, 44, 52
12/10
36
Review