Syllabus

Wk Date Lec
Topic
Reading
Hws
Collected
1
8/31
1
Introduction
    
9/2
2
Logical form and statements
1.1
5, 8, 15, 20, 36, 49
9/4
3
Conditional statements
1.2
6, 8, 13, 21, 39, 46
2
9/7
-
Labor Day
  
9/9
4
Valid and invalid arguments
9, 11, 13, 23, 29, 32
9/11
5
Introduction to Python
Write a python function that calculates the factorial of n. (not collected)
3
9/14
6
Application: Digital Logic Circuits
2, 6, 10, 21, 31
9/16
7
Application: Number Systems and Circuits for Addition
9/18
8
Predicates and quantified statements
4c, 6b, 15, 16b, 27
4
9/21
9
Predicates and quantified statements II
2, 4b, 4d, 8, 12, 43
9/23
10
Statements containing multiple quantifiers
4c, 12e, 39b, 59
9/25
11
Direct proof and counterexample
3.1
3, 5, 12, 13, 27, 32
5
9/28
12
Review
9/30
13
Direct proof and counterexample
3.2-3.5
3.2: 5, 10, 15, 21, 24, 32
3.3: 5, 11, 16, 20, 37
10/2
-
Midterm 1
 
6
10/5
14
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
10/7
15
Application: Algorithms
10/9
16
Sequences
2, 4, 6, 13, 15, 22, 28, 37
7
-
Fall Break!
8
10/19
17
Induction I
4.2
4, 7, 9, 12, 20
10/21
18
Induction II
7, 9, 17, 29, 32
10/23
19
Strong mathematical induction and the well-ordering principle
2, 13, 16, 17, 19
3.8, 4.1, 4.2 and 4.3
9
10/26
20
Application: Correctness of algorithm
2, 9
10/28
21
Basic definitions of set theory
5.1
11, 15, 19, 22, 27, 29
10/30
22
Properties of sets
4, 9, 13, 14, 20, 29
4.4, 4.5 and 5.1 Python project 2
10
11/2
23
Disproofs, algebraic proofs and Boolean algebras
Russell's paradox
5.3 and 5.4
Practice proofs
5.3: 7, 10, 16, 27, 30
5.4: 3, 6, 10
11/4
24
Introduction to counting
11/6
25
Possibility trees and multiplication rule
2, 14c, 15, 30, 36d
5.2, 5.3, 5.4 and 6.1
11
11/9
26
Counting elements of disjoint sets: the addition rule
2, 10, 15, 22, 27
11/11
27
Counting subsets of a set: combinations
6.4
7, 12, 13b, 16, 20a
11/13
28
r-combinations with repetition allowed
2, 6, 12, 13
6.2, 6.3 and 6.4
12
11/16
29
Gambling and Probabilities
6.8 and 6.9
lecture notes
6.8: 15, 21
11/18
-
Midterm 2
11/20
30
Function defined on general sets
7.1
6, 12, 14, 25, 32, 41
6.5 and 6.8
13
11/23
31
One-to-one and onto, inverse functions
7.2
7, 13, 18, 23
11/25
-
Happy Thanksgiving!
    
11/27
-
Happy Thanksgiving!
14
11/30
32
Composition of functions
7.4
2, 4, 6, 10, 17
12/2
33
Application: the pigeonhole principle
11, 14, 19, 30, 33
12/4
34
Recursively defined sequences
8.1
2, 6, 12, 14
7.1, 7.2 and 7.4
Python project 3
15
12/7
35
Solving recurrence relations by iteration
11, 23, 27, 44, 52
12/9
36
Review
7.3, 8.1 and 8.2