BLOCK I

LOGIC, SET THEORY, and INDUCTION

(Note: The schedule given below is tentative.)

Lesson #

Date(s)

Section

Topic

Homework Assignment

1

Aug. 31

1.1

Course Overview

What is a proof?		 Read the Course Policies.

Read Chapter 0 of Chapter Zero (tee hee)

Read Sections: 1.1, 1.2., 1.3, working out all exercises along the way
Quiz next lesson covering Section 1.2

2

Sept. 2

1.2-1.5

Statements and Predicates
Mathematical Implication
Quantification

Read Sections 1.4, 1.5, 1.6, and 1.7 working out all exercises along the way.

Do problems 1-4 at the end of the chapter -- Due Monday, Sept. 7

3

Sept. 4

1.6-1.8

Compound Statements and Truth Tables Read Sections1.8, 1.9, 1.10, working out all exercises along the way.

4

Sept. 7

1.8-1.10

Negating Statements Read Sections 1.11-1.15, working out all exercises along the way.

Do problems 7-9 at the end of the chapter -- Due Friday, Sept. 11

5

Sept. 9

1.11-1.15

Theorems and Methods of Proving Theorems Read Sections 2.1-2.2, working out all exercises along the way.

6

Sept. 11

2.1-2.2

Sets and Set Notation/Subsets Read Section 2.3, working out all exercises along the way.

Quiz next lesson covering Section 2.3

7

Sept. 14

2.3-2.4

Set Operations

The Algebra of Sets

Read Section 2.4, working out all exercises along the way.
Do problems 2,3, and 5 at the end of Chapter 2 -- Due Friday, Sept. 18

Student Presentations on Friday:
Group 1: Theorem 2.4.5 #1
Group 2: Theorem 2.4.6 #1
Group 3: Theorem 2.4.9 #1
What is your group?

Everybody: Write up the proof of part 2 of Theorem 2.4.9 (De Morgan's Laws) and part 1 of Theorem 2.4.11. To be collected on Wed., Sept. 23.

 

8

Sept. 16

2.4

The Algebra of Sets

Student Presentations on Monday:
Group 1: Theorem 2.4.11 #4
Group 2: Theorem 2.4.11 #3
Group 3: Theorem 2.4.11 #2
What is your group?

9

Sept. 18

2.4

The Algebra of Sets (Student Presentations) Read Sections 2.5 and 2.6, working out all exercises along the way.

Do Problem #8 at the end of Chapter 2 (to be collected on Friday, Sept. 25)

10

Sept. 21

2.4

The Algebra of Sets (Student Presentations) Student Presentations for Friday, Sept. 25:
Group 1: Theorem 2.5.4
Group 2: Theorem 2.5.5 #1
Group 3: Theorem 2.5.5 #2
What is your group?

11

Sept. 23

2.5

 The Power Set Problem #8 at the end of Chapter 2 due next lesson.

12

Sept. 25

2.5-2.6

The Power Set and Russel's Paradox (Student Presentations) Read Section 3.1 and 3.2, working out all exercises along the way.

13

Sept. 28

3.1

 Mathematical Induction

Student Presentations for Fri., Oct. 2:
Group 1: Problem 3.2.3
Group 2: Problem 3.2.4
Group 3: Problem 3.2.5
What is your group?

Do Problem 3.2.6 (You will LaTeX your solution to this problem and turn it in on Monday, Oct. 5.)

14

Sept. 30

3.2

 LaTeX workshop (in RBH 203?)
Read Section 3.3, working out all exercises along the way.

Complete the Handout. Your solution to Problem 3.2.6 should be LaTeXed; it will be collected on Monday, Oct. 5. Additionally you will need to submit the COOL Putnam problem on Monday, Oct. 5 (you don't have to LaTeX that one.)

15

Oct. 2

3.2

 Mathematical Induction (Student Presentations)

16

Oct. 5

3.3

More on Induction: Complete Induction Work on Problem 3.3.2 and Theorem 3.3.3. Student presentation of Problem 3.3.2 next lesson.

17

Oct. 7

3.2/3.3

More practice with Induction  

18

Oct. 9

 

EXAM I (in-class) Take-home portion of Exam 1 distributed -- Due Wednesday, October 14
Back to the Kenyon Homepage Back to the Math Homepage Back to JAH's Homepage Back to JAH's Foundations Homepage