BLOCK I

LOGIC, SET THEORY, and INDUCTION

(Note: The information given below should be considered tentative.
While it is largely correct, changes may occur as the semester unfolds.
Check this page on each lesson to make sure you have the current information.)

Lesson #

Date(s)

Section

Topic

Homework Assignment

1

Jan. 16

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 Sections 1.2 and 1.3

2

Jan. 18

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, Jan. 23

3

Jan. 20

1.6-1.8

Compound Statements and Truth Tables Read Sections 1.8, 1.9, 1.10, working out all exercises along the way.

4

Jan. 23

1.8-1.10

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

1. Complete the Negation Handout - Due next lesson.
2. Do problems 6-9 at the end of the chapter -- Due Fri., Jan. 27

5

Jan. 25

1.11-1.15

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

6

Jan. 27

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

Jan. 30

2.3

 Set Operations

Read Section 2.4, working out all exercises along the way.
Do problems 2, 3, and 5 at the end of Chapter 2 (#5 MUST BE LATEXED)-- Due Monday, Feb. 6

Quiz on Friday, Feb. 3 covering the first part of Section 2.4 (starting at the bottom of page 47 through the bottom of page 48). Know and understand the proof of Theorem 2.4.2. Do exercises 2.4.3 and 2.4.4.

 

8

Feb. 1

NA

 LaTeX workshop

Student Presentations on Monday, Feb. 6:
Group 1: Theorem 2.4.5 #1
Group 2: Theorem 2.4.5 #2
Group 3: Theorem 2.4.6 #1
Group 4: 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., Feb. 8. THIS ASSIGNMENT MUST BE LATEXED.

 

9

Feb. 3

2.4

The Algebra of Sets (Quiz)

Student Presentations on Wednesday, Feb. 8:
Group 1: Theorem 2.5.6
Group 2: Theorem 2.5.5 #2
Group 3: Theorem 2.5.5 #1
Group 4: Theorem 2.5.4
What is your group?

9

Feb. 6

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 Monday, Feb. 13)

10

Feb. 8

2.4

The Algebra of Sets (Student Presentations) Student Presentations for Monday, Feb. 13:
Group 1: Problem 2.5.7 parts 1&3
Group 2: Problem 2.5.7 parts 1&3
Group 3: Problem 2.5.7 parts 2&3
Group 4: Problem 2.5.7 parts 2&3
What is your group?

11

Feb. 10

2.5

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

12

Feb. 13

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.

14

Feb. 15

3.1

 Mathematical Induction

Student Presentations for Fri., Feb. 17:
Group 1: Problem 3.2.6
Group 2: Problem 3.2.5
Group 3: Problem 3.2.3
Group 4: Problem 3.2.4
What is your group?

Start working on the Induction Handout. I will collect your proof of the first problem on Monday, Feb. 20. The other three proofs are due on Wed, Feb. 22. You'll want to START THESE PROBLEMS EARLY in case you need help on some of them. NOTE: Your solution to the first problem on the handout must be LaTeXed.

15

Feb. 17

3.2

 Mathematical Induction (Student Presentations)
 Read Section 3.3, working out all exercises along the way.

Continue working on the induction handout.

16

Feb. 20

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

Feb. 22

3.2/3.3

More practice with Induction  

18

Feb. 24

 

EXAM I (in-class) Take-home portion of Exam 1 distributed -- Due Wednesday, Feb. 29.
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