BLOCK I

LOGIC, SET THEORY, and INDUCTION

(Note: The schedule given below is tentative.)

Lesson #

Date(s)

Section

Topic

Homework Assignment

1

Jan. 15

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

Jan. 17

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.

3

Jan. 19

1.6-1.8

Compound Statements and Truth Tables Read Sections1.8, 1.9, 1.10, working out all exercises along the way.
Do problems 1-4 at the end of the chapter -- Due Friday, Jan. 26

4

Jan. 22

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, Jan. 26

5

Jan. 24

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. 26

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. 29

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 (not to be collected)

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., Feb. 7.

 

8

Jan. 31

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

Feb. 2

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, Feb. 9)

10

Feb. 5

2.4

The Algebra of Sets (Student Presentations) Student Presentations for Feb. 9:
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

Feb. 7

2.5

 The Power Set  

12

Feb. 9

2.5-2.6

The Power Set and Russel's Paradox (Student Presentations)  

13

Feb. 12

3.1

 Mathematical Induction Read Section 3.1 and 3.2, working out all exercises along the way.

Do Problems 3.2.3, 3.2.4, and 3.2.5 for Wednesday. Students will present these!

14

Feb. 14

3.2

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

Complete the Handout. Your solution to the cool Putnam Problem should be LaTeXed and will be collected on Monday, Feb. 19

15

Feb. 16

3.2

 LaTeX workshop (in RBH 203?)

16

Feb. 19

3.3

More on Induction: Complete Induction Work on Problem 3.3.2 and Theorem 3.3.3. Somebody will present Problem 3.3.2 next lesson!

17

Feb. 21

3.2/3.3

More practice with Induction  Take-home portion of Exam 1 distributed -- Due Monday, Feb. 26

18

Feb. 23

 

EXAM I (in-class)  
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