Foundations Assignments

Date

Topic

Reading Assignment

Homework

Monday, August 30

Course Procedures and Policies

Thought Experiment

*

*

Wednesday, September 1

Mathematical Statements

Note to the Student
Chapter 0
Sections 1.2-1.5

Problems 1, 3.

Friday, September 3

Compound Statements
Negation
True or False?

Sections 1.6-1.8

Problems 6.

8

Monday, September 6

Methods of Proof
Sections 1.9-1.15.

Problems 7, 8, 9.

Wednesday, September 8

Sets and Set Notation
Subsets

Sections 2.1-2.2

2.2.2
Problems 1, 2, 3.

Friday, September 10

Set Operations

Section 2.3

*

Monday, September 13

The Algebra of Sets

Section 2.4 to bottom of pg. 48

2.4.5, 2.4.8, 2.4.9

(2.4.5(2) and 2.4.9(2) will be written up.)

Wednesday, September 15

The Algebra of Sets (cont.)

Rest of Section 2.4

Friday, September 17

The Algebra of Sets (cont.)

*

Monday, September 20

The Power Set

Section 2.5

2.5.4, 2.5.5

Wednesday, September 22

The Power Set (cont.)

*

Write-ups due for 2.4.5(2) and 2.4.9(2)

Problem 8 at the end of chapter 2 (part (c) will be written up.)

Friday, September 24

Introduction to Mathematical Induction

Section 3.1

Monday, September, 27

Using Mathematical Induction

Section 3.2

3.2.2, 3.2.3, 3.2.4, 3.2.5, 3.2.6

Turn in write-up of problem 8(c) at the end of chapter 2.

Wednesday, September 29

Using Mathematical Induction (cont.)

*

Friday, October 1

Complete Induction

Section 3.3

3.3.3
(3.3.2 and Putnam Problem will be written up.)

Monday, October 4

Finish Mathematical Induction

*

*

Wednesday, October 6

Relations

Section 4.1

Problem 4.1.10, and problems 2, 3, and 4 at the end of the chapter.

Friday, October 8

Introduction to Orderings---class work day.

Section 4.2 (through top of pg. 75.)

Write-ups due for 3.3.2 and the
Putnam Problem

Monday, October 11

No class---October Break!*

Wednesday, October 13

Orderings---maximal/minimal & greatest/least elements
immediate predecessors/successors
Introduction to the Least Upper Bound

Rest of section 4.2

4.2.14, 4.2.15, 4.2.18

Friday, October 15

The Least Upper Bound Property

*

4.2.22.

Monday, October 18

From relations to sets and back---work day!

Section 4.3 (through pg. 81) .

4.3.8 and problems on pgs 80-81.

Wednesday, October 20

Equivalence relations---work day!! Takehome Midterm Distributed!

Rest of section 4.3

Write-ups due for 4.2.25, 4.2.26 4.3.15, 4.3.16, 4.3.17
(to be written up 4.3.20 and 4.3.21)

Friday, October 22

In-Class Midterm

Monday, October 25

Work on 4.3.20 and 4.3.21
Equivalence Classes

*

4.3.23

Wednesday, October 27

Takehome Midterm Due!
Defining functions

*

*

Friday, October 29

Functions---the basic ideas

Section 5.1

Work on exercises.

Monday, November 1

Functions---continued

*

5.1.13. Problems 1, 2ad.
(Problems 2d, 3, and 4 will be written up.)

Wednesday, Novermber 3

Composition and Inverses

Section 5.2

5.2.3, 5.2.4, 5.2.5.
Write-ups due of 4.3.20 and 4.3.21

Friday, November 5

Composition and Inverses---cont.
Images and Inverse images---Introduction

Section 5.3

Monday, November 8

Finish Composition and Inverses
Inverse image of a set under a function.

**

Wednesday, November 10

Inverse Image of a set under a function.

*

Group problems: 5.3.6,
(Problems 9 and 15 will be written up)

Friday, November 12

Finish image of a set under a function.
Introduction to Cardinality and infinite sets
Galileo's paradox.

Group problems: 5.3.11 and 5.3.12.
Write-ups due of problems 2d, 3, and 4 at end of chapter 5.

Monday, November 15

Cardinality and infinite sets

Section 7.1

7.1.3, 7.1.5

Wednesday, November 17

Cardinality and infinite sets (cont.)

Section 7.2

Read carefully for intuition.
7.2.3 (present in class)

Friday, November 19

Iinfinite sets
Countable sets---general discussion

Section 7.3

7.2.6, and 7.2.7--may assume result of 7.2.5
Write-ups due of problems 9 and 15 at end of chapter 5.

Thanksgiving Break

Monday, November 29

Countable sets---work day

Section 7.3---again!

Problems assigned individually

Wednesday, December 1

Uncountable sets---discussion
Cantor's diagonalization argument.

Section 7.4

*

Friday, December 3

Countable and Uncountable sets---class presentations begin!!!

*

*

Monday, December 6

Countable and Uncountable sets---class presentations

*

*

Wednesday, December 8

Countable and Uncountable sets---class presentations

*

*

Friday, December 10

Countable and Uncountable sets---class presentations

*

*

Monday, December 13

Countable and Uncountable sets---class presentations

*

*

Final Examination

Saturday, December 18 at 6:30 p.m.

(Note: This is the scheduled time for the Period 6 courses!)

Date	Topic	Reading Assignment	Homework

Monday, August 30	Course Procedures and Policies Thought Experiment	*	*
Wednesday, September 1	Mathematical Statements	Note to the Student Chapter 0 Sections 1.2-1.5	Problems 1, 3.
Friday, September 3	Compound Statements Negation True or False?	Sections 1.6-1.8	Problems 6.
8
Monday, September 6	Methods of Proof	Sections 1.9-1.15.	Problems 7, 8, 9.
Wednesday, September 8	Sets and Set Notation Subsets	Sections 2.1-2.2	2.2.2 Problems 1, 2, 3.
Friday, September 10	Set Operations	Section 2.3	*

Monday, September 13	The Algebra of Sets	Section 2.4 to bottom of pg. 48	2.4.5, 2.4.8, 2.4.9 (2.4.5(2) and 2.4.9(2) will be written up.)
Wednesday, September 15	The Algebra of Sets (cont.)	Rest of Section 2.4
Friday, September 17	The Algebra of Sets (cont.)	*

Monday, September 20	The Power Set	Section 2.5	2.5.4, 2.5.5
Wednesday, September 22	The Power Set (cont.)	*	Write-ups due for 2.4.5(2) and 2.4.9(2) Problem 8 at the end of chapter 2 (part (c) will be written up.)
Friday, September 24	Introduction to Mathematical Induction	Section 3.1

Monday, September, 27	Using Mathematical Induction	Section 3.2	3.2.2, 3.2.3, 3.2.4, 3.2.5, 3.2.6 Turn in write-up of problem 8(c) at the end of chapter 2.
Wednesday, September 29	Using Mathematical Induction (cont.)	*
Friday, October 1	Complete Induction	Section 3.3	3.3.3 (3.3.2 and Putnam Problem will be written up.)

Monday, October 4	Finish Mathematical Induction	*	*
Wednesday, October 6	Relations	Section 4.1	Problem 4.1.10, and problems 2, 3, and 4 at the end of the chapter.
Friday, October 8	Introduction to Orderings---class work day.	Section 4.2 (through top of pg. 75.)	Write-ups due for 3.3.2 and the Putnam Problem

Monday, October 11	No class---October Break!*
Wednesday, October 13	Orderings---maximal/minimal & greatest/least elements immediate predecessors/successors Introduction to the Least Upper Bound	Rest of section 4.2	4.2.14, 4.2.15, 4.2.18
Friday, October 15	The Least Upper Bound Property	*	4.2.22.

Monday, October 18	From relations to sets and back---work day!	Section 4.3 (through pg. 81) .	4.3.8 and problems on pgs 80-81.
Wednesday, October 20	Equivalence relations---work day!! Takehome Midterm Distributed!	Rest of section 4.3	Write-ups due for 4.2.25, 4.2.26 4.3.15, 4.3.16, 4.3.17 (to be written up 4.3.20 and 4.3.21)
Friday, October 22	In-Class Midterm

Monday, October 25	Work on 4.3.20 and 4.3.21 Equivalence Classes	*	4.3.23
Wednesday, October 27	Takehome Midterm Due! Defining functions	*	*
Friday, October 29	Functions---the basic ideas	Section 5.1	Work on exercises.

Monday, November 1	Functions---continued	*	5.1.13. Problems 1, 2ad. (Problems 2d, 3, and 4 will be written up.)
Wednesday, Novermber 3	Composition and Inverses	Section 5.2	5.2.3, 5.2.4, 5.2.5. Write-ups due of 4.3.20 and 4.3.21
Friday, November 5	Composition and Inverses---cont. Images and Inverse images---Introduction	Section 5.3

Monday, November 8	Finish Composition and Inverses Inverse image of a set under a function.	**
Wednesday, November 10	Inverse Image of a set under a function.	*	Group problems: 5.3.6, (Problems 9 and 15 will be written up)
Friday, November 12	Finish image of a set under a function. Introduction to Cardinality and infinite sets Galileo's paradox.		Group problems: 5.3.11 and 5.3.12. Write-ups due of problems 2d, 3, and 4 at end of chapter 5.

Monday, November 15	Cardinality and infinite sets	Section 7.1	7.1.3, 7.1.5
Wednesday, November 17	Cardinality and infinite sets (cont.)	Section 7.2	Read carefully for intuition. 7.2.3 (present in class)
Friday, November 19	Iinfinite sets Countable sets---general discussion	Section 7.3	7.2.6, and 7.2.7--may assume result of 7.2.5 Write-ups due of problems 9 and 15 at end of chapter 5.
Thanksgiving Break
Monday, November 29	Countable sets---work day	Section 7.3---again!	Problems assigned individually
Wednesday, December 1	Uncountable sets---discussion Cantor's diagonalization argument.	Section 7.4	*
Friday, December 3	Countable and Uncountable sets---class presentations begin!!!	*	*

Monday, December 6	Countable and Uncountable sets---class presentations	*	*
Wednesday, December 8	Countable and Uncountable sets---class presentations	*	*
Friday, December 10	Countable and Uncountable sets---class presentations	*	*

Monday, December 13	Countable and Uncountable sets---class presentations	*	*

Final Examination Saturday, December 18 at 6:30 p.m. (Note: This is the scheduled time for the Period 6 courses!)