BLOCK II

RELATIONS AND FUNCTIONS

(Note: The schedule given below is tentative.)

Lesson #

Date(s)

Section

Topic

Homework Assignment

October 12-13 -- Reading Days

19

Oct. 14

4.1

Relations Read Section 4.1, working all exercises along the way

20

Oct. 16

4.2

Orderings

Read Section 4.2, working all exercises along the way and prepare the presentation of your assigned theorem:
Group 1: Prove Theorem 4.2.14
Group 2: Prove Theorem 4.2.15
Group 3: Prove Theorem 4.2.18
All Groups: Prove Theorem 4.2.22
Presentations on Mon., October 19

Do problems #3, 7, 8, 9 at the end of Chapter 4, pp. 96-99 (to be collected on Wednesday, Oct. 21-at the beginning of class)

21

Oct. 19

4.2

Orderings - Student Presentations Write up the proofs of Lemma 4.2.25 and Theorem 4.2.26 (Due on Friday, Oct. 23)

22

Oct. 21

4.2

Orderings - Problem-solving see previous assignment

23

Oct. 23

4.3

Equivalence Relations Read Section 4.3, pp. 78-81, working all exercises along the way, and prepare the presentation of your assigned theorem:
Group 3: Do Problem 4.3.14 and Prove Theorem 4.3.15
Groups 1&2: Prove Theorem 4.3.16 and Corollary 4.3.17
Presentations on Monday, October 26

Also do problems #14, 15, 16 at the end of Chapter 4, pp. 96-99 (not to be collected)

24

Oct. 26

4.3

Equivalence Relations Write up the proofs of Lemma 4.3.20 and Theorem 4.3.21 (to be collected on Friday, October 30)

25

Oct. 28

4.3

 Problem-solving with Equivalence Relations Read Section 5.1, working all exercises along the way

26

Oct. 30

5.1

The Basics of Functions

Group 2: Prove Theorem 5.1.7
Group 1&3: Prove Theorem 5.1.13
Presentations on Monday, November 2

Do problems #1, 3, 4 at the end of Chapter 5, pp. 130-131 (to be collected on Fri. Nov. 6)

27

Nov. 2

5.1

The Basics of Functions Be prepared to present Exercises 5.1.14 and 5.1.15 on Wed. Nov. 4.

28

Nov. 4

5.1

 

The Basics of Functions

 

Read Section 5.2, working all exercises along the way

Write-up the proofs of Theorem 5.2.9 (Part II only) and Theorem 5.2.10 (to be collected on Wednesday, Nov. 11--This assignment must be LaTeXed.)

Read Section 5.3, working all exercises along the way

29

Nov. 6

5.2

Compositions and Inverses Group 1: Present Problem 5.2.4, #1 and #2
Group 2: Present Problem 5.2.4, #3 and #4
Group 3: Present Theorem 5.2.9, Part I, #1 and #2
Presentations on Mon., Nov. 9

Do problems #5, 6, 7 at the end of Chapter 5, pp. 131-132 (not to be collected)

30

Nov. 9

5.2

Compositions and Inverses

Read Section 5.3, working all exercises along the way

31

Nov. 11

5.3

Images and Inverse Images

Make sure you can prove Theorems 5.3.6, 5.3.11, and 5.3.12

Work on problems #9, 15, 16 at the end of Chapter 5, pp. 132-133 -- on Friday students will present their progress on these problems (starting with 9ab and 15).

32

Nov. 13

5.3

Problem-solving with Images and Inverse Images Reading quiz next lesson covering Section 7.1; We will present the theorems in class.

33

Nov. 16

7.1

Galileo's Paradox Take-home portion of Exam II distributed -- Due on Fri., Nov. 20

34

Nov. 18

7.2

Infinite Sets  

35

Nov. 20

   EXAM II (in-class)  
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