BLOCK II

RELATIONS AND FUNCTIONS

(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

19

Feb. 27

4.1

Relations Read Section 4.1, working all exercises along the way

20

Feb. 29

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 3: Prove Theorem 4.2.15
Group 4: Prove Theorem 4.2.18
Group 2: Prove Theorem 4.2.22
What is your NEW group?

NOTE: It is imperative that you work from definitions when proving these theorems; do not assume that works in the reals holds for all sets. This is a common pitfall for students.
Presentations on Friday., March 2

Do problems #3, 7, 8, 9 at the end of Chapter 4, pp. 96-99 (to be collected on Monday, March 19-at the beginning of class)

21

March 2

4.2

Orderings - Student Presentations Write up the proofs of Lemma 4.2.25 and Theorem 4.2.26 (Due on Wednesday, March 21)
SPRING BREAK - - - March 3-18

22

March 19

4.2

Orderings - Problem-solving see previous assignment

23

March 21

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&4: 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 next lesson

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

24

March 23

4.3

Equivalence Relations (Student Presentations)

Write up the proofs of Lemma 4.3.20 and Theorem 4.3.21 (to be collected next lesson)

Read Section 5.1, working all exercises along the way

25

March 26

5.1

The Basics of Functions

Present problems from the one-to-one/onto handout next lesson.

 

26

March 28

5.1

The Basics of Functions (Student Presentations)

Group 1&4: Prove Theorem 5.1.7
Group 2: Prove Theorem 5.1.13
Group 3: Prove Theorem 5.1.16
What is your group?
Presentations on Friday, March 30

Do problems #1, 3, 4 at the end of Chapter 5, pp. 130-131 (to be collected on Mon. April 2)

27

March 30

5.1

 

The Basics of Functions (Student Presentations)

 

Read Section 5.2, working all exercises along the way

Write-up the proofs of Theorem 5.2.9 (Part II) and Theorem 5.2.10 (to be collected on Friday, April 6 --This assignment must be LaTeXed.)

Next lesson we'll be presenting the proofs of Theorems 5.2.3 and 5.2.7.

Read Section 5.3, working all exercises along the way

28

April 2

5.2

Compositions and Inverses Group 1: Present Problem 5.2.4, #1 and Theorem 5.2.9, Part I, #1
Group 2: Present Problem 5.2.4, #2 and Theorem 5.2.9, Part I, #1
Group 3: Present Problem 5.2.4, #3 and Theorem 5.2.9, Part I, #2
Group 4: Present Problem 5.2.4, #4 and Theorem 5.2.9, Part I, #2
Presentations next lesson - What is your group?

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

29

April 4

5.2

Compositions and Inverses

Read Section 5.3, working all exercises along the way

30

April 6

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 -- Next lesson students will present their progress on these problems (starting with 9ab and 15).

31

April 9

5.3

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

32

April 11

7.1

Galileo's Paradox Do problems #11, 12 at the end of Chapter 5, pg.132; We will present these problems in class on Friday.
33

April 13

 

Presentations of #11, 12 at the end of Chapter 5 Take-home portion of Exam II distributed -- Due on Wed., April 18.

34

April 16

7.1/7.2

Problem-solving/Cardinality STUDY for in-class portion of Exam I

35

April 18

7.1/7.2

EXAM II (in-class)
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