Lesson #

Date(s)

Topic

Homework Assignment

1

Aug. 29

Read: Chapters 1 and 2

Chapter 1 Exercises:
1.1, 1.2, 1.3 (volunteer presentations
on Thurs., Sept. 1)
Some comments about this assignment

Chapter 2 Exercises:
2.1, 2.2, 2.3, 2.5 (to be collected on
Tues., Sept. 6)
Warning: There is a typo in Exercise 2.5(a)

2

Sept. 1

Student Presentations

Pythagorean Triples and the Unit Circle

Sums of Higher Powers and Fermat's Last Theorem

Read: Chapters 3 and 4

Chapter 3 Exercises:
3.3, 3.4 (not to be collected)

3

Sept. 6

Read: Chapter 5

Chapter 5 Exercises:
5.1, 5.3, 5.4a), 5.4b)
and three additional exercises
(not to be collected; however, I will ask for volunteers to present 5.3 and additional exercise #2 on Tues, Sept. 13)

4

Sept. 8

The 3n+1 Conjecture

5

Sept. 13

Student Presentations

Linear Equations and the Greatest Common Divisor

Read: Chapter 6

Chapter 6 Exercises:
6.2, 6.5 (not to be collected)
Prove the two theorems from the handout (to be collected on Thurs., Sept. 15)

6

Sept. 15

Factorization and the Fundamental Theorem of Arithmetic

Read: Chapter 7

Chapter 7 Exercises:
7.4, 7.5 (not to be collected)

The RSA Challenge Numbers

If you have had Abstract Algebra II, then you might be interested in reading this article about Unique Factorization: http://www.ams.org/featurecolumn/archive/factorization.html

7

Sept. 20

Read: Chapter 8

Work through the exercises from the handout. I will ask volunteers to present these at the board on Thurs (Sept 22.) I will collect any that we do not present in class (on Tues, Sept. 27.)

Chapter 8 Exercises:
8.3, 8.4, 8.5 (not to be collected)

8

Sept. 22

Student Presentations

Linear Congruences

9

Sept. 27

Read: Chapters 9 and 10

Work through the Euler Phi function exercises from the handout. I will ask volunteers to present these at the board next lesson.

Chapter 9 Exercises: 9.1, 9.4

Note: If you are itch'in to do more, then you can start the exercises for Chapter 10 listed below!

10

Sept. 29

Euler's Phi Function (Student Presentations)

The Chinese Remainder Theorem

Read: Chapter 11

Chapter 10 Exercises: 10.1a), 10.2, 10.3

Chapter 11 Exercises: 11.2. 11.3, 11.5, 11.7, 11.12a)
(I will ask volunteers to present solutions next lesson)

11

Oct. 4

12

Oct. 6