Lesson #

Date(s)

Topic

Homework Assignment

1

Aug. 25

Read: Chapters 1 and 2

Read about the Plimpton 322 tablet!

Chapter 1 Exercises:
#1.1, 1.2, 1.3 (volunteer presentation of 1.1
on Tues., Aug. 30)
Some comments about this assignment

Chapter 2 Exercises:
#2.1, 2.2, 2.5, 2.7 (to be collected on
Tues., Aug. 30)
Warning: There is a typo in Exercise 2.5(a)

2

Aug. 30

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:
#3.2, 3.3, 3.4 (to be collected on
Tues., Sept. 6)

And do Exercises 1-5 from the Divisibility Handout (Presentations of #3 and 5 next lesson)

3

Sept. 1

Read: Chapter 5

Chapter 5 Exercises:
#5.1, 5.3, 5.4a), 5.4b) (Due Tues, Sept 6, but not to be collected)

Also do the continued fractions problem from the handout (not to be collected)

4

Sept. 6

Linear Equations and the Greatest Common Divisor

Read: Chapter 6

Chapter 6 Exercises: #6.2a) and 6.5 in your text (pp. 41-42) (not to be collected)

Complete items 2 and 3 from handout (to be collected on Thursday, September 8)

5

Sept. 8

Factorization and the Fundamental Theorem of Arithmetic

Read: Chapter 7

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

Read the "Congruence" handout, completing all exercises along the way...
Do #5, 6, 7 for submission on Tuesday and #12, 13, 14, 15, 17 for presentation on Tuesday (or Thursday)

Theorem 12, part 1) - Group Door
Theorem 12, part 2) - Group Window
Exercise 14 - Group Door
Exercise 15 part a) - Group Window
Exercise 15 part b) - Group Door
Exercise 15 part c) - Group Window
Exercise 17 - Groups Door and Window

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

6

Sept. 13

Congruences

Read: Chapter 8

Chapter 8 Exercises: 8.3,8.4,8.5 (to be collected on Thursday, September 22)

7

Sept. 15

8

Sept. 20

Student Presentations

Linear Congruences

9

Sept. 22

Read: Chapters 9 and 10

Chapter 9 Exercises: 9.1, 9.4 (not to be collected)
and complete the "Mastering the Euler Phi function" exercises from the handout. Volunteers will present the solutions to these exercises next time.

10

Sept. 27

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)

You will present the solutions to these problems next lesson.

11

Sept. 29

12

Oct. 4

Exam I (in-class)
Take-home portion will be distributed