- BLOCK I -
Pythagorean Triples, Divisibility,
Unique Factorization and Modular Arithmetic

Lesson #

Date(s)

Chapter(s)

Topic

Homework Assignment

1

Aug. 29

1, 2
Course Admin.

Pythagorean Triples

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

3, 4

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

5
Divisibility and the Greatest Common Divisor

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

5

The 3n+1 Conjecture

5

Sept. 13

6

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

7

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

8
Congruences

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

8

Student Presentations

Linear Congruences

9

Sept. 27

9, 10
Fermat's Little Theorem and
Euler's Generalization

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

11

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

9 - 11
Problem Solving Study Study Study!!!

12

Oct. 6

1 - 11
Exam 1 (in-class) The take-home portion of the exam is due at the beginning of class on Thursday, October 13. Choose any 48-hour period between now and then to complete the exam.
~ ~ ~ OCTOBER 10-11 ~ ~ READING DAYS ~ ~ ~
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