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

Lesson #

Date(s)

Chapter(s)

Topic

Homework Assignment

1

Aug. 29

1, 2

Pythagorean Triples

Chapter 1 Exercises:
1.1, 1.2, 1.3 (volunteer presentations
on Thurs., Sept. 1)

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

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

3

Sept. 6

5
Divisibility and the Greatest Common Divisor

Chapter 5 Exercises:
5.1, 5.3, 5.4a), 5.4b)

(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

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

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

The RSA Challenge Numbers

7

Sept. 20

8
Congruences

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

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

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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