Date 
No. 
Title 
12 Sep 17  01/02

Math 211  Course Information and Course Outline
(2 pages)

 *

Algebraic Methods (2 pages)

 *

Number Systems

14 Sep 17  *

Divisibility

 *

Course Guidelines

15 Sep 17  *

The Principle of Induction

 *

The Euclidean Algorithm

19 Sep 17  *

The Greatest Common Divisor

21 Sep 17  *

The Division Algorithm

 *

The Euclidean Algorithm: First and Second
Version 
22 Sep 17  03

MAPLE Homework Instructions

 04

MAPLE hints

 *

Computer Lab: MAPLE printout (5pp.)

 *

Basic MAPLE commands (4pp.)

26 Sep 17  *

The Euclidean Algorithm: Second Version
(formal procedure) 
 *

The Extended Euclidean Algorithm:
Examples 1 and 2 (2pp.) 
 *

The Extended Euclidean Algorithm: Theorem 3

28 Sep 17  *

Diophantine equations (2 pages)

 *

The Plimpton 322 Clay Tablet

 *

The GCDcriterion and its consequences

29 Sep 17  *

The General Solution of the Dioph. Eq'n
mx + ny = c 
03 Oct 17  *

How to solve mx + ny =
c 
05 Oct 17  *

Proof of the Formula (2pp.)

06 Oct 17  *

How to solve mx + ny + kz = c

10 Oct 17  *

Prime numbers

 *

Some unsolved conjectures about primes

12 Oct 17  *

The Fundamental Theorem of Arithmetic

13 Oct 17  *

The GCDformula

 *

The GCDformula vs. the Euclidean algorithm

17 Oct 17  *

The Calculus of Remainders

19 Oct 17  *

Computing a^n efficiently

20 Oct 17  *

The Cancellation Law

24 Oct 17  *

Solving the Congruence
ax = b (mod m)

 *

The Ring Z/mZ and the Field F_p

27 Oct 17  *

The Wheel Problem

 *

The Chinese Remainder Theorem

02 Nov 17  *

Fermat's Little Theorem

 *

Mersenne Numbers

03 Nov 17  *

The Binomial Theorem (2pp.)

07 Nov 17  *

Public Key Cryptography (2pp.)

 *

The Dancing Men

09 Nov 17  *

The RSA Method (2pp.)

 *

The RSA155 Challenge

 *

The History of Algebra

 *

Complex Numbers (History)

10 Nov 17  *

Complex Numbers

 *

Arctan and Argument

14 Nov 17  *

Solutions of z^n = a

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The sixth roots of a = 1 + i etc.

 *

Solutions of z^6 = 1 + sqrt(3) etc.

16 Nov 17  *

Polynomials

 *

The Degree of a Polynomial

17 Nov 17  *

The Division Algorithm (for Polynomials)

21 Nov 17  *

The Remainder Theorem (2pp.)

23 Nov 17  *

The Euclidean Algorithm (for Polynomials)

24 Nov 17  *

The GCDcriterion (for Polynomials)

 *

Irreducible Polynomials

28 Nov 17  *

The Quadratic Formula

 *

Irreducible Quadratic Polynomials over
Fp for p le 5

 *

Unique Factorization for Polynomials

30 Nov 17  *

The Multiplicity of a Root

 *

Rules for Factoring over Q (2pp.)

01 Dec 17  *

The Fundamental Theorem of Algebra

 *

The Factorization Theorem over R[x]
