Date 
No. 
Title 
07 Sep 21  *

Math 211  Course Information and Course Outline
(2 pages)

 *

Algebraic Methods (2 pages)

 *

Number Systems

08 Sep 21  *

Divisibility

 *

Course Guidelines

 *

The Principle of Induction

10 Sep 21  *

The Euclidean Algorithm

14 Sep 21  *

The Greatest Common Divisor

15 Sep 21  *

MAPLE Homework Instructions

 *

MAPLE Lab #1

 *

MAPLE Hints

 *

Basic MAPLE commands (4pp.)

17 Sep 21  *

The Division Algorithm

 *

The Euclidean Algorithm: First and Second
Version 
 *

The Euclidean Algorithm: Second Version
(formal procedure) 
 *

The Euclidean Algorithm: Example

21 Sep 21  *

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

The Extended Euclidean Algorithm: Theorem 3

 *

Diophantine equations (2 pages)

22 Sep 21  *

The Plimpton 322 Clay Tablet

 *

The GCDcriterion and its consequences

24 Sep 21  *

The General Solution of the Dioph. Eq'n
mx + ny = c 
28 Sep 21  *

How to solve mx + ny =
c 
29 Sep 21  *

Proof of the Formula (2pp.)

 *

How to solve mx + ny + kz = c

01 Oct 21  *

Prime numbers

05 Oct 21  *

Some unsolved conjectures about primes

 *

The Fundamental Theorem of Arithmetic

06 Oct 21  *

The GCDformula

 *

The GCDformula vs. the Euclidean algorithm

08 Oct 21  *

The Calculus of Remainders

19 Oct 21  *

Computing a^n efficiently

22 Oct 21  *

The Cancellation Law

26 Oct 21  *

Solving the Congruence
ax = b (mod m)

27 Oct 21  *

The Ring Z/mZ and the Field F_p

 *

The Wheel Problem

29 Oct 21  *

The Chinese Remainder Theorem

02 Nov 21  *

Fermat's Little Theorem

03 Nov 21  *

Mersenne Numbers

 *

The Binomial Theorem (2pp.)

05 Nov 21  *

Public Key Cryptography (2pp.)

 *

The Dancing Men

09Nov 21  *

The RSA Method (2pp.)

 *

The RSA155 Challenge (3pp.)

 *

The History of Algebra

10 Nov 21  *

Complex Numbers (History)

 *

Complex Numbers

12 Nov 21  *

Complex Numbers (pages 2 and 3)

 *

Arctan and Argument

 *

Solutions of z^n = a

16 Nov 21  *

The sixth roots of a = 1 + i etc.

 *

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

 *

Polynomials

 *

The Degree of a Polynomial

17 Nov 21  *

The Division Algorithm (for Polynomials)

19 Nov 21  *

The Remainder Theorem (2pp.)

23 Nov 21  *

The Euclidean Algorithm (for Polynomials)

24 Nov 21  *

The GCDcriterion (for Polynomials)

 *

Irreducible Polynomials

 *

The Quadratic Formula

26 Nov 21  *

Irreducible Quadratic Polynomials over
Fp for p le 5

 *

Unique Factorization for Polynomials

 *

The Multiplicity of a Root

30 Nov 21  *

Rules for Factoring over Q (3pp.)

 *

The Fundamental Theorem of Algebra (2pp.)

01 Dec 21  *

The Factorization Theorem over R[x]

03 Dec 21  *

Solutions of Polynomial Equations (2pp.)

 *

Term 1 Review (2pp.)
