Math 211

Index of Hand-outs



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 GCD-criterion 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 GCD-formula
* The GCD-formula 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 RSA-155 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 GCD-criterion (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