Math 211

Index of Hand-outs



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 print-out (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 GCD-criterion 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 GCD-formula
* The GCD-formula 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 RSA-155 Challenge
* The History of Algebra
* Complex Numbers (History)
10 Nov 17 * Complex Numbers
* Arctan and Argument
14 Nov 17 * Solutions of z^n = a
* 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 GCD-criterion (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]



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