## 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]