## 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 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.)