## Math 211

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 Section Title Chapter 0: Introduction What is Algebra? Al-Khwarizmi 780-850 (St. Andrew's U.) Arabic Numerals (St. Andrew's U.) Indian Numerals (St. Andrew's U.) Number Systems Leopold Kronecker 1823-1891 (St. Andrew's U.) Chapter 1: The Integers 1.1 Introduction 1.2 Divisibility 1.3 The Euclidean Algorithm, First Version Euclid 325-265 B.C. (St. Andrew's U.) 1.4 The Greatest Common Divisor 1.5 The Division Algorithm 1.6 The Euclidean Algorithm, Second Version 1.7 The Extended Euclidean Algorithm Indian Mathematics (Overview) (St. Andrew's U.) 1.8 Linear Diophantine Equations Diophantus 200-284 (St. Andrew's U.) Pierre Fermat 1601-1665 (St. Andrew's U.) Plimpton 322 Tablet (St. Andrew's U.) Fermat's Last Theorem (St. Andrew's U.) Fermat's Last Theorem (Queen's U.) 1.9 Unique Factorization Eratosthenes of Cyrene 276-194 B.C. (St. Andrew's U.) Prime Numbers (St. Andrew's U.) Chapter 2: Modular Arithmetic 2.1 Introduction 2.2 The Calculus of Remainders Carl Friederich Gauss 1777-1855 (St. Andrew's U.) A computer game based on the "Casting-out Nines" rule 2.3 The Cancellation Law 2.4 Solving Congruence Equations 2.5 The Ring Z/mZ and the Field F_p 2.6 The Chinese Remainder Theorem Indian Mathematics (Overview) (St. Andrew's U.) 2.7 Fermat's Theorem Pierre Fermat 1601-1665 (St. Andrew's U.) Father Marin Mersenne 1588-1641 (St. Andrew's U.) Prime Numbers (and Fermat's Theorem) (St. Andrew's U.) Blaise Pascal 1623-1665 (St. Andrew's U.) 2.8 Public Key Cryptography Introduction to Cryptography (PGP) RSA on the internet Chapter 3: Polynomials 3.1 Introduction Scipione del Ferro 1465-1526 (St. Andrew's U.) Nicolo Tartaglia 1499-1557 (St. Andrew's U.) Girolamo Cardano 1501-1576 (St. Andrew's U.) Ludovico Ferrari 1522-1565 (St. Andrew's U.) Paolo Ruffini 1765-1822 (St. Andrew's U.) Abel 1802-1829 (St. Andrew's U.) Evariste Galois 1811-1832 (St. Andrew's U.) The Fundamental Theorem of Algebra (St. Andrew's U.) Quadratic, Cubic and Quartic Equations (St. Andrew's U.) 3.2 Review of Complex Numbers Rafael Bombelli 1526-1572 (St. Andrew's U.) Jacob Benoulli 1654-1705 (St. Andrew's U.) Albert Girard 1595-1632 (St. Andrew's U.) Rene Descartes 1596-1650 (St. Andrew's U.) Abraham De Moivre 1667-1754 (St. Andrew's U.) Leonard Euler 1707-1783 (St. Andrew's U.) Caspar Wessel 1745-1818 (St. Andrew's U.) Jean Robert Argand 1768-1822 (St. Andrew's U.) Gauss 1777-1855 (St. Andrew's U.) 3.3 Polynomials: First Properties 3.4 The Division Algorithm 3.5 The Remainder Theorem Rene Descartes 1596-1650 (St. Andrew's U.) Jean Le Ronde Alembert 1717-1783 (St. Andrew's U.) 3.6 The Euclidean Algorithm 3.7 Unique Factorization 3.8 Factoring Methods Abel 1802-1829 (St. Andrew's U.) Evariste Galois 1811-1832 (St. Andrew's U.) The Fundamental Theorem of Algebra (St. Andrew's U.) Quadratic, Cubic and Quartic Equations (St. Andrew's U.)