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.)




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