The History of Mathematics: An Introduction
, by Burton, David ISBN: 9780073383156  0073383155
 Cover: Hardcover
 Copyright: 2/9/2010

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The History of Mathematics: An Introduction, Seventh Edition, is written for the one or twosemester math history course taken by juniors or seniors, and covers the history behind the topics typically covered in an undergraduate math curriculum or in elementary schools or high schools.
Elegantly written in David Burton’s imitable prose, this classic text provides rich historical context to the mathematics that undergrad math and math education majors encounter every day. Burton illuminates the people, stories, and social context behind mathematics’ greatest historical advances while maintaining appropriate focus on the mathematical concepts themselves. Its wealth of information, mathematical and historical accuracy, and renowned presentation make The History of Mathematics: An Introduction, Seventh Edition a valuable resource that teachers and students will want as part of a permanent library.
Preface  
Early Number Systems and Symbols  
Primitive Counting  
A Sense of Number  
Notches as Tally Marks  
The Peruvian Quipus: Knots as Numbers  
Number Recording of the Egyptians and Greeks  
The History of Herodotus  
Hieroglyphic Representation of Numbers  
Egyptian Hieratic Numeration  
The Greek Alphabetic Numeral System  
Number Recording of the Babylonians  
Babylonian Cuneiform Script  
Deciphering Cuneiform: Grotefend and Rawlinson  
The Babylonian Positional Number System  
Writing in Ancient China  
Mathematics in Early Civilizations  
The Rhind Papyrus  
Egyptian Mathematical Papyri  
A Key to Deciphering: The Rosetta Stone  
Egyptian Arithmetic  
Early Egyptian Multiplication  
The Unit Fraction Table  
Representing Rational Numbers  
Four Problems from the Rhind Papyrus  
The Method of False Position  
A Curious Problem  
Egyptian Mathematics as Applied Arithmetic  
Egyptian Geometry  
Approximating the Area of a Circle  
The Volume of a Truncated Pyramid  
Speculations About the Great Pyramid  
Babylonian Mathematics  
A Tablet of Reciprocals  
The Babylonian Treatment of Quadratic Equations  
Two Characteristic Babylonian Problems  
Plimpton  
A Tablet Concerning Number Triples  
Babylonian Use of the Pythagorean Theorem  
The Cairo Mathematical Papyrus  
The Beginnings of Greek Mathematics  
The Geometric Discoveries of Thales  
Greece and the Aegean Area  
The Dawn of Demonstrative Geometry: Thales of Miletos  
Measurements Using Geometry  
Pythagorean Mathematics  
Pythagoras and His Followers  
Nichomachus' Introductio Arithmeticae  
The Theory of Figurative Numbers  
Zeno's Paradox  
The Pythagorean Problem  
Geometric Proofs of the Pythagorean Theorem  
Early Solutions of the Pythagorean Equation  
The Crisis of Incommensurable Quantities  
Theon's Side and Diagonal Numbers  
Eudoxus of Cnidos  
Three Construction Problems of Antiquity  
Hippocrates and the Quadrature of the Circle  
The Duplication of the Cube  
The Trisection of an Angle  
The Quadratrix of Hippias  
Rise of the Sophists  
Hippias of Elis  
The Grove of Academia: Plato's Academy  
The Alexandrian School: Euclid  
Euclid and the Elements  
A Center of Learning: The Museum  
Euclid's Life and Writings  
Euclidean Geometry  
Euclid's Foundation for Geometry  
Book I of the Elements  
Euclid's Proof of the Pythagorean Theorem  
Book II on Geometric Algebra  
Construction of the Regular Pentagon  
Euclid's Number Theory  
Euclidean Divisibility Properties  
The Algorithm of Euclid  
The Fundamental Theorem of Arithmetic  
An Infinity of Primes  
Eratosthenes, the Wise Man of Alexandria  
The Sieve of Eratosthenes  
Measurement of the Earth  
The Almagest of Claudius Ptolemy  
Ptolemy's Geographical Dictionary  
Archimedes  
The Ancient World's Genius  
Estimating the Value of p  
The SandReckoner  
Quadrature of a Parabolic Segment  
Apollonius of Perga: The Conics  
The Twilight of Greek Mathematics: Diophantus  
The Decline of Alexandrian Mathematics  
The Waning of the Golden Age  
The Spread of Christianity  
Constantinople, A Refuge for Greek Learning  
The Arithmetica  
Diophantus's Number Theory  
Problems from the Arithmetica  
Diophantine Equations in Greece, India, and China  
The Cattle Problem of Archimedes  
Early Mathematics in India  
The Chinese Hundred Fowls Problem  
The Later Commentators  
The Mathematical Collection of Pappus  
Hypatia, the First Woman Mathematician  
Roman Mathematics: Boethius and Cassiodorus  
Mathematics in the Near and Far East  
The Algebra of alKhowârizmî  
Abû Kamil and Thâbit ibn Qurra  
Omar Khayyam  
The Astronomers alTusi and alKarashi  
The Ancient Chinese Nine Chapters  
Later Chinese Mathematical Works  
The First Awakening: Fibonacci  
The Decline and Revival of Learning  
The Carolingian PreRenaissance  
Transmission of Arabic Learning to the West  
The Pioneer Translators: Gerard and Adelard  
The Liber Abaci and Liber Quadratorum  
The HinduArabic Numerals  
Fibonacci's Liver Quadratorum  
The Works of Jordanus de Nemore  
The Fibonacci Sequence  
The Liber Abaci's Rabbit Problem  
Some Properties of Fibonacci Numbers  
Fibonacci and the Pythagorean Problem  
Pythagorean Number Triples  
Fibonacci's Tournament Problem  
The Renaissance of Mathematics: Cardan and Tartaglia  
Europe in the Fourteenth and Fifteenth Centuries  
The Italian Renaissance  
Artificial Writing: The Invention of Printing  
Founding of the Great Universities  
A Thirst for Classical Learning  
The Battle of the Scholars  
Restoring the Algebraic Tradition: Robert Recorde  
The Italian Algebraists: Pacioli, del Ferro and Tartaglia  
Cardan, A Scoundrel Mathematician  
Cardan's Ars Magna  
Cardan's Solution of the Cubic Equation  
Bombelli and Imaginary Roots of the Cubic  
Ferrari's Solution of the Quartic Equation  
The Resolvant Cubic  
The Story of the Quintic Equation: Ruffini, Abel and Galois  
The Mechanical World: Descartes and Newton  
The Dawn of Modern Mathematics  
The Seventeenth Century Spread of Knowledge  
Galileo's Telescopic Observations  
The Beginning of Modern Notation: Francois Vièta  
The Decimal Fractions of Simon Steven  
Napier's Invention of Logarithms  
The Astronomical Discoveries of Brahe and Kepler  
Descartes: The Discours de la Méthod  
The Writings of Descartes  
Inventing Cartesian Geometry  
The Algebraic Aspect of La Géometrie  
Descartes' Principia Philosophia  
Perspective Geometry: Desargues and Poncelet  
Newton: The Principia Mathematica  
The Textbooks of Oughtred and Harriot  
Wallis' Arithmetica Infinitorum  
The Lucasian Professorship: Barrow and Newton  
Newton's Golden Years  
The Laws of Motion  
Later Years: Appointment to the Mint  
Gottfried Leibniz: The Calculus Controversy  
The Early Work of Leibniz  
Leibniz's Creation of the Calculus  
Newton's Fluxional Calculus  
The Dispute over Priority  
Maria Agnesi and Emilie du Châtelet  
The Development of Probability Theory: Pascal, Bernoulli, and Laplace  
The Origins of Probability Theory  
Graunt's Bills of Mortality  
Games of Chance: Dice and Cards  
The Precocity of the Young Pascal  
Pascal and the Cycloid  
De Méré's Problem of Points  
Pascal's Arithmetic Triangle  
The Traité du Triangle Arithmétique  
Mathematical Induction  
Francesco Maurolico's Use of Induction  
The Bernoullis and Laplace  
Christiaan Huygens's Pamphlet on Probability  
The Bernoulli Brothers: John and James  
De Moivre's Doctrine of Chances  
The Mathematics of Celestial Phenomena: Laplace  
Mary Fairfax Somerville  
Laplace's Research on Probability Theory  
Daniel Bernoulli, Poisson, and Chebyshev  
The Revival of Number Theory: Fermat, Euler, and Gauss  
Martin Mersenne and the Search for Perfect Numbers  
Scientific Societies  
Marin Mersenne's Mathematical Gathering  
Numbers, Perfect and Not So Perfect  
From Fermat to Euler  
Fermat's Arithmetica  
The Famous Last Theorem of Fermat  
The EighteenthCentury Enlightenment  
Maclaurin's Treatise on Fluxions  
Euler's Life and Contributions  
The Prince of Mathematicians: Carl Friedrich Gauss  
The Period of the French Revolution: Lagrange, Monge, and Carnot  
Gauss's Disquisitiones Arithmeticae  
The Legacy of Gauss: Congruence Theory  
Dirichlet and Jacobi  
NineteenthCentury Contributions: Lobachevsky to Hilbert  
Attempts to Prove the Parallel Postulate  
The Efforts of Proclus, Playfair, and Wallis  
Saccheri Quadrilaterals  
The Accomplishments of Legendre  
Legendre's Eléments de géometrie  
The Founders of NonEuclidean Geometry  
Gauss's Attempt at a New Geometry  
The Struggle of John Bolyai  
Creation of NonEuclidean Geometry: Lobachevsky  
Models of the New Geometry: Riemann, Beltrami, and Klein  
Grace Chisholm Young  
The Age of Rigor  
D'Alembert and Cauchy on Limits  
Fourier's Series  
The Father of Modern Analysis, Weierstrass  
Sonya Kovalevsky  
The Axiomatic Movement: Pasch and Hilbert  
Arithmetic Generalized  
Babbage and the Analytical Engine  
Peacock's Treatise on Algebra  
The Representations of Complex Numbers  
Hamilton's Discovery of Quaternions  
Matrix Algebra: Cayley and Sylvester  
Boole's Algebra of Logic  
Transition to the Twenthieth Century: Cantor and Kronecker  
The Emergence of American Mathematics  
Ascendency of the German Universities  
American Mathematics Takes Root: 18001900  
The Twentieth Century Consolidation  
Counting the Infinite  
The Last Universalist: Poincaré  
Cantor's Theory of Infinite Sets  
Kronecker's View of Set Theory  
Countable and Uncountable Sets  
Transcendental Numbers  
The Continuum Hypothesis  
The Paradoxes of Set Theory  
The Early Paradoxes  
Zermelo and the Axiom of Choice  
The Logistic School: Frege, Peano and Russell  
Hilbert's Formalistic Approach  
Brouwer's Intuitionism  
Extensions and Generalizations: Hardy, Hausdorff, and Noether  
Hardy and Ramanujan  
The Tripos Examination  
The Rejuvenation of English Mathematics  
A Unique Collaboration: Hardy and Littlewood  
India's Prodigy, Ramanujan  
The Beginnings of PointSet Topology  
Frechet's Metric Spaces  
The Neighborhood Spaces of Hausdorff  
Banach and Normed Linear Spaces  
Some TwentiethCentury Developments  
Emmy Noether's Theory of Rings  
Von Neumann and the Computer  
Women in Modern Mathematics  
A Few Recent Advances  
General Bibliography  
Additional Reading  
The Greek Alphabet  
Solutions to Selected Problems  
Index  
Table of Contents provided by Publisher. All Rights Reserved. 