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A History of Mathematics

by ;
Edition:
3rd
ISBN13:

9780470525487

ISBN10:
0470525487
Format:
Paperback
Pub. Date:
1/11/2011
Publisher(s):
Wiley
List Price: $42.61

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Summary

The updated new edition of the classic and comprehensive guide to the history of mathematicsFor more than forty years, A History of Mathematics has been the reference of choice for those looking to learn about the fascinating history of humankind's relationship with numbers, shapes, and patterns. This revised edition features up-to-date coverage of topics such as Fermat's Last Theorem and the Poincare Conjecture, in addition to recent advances in areas such as finite group theory and computer-aided proofs. Distills thousands of years of mathematics into a single, approachable volume Covers mathematical discoveries, concepts, and thinkers, from Ancient Egypt to the present Includes up-to-date references and an extensive chronological table of mathematical and general historical developments.Whether you're interested in the age of Plato and Aristotle or Poincare and Hilbert, whether you want to know more about the Pythagorean theorem or the golden mean, A History of Mathematics is an essential reference that will help you explore the incredible history of mathematics and the men and women who created it.

Author Biography

Uta C. Merzbach is Curator Emeritus of Mathematics at the Smithsonian Institution and Director of the LHM Institute

The late Carl B. Boyer was a professor of Mathematics at Brooklyn College and the author of several classic works on the history of mathematics.

Table of Contents

Foreword
Preface to the First Edition
Preface to the Second Edition
Traces
Concepts and Relationships
Early Number Bases
Number Language and Counting
Spatial Relationships
Ancient Egypt
The Era and the Sources
Numbers and Fractions
Arithmetic Operations
"Heap" Problems
Geometric Problems
Slope Problems
Arithmetic Pragmatism
Mesopotamia
The Era and the Sources
Cuneiform Writing
Numbers and Fractions; Sexagesimals
Positional Numeration
Sexagesimal Fractions
Approximations
Tables
Equations
Measurements: Pythagorean Triads
Polygonal Areas
Geometry as Applied Arithmetic
Hellenic Traditions
The Era and the Sources
Thales and Pythagoras
Numeration
Arithmetic and Logistic
Fifth Century Athens
Three Classical Problems
Incommensurability
Paradoxes of Zeno
Deductive Reasoning
Democritus of Abdera
Mathematics and the Liberal Arts
The Academy
Aristotle
Euclid of Alexandria
Alexandria
Lost Works
Extant Works
The Elements
Archimedes of Syracuse
The Siege of Syracuse
On the Equilibriums of Planes
On Floating Bodies
The Sand-Reckoner
Measurement of the Circle
On Spirals
Quadrature of the Parabola
On Conoids and Spheroids
On the Sphere and Cylinder
Book of Lemmas
Semiregular Solids and Trigonometry
The Method
Apollonius of Perge
Works and Tradition
Lost Works
Cycles and Epicycles
The Conics
Cross-Currents
Changing Trends
Eratosthenes
Angles and Chords
Ptolemy's Almagest
Heron of Alexandria
Decline of Greek Mathematics
Nichomachus of Gerasa
Diophantus of Alexandria
Pappus of Alexandria
The End of Alexandrian Dominance
Proclus of Alexandria
Boethius
Athenian Fragments
Byzantine Mathematicians
Ancient and Medieval China
The Oldest Known Texts
The Nine Chapters
Rod Numerals
The Abacus and Decimal Fractions
Values of Pi
Thirteenth-Century Mathematics
Ancient and Medieval India
Early Mathematics in India
The Sulbasutras
The Siddhantas
Aryabhata
Numerals
Trigonometry
Multiplication
Long Division
Brahmagupta
Indeterminate Equations
Bhaskara
Madhava and the Keralese School
The Islamic Hegemony
Arabic Conquests
The House of Wisdom
al-Khwarizmi
'Abd Al-Hamid ibn-Turk
Thabit ibn Qurra
Numerals
Trigonometry
Abu'l-Wefa and Al-Karkhi
Al-Biruni and Alhazen
Omar Khayyam
The Parallel Postulate
Nasir al-Din al-Tusi
Al-Kashi
The Latin West
Introduction
Compendia of the Dark Ages
Gerbert
The Century of Translation
Abacists and Algorists
Fibonacci
Jordanus Nemorarius
Campanus of Novara
Learning in the Thirteenth Century
Archimedes Revived
Medieval Kinematics
Thomas Bradwardine
Nicole Oresme
The Latitude of Forms
Infinite Series
Levi ben Gerson
Nicholas of Cusa
Decline of Medieval Learning
The European Renaissance
Overview
Regiomontanus
Nicolas Chuquet's Triparty
Luca Pacioli's Summa
German Algebras and Arithmetics
Cardan's Ars Magna
Rafael Bombelli
Robert Recorde
Trigonometry
Geometry
Renaissance Trends
François Viète
Early Modern Problem Solvers
Accessibility of Computation
Decimal Fractions
Notation
Logarithms
Mathematical Instruments
The Infinite and Italian Curves
Infinitesimal Methods: Stevin
Johannes Kepler
Galileo's Two New Sciences
Bonaventura Cavalieri
Evangelista Torricelli
Analysis, Synthesis, and Numbers
Mersenne's Communicants
Descartes
Fermat's Loci
Gregory of St. Vincent
Theory of Numbers
Gilles Persone de Roberval
Girard Desargues and Projective Geometry
Blaise Pascal
Philippe de Lahire
Georg Mohr
Pietro Mengoli
Frans van Schooten
Jan de Witt
Johann Hudde
René François de Sluse
Christiaan Huygens
Newton and British Techniques
John Wallis
James Gregory
Nicolaus Mercator and William Brouncker
Barrow's Method of Tangents
Newton
Abraham De Moivre
Leibniz and Continental Methods
Leibniz: Early Career and Travels
The Bernoulli Family
Tschirnhaus Transformations
Solid Analytic Geometry
Michel Rolle and Pierre Varignon
The Clairauts
Mathematics in Italy
The Parallel Postulate
Divergent Series
Euler
Life of Euler
Notation
Foundation of Analysis
Logarithms and the Euler Identities
Differential Equations
Probability
Theory of Numbers
Textbooks
Analytic Geometry
The Parallel Postulate: Lambert
Pre- to Post-Revolutionary France
Men and Institutions
The Committee on Weights and Measures
D?Alembert
B‚zout
Condorcet
Lagrange
Monge
Carnot
Laplace
Legendre
Aspects of Abstraction
Paris in the 1820s
Fourier
Cauchy
Diffusion
Gauss
Nineteenth-Century Overview
Gauss: Early Work
Number Theory
Reception of the Disquisitiones Arithmeticae
Astronomy
Gauss's Middle Years
Differential Geometry
Gauss's Later Work
Gauss's Influence
Geometry
The School of Monge
Projective Geometry: Poncelet and Chasles
Synthetic Metric Geometry: Steiner
Synthetic Nonmetric Geometry: von Staudt
Analytic Geometry
Non-Euclidean Geometry
Riemannian Geometry
Spaces of Higher Dimensions
Felix Klein
Post-Riemannian Algebraic Geometry
Algebra
Introduction
British Algebra and the Operational Calculus of Functions
Boole and the Algebra of Logic
Augustus De Morgan
William Rowan Hamilton
Grassmann and Ausdehnungslehre
Cayley and Sylvester
Linear Associative Algebras
Algebraic Geometry
Algebraic and Arithmetic Integers
Axioms of Arithmetic
Analysis
Berlin and Göttingen at Mid-Century
Riemann in Göttingen
Mathematical Physics in Germany
Mathematical Physics in English-Speaking Countries
Weierstrass and Students
The Arithmetization of Analysis
Dedekind
Cantor and Kronecker
Analysis in France
Poincaé and Hilbert
Turn-of-the-Century Overview
Poincar‚
Hilbert
Twentieth Century Legacies: Pre-1930
General Overview
Integration and Measure
Functional Analysis and General Topology
Algebra
Differential Geometry and Tensor Analysis
Probability
Bounds and Approximations
Twentieth Century Legacies: Post-1930
The 1930s and World War II
Homological Algebra and Category Theory
Bourbaki
Algebraic Geometry
Logic and Computing
Recent Trends
Overview
The Four Color Conjecture
Classification of Finite Simple Groups
Fermat's Last Theorem
Poincaré's Query
Future Outlook
References
General Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.


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