ABSTRACT
First published in 2004. This book examines the history and philosophy of the mathematical sciences in a cultural context, tracing their evolution from ancient times up to the twentieth century. Includes 176 articles contributed by authors of 18 nationalities. With a chronological table of main events in the development of mathematics. Has a fully integrated index of people, events and topics; as well as annotated bibliographies of both classic and contemporary sources and provide unique coverage of Ancient and non-Western traditions of mathematics. Presented in Two Volumes.
TABLE OF CONTENTS
part 101|15 pages
Introduction
entry 1
Introduction
part 1|150 pages
Ancient and non-Western traditions
entry 1.0
Introduction
entry 1.1
Babylonian mathematics
entry 1.2
Egyptian mathematics
entry 1.3
Greek mathematics to ad 300
entry 1.4
Greek applied mathematics
entry 1.5
Later Greek and Byzantine mathematics
entry 1.6
Pure mathematics in Islamic civilization
entry 1.7
Mathematics applied to aspects of religious ritual in Islam
entry 1.8
Mathematics in Africa: Explicit and implicit
entry 1.9
Chinese mathematics
entry 1.10
Indigenous Japanese mathematics, Wasan
entry 1.11
Korean mathematics
entry 1.12
Indian mathematics
entry 1.13
Tibetan astronomy and mathematics
entry 1.14
Mathematics in medieval Hebrew literature
entry 1.15
Maya mathematics
entry 1.16
The beginnings of counting and number
entry 1.17
Some ancient solutions to the problem of fractioning numbers
part 2|119 pages
The Western Middle Ages and the Renaissance
entry 2.0
Introduction
entry 2.1
Euclidean and Archimedean traditions in the Middle Ages and the Renaissance
entry 2.2
Practical geometry in the Middle Ages and the Renaissance
entry 2.3
The ‘Coss’ tradition in algebra
entry 2.4
Abbacus arithmetic
entry 2.5
Logarithms
entry 2.6
Medieval and Renaissance mechanics
entry 2.7
Astronomy
entry 2.8
Mathematical methods in medieval and Renaissance technology, and machines
entry 2.9
Mathematical optics from Antiquity to the seventeenth century
entry 2.10
Musical intervals
entry 2.11
The teaching of mathematics in the Middle Ages and the Renaissance
entry 2.12
The philosophical context of medieval and Renaissance mathematics
part 3|202 pages
Calculus and Mathematical Analysis
entry 3.0
Introduction
entry 3.1
Precalculus, 1635–1665
entry 3.2
Three traditions in the calculus: Newton, Leibniz and Lagrange
entry 3.3
Real-variable analysis from Cauchy to non-standard analysis
entry 3.4
Differential geometry
entry 3.5
Calculus of variations
entry 3.6
Set theory and point set topology
entry 3.7
Integral, content and measure
entry 3.8
The early history of fractals, 1870–1920
entry 3.9
Functional analysis
entry 3.10
Integral equations
entry 3.11
Harmonic analysis
entry 3.12
Three traditions in complex analysis: Cauchy, Riemann and Weierstrass
entry 3.13
Geometry in complex function theory
entry 3.14
Ordinary differential equations
entry 3.15
Partial differential equations
entry 3.16
Differential equations and groups
entry 3.17
Potential theory
part 4|106 pages
Functions, Series and Methods in Analysis
entry 4.0
Introduction
entry 4.1
The binomial theorem
entry 4.2
An overview of trigonometry and its functions
entry 4.3
Infinite series and solutions of ordinary differential equations, 1670–1770
entry 4.4
Special functions
entry 4.5
Elliptic integrals and functions
entry 4.6
Abelian integrals
entry 4.7
Operator methods
entry 4.8
The Laplace transform
entry 4.9
Functional equations
entry 4.10
The roots of equations: Detection and approximation
entry 4.11
Solving higher-degree equations
entry 4.12
Nomography
entry 4.13
General numerical mathematics
part 5|113 pages
Logics, Set Theories and the Foundations of Mathematics
entry 5.0
Introduction
entry 5.1
Algebraic logic from Boole to Schröder,1840–1900
entry 5.2
Mathematical logic and logicism from Peano to Quine, 1890–1940
entry 5.3
The set-theoretic paradoxes
entry 5.4
Logic and set theory
entry 5.5
Metamathematics and computability
entry 5.6
Constructivism
entry 5.7
Polish logics
entry 5.8
Model theory
entry 5.9
Some current positions in the philosophy of mathematics
entry 5.10
Algorithms and algorithmic thinking through the ages
entry 5.11
5.11 Calculating machines
entry 5.12
Computing and computers
part 6|134 pages
Algebras and Number Theory
entry 6.0
Introduction
entry 6.1
The theory of equations from Cardano to Galois, 1540–1830
entry 6.2
Complex numbers and vector algebra
entry 6.3
Continued fractions
entry 6.4
Fundamental concepts of abstract algebra
entry 6.5
Lie groups
entry 6.6
Determinants
entry 6.7
Matrix theory
entry 6.8
Invariant theory
entry 6.9
The philosophy of algebra
entry 6.10
Number theory
entry 6.11
Linear optimization
entry 6.12
Operational research