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.

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