Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences

Babylonian Mathematics

Egyptian Mathematics

Greek Mathematics to AD 300

Greek Applied Mathematics

Later Greek and Byzantine mathematics

Pure mathematics in Islamic civilization

Mathematics Applied to Aspects of Religious Ritual in Islam

Mathematics in Africa

Chinese Mathematics

Indigenous Japanese Mathematics, Wasan

Korean Mathematics

Indian Mathematics

Tibetan Astronomy and Mathematics

Mathematics in Medieval Hebrew Literature

Maya Mathematics

The Beginnings of Counting and Number

Some ancient Solutions to the Problem of Fractioning Numbers

Introduction

Euclidean and Archimedean Traditions in the Middle Ages and the Renaissance

Practical Geometry in the Middle Ages and the Renaissance

The ‘ Coss' Tradition in algebra

Abbacus Arithmetic

Logarithms

Medieval and Renaissance Mechanics

Astronomy

Mathematical Methods in Medieval and Renaissance Technology, and Machines

Mathematical Optics from Antiquity to the Seventeenth Century

Musical Intervals

The teaching of Mathematics in the Middle Ages and the Renaissance

The Philosophical Context of Medieval and Renaissance Mathematics

Introduction

Precalculus, 1635–1665

Three Traditions in the Calculus

Real-Variable Analysis from Cauchy to Non-Standard Analysis

Differential Geometry

Calculus of variations

Set Theory and Point Set Topology

Integral, Content and Measure

The Early History of Fractals, 1870–1920

Functional Analysis

Integral Equations

Harmonic Analysis

Three Traditions in Complex Analysis

Geometry in Complex Function Theory

Ordinary Differential Equations

Partial Differential Equations

Differential Equations and Groups

Potential Theory

Introduction

The Binomial Theorem

An Overview of Trigonometry and its Functions

Infinite Series and Solutions of Ordinary Differential Equations, 1670–1770

Special Functions

Elliptic Integrals and Functions

Abelian Integrals

Operator Methods

The Laplace Transform

Functional Equations

The Roots of Equations

Solving Higher-Degree Equations

Nomography

General Numerical Mathematics

Introduction

Algebraic Logic from Boole to Schröder, 1840–1900

Mathematical Logic and Logicism from Peano to Quine, 1890–1940

The Set-Theoretic Paradoxes

Logic and Set Theory

Metamathematics and Computability

Constructivism

Polish Logics

Model Theory

Some Current Positions in The Philosophy of Mathematics

Algorithms and Algorithmic Thinking Through the Ages

Calculating Machines

Computing and Computers

Introduction

The Theory of Equations from Cardano to Galois, 1540–1830

Complex Numbers and Vector Algebra

Continued Fractions

Fundamental Concepts of Abstract Algebra

Lie Groups

Determinants

Matrix Theory

Determinants

The Philosophy of Algebra

Number theory

Linear optimization

Operational research

Introduction

Algebraic and analytic geometry

Curves

Regular polyhedra

Euclidean and non-Euclidean geometry

Descriptive geometry

Projective geometry

Line geometry

The philosophy of geometry to 1900

Early modern algebraic geometry

Topology

Topology

Finite-dimensional vector spaces

Combinatorics

Introduction

Classical mechanics

Graphical statics

Kinematics

Feedback control systems

Hydrodynamics and hydraulics

Theories of elasticity

The theory of structures

The dynamics of the Solar System

The three-body problem

Astrophysics and cosmology

Ballistics and Projectiles

The pendulum:

Geodesy

Cartography

The Tides

Shipbuilding and Ship Operation

Astronomical navigation

Physical optics

The velocity of light

Optics and optical instruments, 1600–1800

Heat diffusion

Thermodynamics

Geophysics

Meteorology

Acoustics

Capillarity

Mathematical theories of electricity and magnetism to 1900

Telecommunication Theory

Electrical machines

Relativity

Statistical mechanics

Quantum mechanics

Mathematics in chemistry

Crystallography

Mathematical biology

Introduction

Combinatorial Probability

The Early Development of Mathematical Probability

Actuarial Mathematics

Estimating and Testing the Standard Linear Statistical Model

Theory of Errors

Russian Probability and Statistics Before Kolmogorov

The English Biometric Tradition

Probability, Statistics and the Social Sciences

Psychology and Probability

Probability and statistics in genetics

Probability and Statistics in Agronomy

Probabilistic and Statistical Methods in Medicine

Probability and Statistics in Mechanics

Statistical Control of Manufacture

The Social Organization of Probability and Statistics

Foundations of Probability

Philosophies of Probability

Mathematical Economics

Introduction

France

Germany to 1933

Austria and Hungary

The Netherlands

Scandinavia

Russia and the Soviet Union

The British Isles

The Italian States

Spain, Portugal and Ibero-America, 1780–1930

The United States of America, and Canada

Women and Mathematics

Mathematical Journals

Introduction

Ethnomathematics

Mathematical Games

Recreational Mathematics

The Golden Number, and Division in Extreme and Mean Ratio

Numerology and Gematria

Art and Architecture

Symmetries in Mathematics

Tilings

Mathematics and Prose Literature

Mathematics and Poetry

Stamping Mathematics

Monuments to Mathematics and Mathematicians

Talepiece

Introduction

Select Bibliography of General Sources

Chronology

Biographical Notes

List of Authors and Board Members