A History of Algorithms - From the Pebble to the Microchip

A Source Book for the History of Mathematics, but one which offers a different perspective by focusinng on algorithms. With the development of computing has come an awakening of interest in algorithms. Often neglected by historians and modern scientists, more concerned with the nature of concepts, algorithmic procedures turn out to have been instrumental in the development of fundamental ideas: practice led to theory just as much as the other way round. The purpose of this book is to offer a historical background to contemporary algorithmic practice.

Contents

1 Algorithms for Arithmetic Operations 7
2 Magic Squares 49
3 Methods of False Position 83
4 Euclid's Algorithm 113
5 From Measuring the Circle to Calculating [pi] 139
6 Newton's Methods 169
7 Solving Equations by Successive Approximations 199
8 Algorithms in Arithmetic 239
9 Solving Systems of Linear Equations 283
10 Tables and Interpolation 319
11 Approximate Quadratures 353
12 Approximate Solutions of Differential Equations 373
13 Approximation of Functions 405
14 Acceleration of Convergence 429
15 Towards the Concept of Algorithm 455

Biographies 481
General Index 517
Index of Names 521