A History of Algorithms: From the Pebble to the Microchip [Paperback]

The development of computing has reawakened interest in algorithms. Often neglected by historians and modern scientists, algorithmic procedures 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.

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.1 Algorithms for Arithmetic Operations.- 1.1 Sumerian Division.- 1.2 A Babylonian Algorithm for Calculating Inverses.- 1.3 Egyptian Algorithms for Arithmetic.- 1.4 Tableau Multiplication.- 1.5 Optimising Calculations.- 1.6 Simple Division by Difference on a Counting Board.- 1.7 Division on the Chinese Abacus.- 1.8 Numbers Written as Decimals.- 1.9 Binary Arithmetic.- 1.10 Computer Arithmetic.- 2 Magic Squares.- Squares with Borders.- The Marking Cells Method.- Proceeding by 2 and by 3.- Arnauld's Borders Method.- 3 Methods of False Position.- 3.1 Mesopotamia: a Geometric False Position.- 3.2 Egypt: Problem 26 of the Rhind Papyrus.- 3.3 China: Chapter VII of the Jiuzhang Suanshu.- 3.4 India: Bh?skara and the Rule of Simple False Position.- 3.5 Qust? Ibn L?q?: A Geometric Justification.- 3.6 Ibn al-Bann?: The Method of the Scales.- 3.7 Fibonacci: the Elchatayn rule.- 3.8 Pellos: The Rule of Three and The Method of Simple False Position.- 3.9 Clavius: Solving a System of Equations.- 4 Euclid's Algorithm.- 4.1 Euclid's Algorithm.- 118 Comparing Ralól