Numbers: Computers, Philosophers, and the Search for Meaning

Numbers: Computers, Philosophers, and the Search for Meaning

by John Tabak
     
 

ISBN-10: 0816049556

ISBN-13: 9780816049554

Pub. Date: 06/28/2004

Publisher: Facts on File, Incorporated

The History of Mathematics is a fascinating survey of the development of math through discovery, innovation, collaboration, and experimentation. The set presents a compelling overview of myriad aspects of mathematics using understandable language and appealing line illustrations and photographs. Numbers is an insightful look at the properties and uses of numerical…  See more details below

Overview

The History of Mathematics is a fascinating survey of the development of math through discovery, innovation, collaboration, and experimentation. The set presents a compelling overview of myriad aspects of mathematics using understandable language and appealing line illustrations and photographs. Numbers is an insightful look at the properties and uses of numerical quantities, from fractions to algebraic numbers, transcendental numbers, and complex numbers. We rely on numbers to carry out countless daily activities -- from mapping the universe to running word-processing programs to buying lunch. Author John Tabak points out that numbers are a human invention, as seen through the compelling histories of Babylonian, Roman, and Arab thinkers and their influential systems for representing numbers. The book examines in detail the number pi, the evolution of the idea of infinity, the representation of numbers in computers, the metric and American systems of measurement, and the application of some historical concepts of numbers in such modern forms as cryptography and hand calculators. Numbers includes an index, a chronology of notable events, a glossary of terms, a helpful list of Internet resources, and an array of historical and current print sources for further research. Keyed to current principles and standards in teaching math, The History of Mathematics set is essential for young readers who require information on relevant topics in mathematics.

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Product Details

ISBN-13:
9780816049554
Publisher:
Facts on File, Incorporated
Publication date:
06/28/2004
Series:
Facts on File Math Library
Pages:
240
Product dimensions:
6.10(w) x 9.20(h) x 0.80(d)
Age Range:
11 - 17 Years

Table of Contents

Acknowledgmentsx
Introduction: Number and Imaginationxi
Part 1Numbers for Computation1
1The First Problems3
2Early Counting Systems11
A Mesopotamian Education13
The Mesopotamian Number System14
Mesopotamian Mathematics Homework18
The Egyptian Number System20
A Problem from the Ahmes Papyrus24
The Mayan Number System26
The Chinese Number System30
A Problem from the Nine Chapters32
3Our Place Value Number System34
Explaining the New System38
4Analytical Engines46
Calculators, Computers, and the Human Imagination48
Charles Babbage and the Analytical Engine50
An Early Electronic Representation of Our Number System52
Floating-Point Representation56
Floating-Point Arithmetic and Your Calculator58
Why Computers?60
Part 2Extending the Idea of a Number65
5An Evolving Concept of a Number67
Irrational Numbers70
Pythagoras of Samos73
The Irrationality of [radical]275
6Negative Numbers77
Ancient Mathematical Texts from the Indian Subcontinent82
Out of India83
7Algebraic Numbers85
Tartaglia, Ferrari, and Cardano88
Girard and Wallis93
Euler and d'Alembert97
The Debate over "Fictitious" Numbers98
The Complex Numbers: A Modern View103
Using Complex Numbers104
8Transcendental Numbers and the Search for Meaning107
Dedekind and the Real Number Line111
Part 3The Problem of Infinity117
9Early Insights119
10Galileo and Bolzano130
Infinity as a Number136
The Life and Opinions of Tristram Shandy, Gentleman140
11Georg Cantor and the Logic of the Infinite143
There Are No More Rational Numbers than Natural Numbers146
There Are More Real Numbers than Natural Numbers148
The Russell Paradox154
Resolving the Russell Paradox159
12Cantor's Legacy165
Kurt Godel170
Formal Languages Today173
Alan Turing174
Chronology181
Glossary199
Further Reading203
Index213

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