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Numbers: Computers, Philosophers, and the Search for Meaning [Hardback]

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  • Formāts: Hardback, 240 pages, height x width x depth: 229x152x25 mm, weight: 522 g, 29 b&w photographs, 21 line drawings
  • Sērija : History of Mathematics
  • Izdošanas datums: 01-Jun-2004
  • Izdevniecība: Facts On File Inc
  • ISBN-10: 0816049556
  • ISBN-13: 9780816049554
Citas grāmatas par šo tēmu:
  • Formāts: Hardback, 240 pages, height x width x depth: 229x152x25 mm, weight: 522 g, 29 b&w photographs, 21 line drawings
  • Sērija : History of Mathematics
  • Izdošanas datums: 01-Jun-2004
  • Izdevniecība: Facts On File Inc
  • ISBN-10: 0816049556
  • ISBN-13: 9780816049554
Citas grāmatas par šo tēmu:
One of the most fundamental concepts influencing the development of human civilization is numbers. While societies today rely on their understanding of numbers for everything from mapping the universe to running word processing programs on computers to buying lunch, numbers are a human invention. Babylonian, Roman, and Arabic societies devised influential systems for representing numbers, yet the story of how numbers developed is far more complicated. Concepts such as zero, negative numbers, fractions, irrational numbers, and roots of numbers were often controversial in the past. Numbers deals with the development of numbers from fractions to algebraic numbers to transcendental numbers to complex numbers and their uses. The book also examines in detail the number pi, the evolution of the idea of infinity, and the representation of numbers in computers. The metric and American systems of measurement as well as the applications of some historical concepts of numbers in such modern forms as cryptography and hand calculators are also covered. Illustrations, thought-provoking text, and other supplemental material cover the key ideas, figures, and events in the historical development of numbers.
Acknowledgments x
Introduction: Number and Imagination xi
Part One: Numbers for Computation
1(64)
The First Problems
3(8)
Early Counting Systems
11(23)
A Mesopotamian Education
13(5)
The Mesopotamian Number System
14(4)
Mesopotamian Mathematics Homework
18(6)
The Egyptian Number System
20(4)
A Problem from the Ahmes Papyrus
24(8)
The Mayan Number System
26(4)
The Chinese Number System
30(2)
A Problem from the Nine
Chapters
32(2)
Our Place Value Number System
34(12)
Explaining the New System
38(8)
Analytical Engines
46(19)
Calculators, Computers, and the Human Imagination
48(4)
Charles Babbage and the Analytical Engine
50(2)
An Early Electronic Representation of Our Number System
52(6)
Floating-Point Representation
56(2)
Floating-Point Arithmetic and Your Calculator
58(2)
Why Computers?
60(5)
Part Two: Extending the Idea of a Number
65(52)
An Evolving Concept of a Number
67(10)
Irrational Numbers
70(3)
Pythagoras of Samos
73(2)
The Irrationality of √2
75(2)
Negative Numbers
77(8)
Ancient Mathematical Texts from the Indian Subcontinent
82(1)
Out of India
83(2)
Algebraic Numbers
85(22)
Tartaglia, Ferrari, and Cardano
88(5)
Girard and Wallis
93(4)
Euler and d'Alembert
97(1)
The Debate over ``Fictitious'' Numbers
98(6)
The Complex Numbers: A Modern View
103(1)
Using Complex Numbers
104(3)
Transcendental Numbers and the Search for Meaning
107(10)
Dedekind and the Real Number Line
111(6)
Part Three: The Problem of Infinity
117(64)
Early Insights
119(11)
Galileo and Bolzano
130(13)
Infinity as a Number
136(7)
The Life and Opinions of Tristram Shandy, Gentleman
140(3)
Georg Cantor and the Logic of the Infinite
143(22)
There Are No More Rational Numbers than Natural Numbers
146(2)
There Are More Real Numbers than Natural Numbers
148(17)
The Russell Paradox
154(5)
Resolving the Russell Paradox
159(6)
Cantor's Legacy
165(16)
Kurt Godel
170(3)
Formal Languages Today
173(8)
Alan Turing
174(7)
Chronology 181(18)
Glossary 199(4)
Further Reading 203(10)
Index 213
John Tabak, Ph.D., performed graduate work at Suny at Stony Brook and received a degree in mathematics from Rensselaer Polytechnic Institute. He is the author of A Look at Earth and A Look at Neptune, two astronomy titles for middle school readers. He is presently writing a history of American sign language.