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Book Categories |
| Acknowledgments | x | |
| Introduction: Number and Imagination | xi | |
| Part 1 | Numbers for Computation | 1 |
| 1 | The First Problems | 3 |
| 2 | Early Counting Systems | 11 |
| A Mesopotamian Education | 13 | |
| The Mesopotamian Number System | 14 | |
| Mesopotamian Mathematics Homework | 18 | |
| The Egyptian Number System | 20 | |
| A Problem from the Ahmes Papyrus | 24 | |
| The Mayan Number System | 26 | |
| The Chinese Number System | 30 | |
| A Problem from the Nine Chapters | 32 | |
| 3 | Our Place Value Number System | 34 |
| Explaining the New System | 38 | |
| 4 | Analytical Engines | 46 |
| Calculators, Computers, and the Human Imagination | 48 | |
| Charles Babbage and the Analytical Engine | 50 | |
| An Early Electronic Representation of Our Number System | 52 | |
| Floating-Point Representation | 56 | |
| Floating-Point Arithmetic and Your Calculator | 58 | |
| Why Computers? | 60 | |
| Part 2 | Extending the Idea of a Number | 65 |
| 5 | An Evolving Concept of a Number | 67 |
| Irrational Numbers | 70 | |
| Pythagoras of Samos | 73 | |
| The Irrationality of [radical]2 | 75 | |
| 6 | Negative Numbers | 77 |
| Ancient Mathematical Texts from the Indian Subcontinent | 82 | |
| Out of India | 83 | |
| 7 | Algebraic Numbers | 85 |
| Tartaglia, Ferrari, and Cardano | 88 | |
| Girard and Wallis | 93 | |
| Euler and d'Alembert | 97 | |
| The Debate over "Fictitious" Numbers | 98 | |
| The Complex Numbers: A Modern View | 103 | |
| Using Complex Numbers | 104 | |
| 8 | Transcendental Numbers and the Search for Meaning | 107 |
| Dedekind and the Real Number Line | 111 | |
| Part 3 | The Problem of Infinity | 117 |
| 9 | Early Insights | 119 |
| 10 | Galileo and Bolzano | 130 |
| Infinity as a Number | 136 | |
| The Life and Opinions of Tristram Shandy, Gentleman | 140 | |
| 11 | Georg Cantor and the Logic of the Infinite | 143 |
| There Are No More Rational Numbers than Natural Numbers | 146 | |
| There Are More Real Numbers than Natural Numbers | 148 | |
| The Russell Paradox | 154 | |
| Resolving the Russell Paradox | 159 | |
| 12 | Cantor's Legacy | 165 |
| Kurt Godel | 170 | |
| Formal Languages Today | 173 | |
| Alan Turing | 174 | |
| Chronology | 181 | |
| Glossary | 199 | |
| Further Reading | 203 | |
| Index | 213 |
| Price | Condition | Delivery | Seller | Action |
| $99.99 | Digital |
| WonderClub |
Laura Mctaggart
reviewed Numbers: Computers, Philosophers, and the Search for Meaning on October 11, 2015
Numbers
This was way lower level than I was initially expecting, but a great historical overlook. Would be great for a middle or early high schooler interested in numbers or infinity. Would make simple and clear material for a school report, and provides a short list of age appropriate math journals and email lists related to the subject for those who want to dig deeper.
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Add Numbers: Computers, Philosophers, and the Search for Meaning, 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 appe, Numbers: Computers, Philosophers, and the Search for Meaning to the inventory that you are selling on WonderClubX
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Add Numbers: Computers, Philosophers, and the Search for Meaning, 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 appe, Numbers: Computers, Philosophers, and the Search for Meaning to your collection on WonderClub |
