Number: The Language of Science, the Masterpiece Science Edition

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"Number is an open doorway into the world of math. Tobias Dantzig explains the foundations of mathematics with ease, and eloquently explores deeper philosophical questions that arise along the way. He describes the properties of all kinds of numbers - integers, primes, irrationals, transcendentals, and more. He explains the significance of zero, and shows that its invention has revolutionary consequences for arithmetic. He shows how the invention of symbols for use in algebra - a radical departure from tradition at the time - ushered in a new era ...
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Overview

"Number is an open doorway into the world of math. Tobias Dantzig explains the foundations of mathematics with ease, and eloquently explores deeper philosophical questions that arise along the way. He describes the properties of all kinds of numbers - integers, primes, irrationals, transcendentals, and more. He explains the significance of zero, and shows that its invention has revolutionary consequences for arithmetic. He shows how the invention of symbols for use in algebra - a radical departure from tradition at the time - ushered in a new era of math; how arithmetic and geometry reflect each other; and how calculus uses infinity to model the continuity of space and time." With a new afterword, notes section, and bibliography written by math professor and author Joseph Mazur, and a new foreword by mathematician Barry Mazur, the Masterpiece Science edition of Number - which was first published in 1930 - is the first update of Dantzig's classic work in over fifty years. It is a story that ranges from the dawn of man to the genius of history's greatest mathematicians, vividly revealing how the pursuit of knowledge transcends the rise and fall of civilizations.
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Product Details

  • ISBN-13: 9780131856271
  • Publisher: Penguin Group (USA)
  • Publication date: 3/16/2005
  • Edition description: Masterpiece Science Edition
  • Edition number: 5
  • Pages: 416
  • Product dimensions: 5.74 (w) x 8.50 (h) x 1.34 (d)

Table of Contents

1 Fingerprints 1
2 The empty column 19
3 Number-lore 37
4 The last number 59
5 Symbols 79
6 The unutterable 103
7 This flowing world 125
8 The art of becoming 145
9 Filling the gaps 171
10 The domain of number 187
11 The anatomy of the infinite 215
12 The two realities 239
App. A On the recording of numbers 261
App. B Topics in integers 277
App. C On roots and radicals 303
App. D On principles and arguments 327
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Introduction

A quarter of the century ago, when this book was first written, I had grounds to regard the work as a pioneering effort, inasmuch as the evolution of the number concept—though a subject of lively discussion among professional mathematicians, logicians and philosophers—had not yet been presented to the general public as a cultural issue. Indeed, it was by no means certain at the time that there were enough lay readers interested in such issues to justify the publication of the book. The reception accorded to the work both here and abroad, and the numerous books on the same general theme which have followed in its wake have dispelled these doubts. The existence of a sizable body of readers who are concerned with the cultural aspects of mathematics and of the sciences which lean on mathematics is today a matter of record.

It is a stimulating experience for an author in the autumn of life to learn that the sustained demand for his first literary effort has warranted a new edition, and it was in this spirit that I approached the revision of the book. But as the work progressed, I became increasingly aware of the prodigious changes that have taken place since the last edition of the book appeared. The advances in technology, the spread of the statistical method, the advent of electronics, the emergence of nuclear physics, and, above all, the growing importance of automatic computors—have swelled beyond all expectation the ranks of people who live on the fringes of mathematical activity; and, at the same time, raised the general level of mathematical education. Thus was I confronted not only with avastly increased audience, but with a far more sophisticated and exacting audience than the one I had addressed twenty odd years earlier. These sobering reflections had a decisive influence on the plan of this new edition. As to the extent I was able to meet the challenge of these changing times—it is for the reader to judge.

Except for a few passages which were brought up to date, the Evolution of the Number Concept, Part One of the present edition, is a verbatim reproduction of the original text. By contrast, Part Two—Problems, Old and New—is, for all intents and purposes, a new book. Furthermore, while Part One deals largely with concepts and ideas. Still, Part Two should not be construed as a commentary on the original text, but as an integrated story of the development of method and argument in the field of number. One could infer from this that the four chapters of Problems, Old and New are more technical in character than the original twelve, and such is indeed the case. On the other hand, quite a few topics of general interest were included among the subjects treated, and a reader skilled in the art of "skipping" could readily circumvent the more technical sections without straying off the main trail.

Tobias Dantzig

Pacific Palisades

California

September 1, 1953

© Copyright Pearson Education. All rights reserved.

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