Автор: Lancelot Hogben
Название: Mathematics for the Million: How to Master the Magic of Numbers
Издательство: W.W. Norton
Год: 1983
ISBN: 978-0393300352
Язык: English
Формат: pdf, djvu
Размер: 19,4 mb
Страниц: 579
This book will narrate how the grammar of measurement and counting has evolved under the pressure of man’s changing social achievements, how in successive stages it has been held in check by the barriers of custom, how it has been used in charting a universe which can be commanded when its laws are obeyed, but can never be propitiated by ceremonial and sacrifice. As the outline of the story develops, one difficulty which many people experience will become less formidable.
The expert in mathematics is essentially a technician. Hence mathematical books are largely packed with exercises designed to give proficiency in workmanship. This makes us discouraged because of the immense territory which we have to traverse before we can get insight into the kind of mathematics which is used in modern science and social statistics. The fact is that modern mathematics does not borrow so very much from antiquity. To be sure, every useful development in mathematics rests on the historical foundation of some earlier branch. At the same time every new branch liquidates the usefulness of clumsier tools which preceded it. Although algebra, trigonometry, the use of graphs, the calculus all depend on the rules of Greek geometry, less than a dozen from the two hundred propositions of Euclid's elements are essential to help us in understanding how to use them.
This illuminating explanation is addressed to the person who wants to understand the place of mathematics in modern civilization but who has been intimidated by its supposed difficulty. Mathematics is the language of size, shape, and order—a language Hogben shows one can both master and enjoy.
PROLOGUE
1 MATHEMATICS IN REMOTE ANTIQUITY
2 THE GRAMMAR OF SIZE, ORDER, AND SHAPE
3 EUCLID AS A SPRINGBOARD
4 NUMBER LORE IN ANTIQUITY
5 THE RISE AND DECLINE OF THE ALEXANDRIAN CULTURE
6 THE DAWN OF NOTHING
7 MATHEMATICS FOR THE MARINER
8 THE GEOMETRY OF MOTION
9 LOGARITHMS AND THE SEARCH FOR SERIES
10 THE CALCULUS OF NEWTON AND LEIBNITZ
11 THE ALGEBRA OF THE CHESSBOARD
12 THE ALGEBRA OF CHOICE AND CHANCE TABLES
ANSWERS TO SOME OF THE EXERCISES
INDEX
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Mathematics for the Million: How to Master the Magic of Numbers 
