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The History of the Calculus and Its Conceptual Development

by

The History of the Calculus and Its Conceptual Development Cover

 

Synopses & Reviews

Publisher Comments:

This book, for the first time, provides laymen and mathematicians alike with a detailed picture of the historical development of one of the most momentous achievements of the human intellect ― the calculus. It describes with accuracy and perspective the long development of both the integral and the differential calculus from their early beginnings in antiquity to their final emancipation in the 19th century from both physical and metaphysical ideas alike and their final elaboration as mathematical abstractions, as we know them today, defined in terms of formal logic by means of the idea of a limit of an infinite sequence.

But while the importance of the calculus and mathematical analysis ― the core of modern mathematics ― cannot be overemphasized, the value of this first comprehensive critical history of the calculus goes far beyond the subject matter. This book will fully counteract the impression of laymen, and of many mathematicians, that the great achievements of mathematics were formulated from the beginning in final form. It will give readers a sense of mathematics not as a technique, but as a habit of mind, and serve to bridge the gap between the sciences and the humanities. It will also make abundantly clear the modern understanding of mathematics by showing in detail how the concepts of the calculus gradually changed from the Greek view of the reality and immanence of mathematics to the revised concept of mathematical rigor developed by the great 19th century mathematicians, which held that any premises were valid so long as they were consistent with one another. It will make clear the ideas contributed by Zeno, Plato, Pythagoras, Eudoxus, the Arabic and Scholastic mathematicians, Newton, Leibnitz, Taylor, Descartes, Euler, Lagrange, Cantor, Weierstrass, and many others in the long passage from the Greek "method of exhaustion" and Zeno's paradoxes to the modern concept of the limit independent of sense experience; and illuminate not only the methods of mathematical discovery, but the foundations of mathematical thought as well.

Synopsis:

Fluent description of the development of both the integral and differential calculus — its early beginnings in antiquity, medieval contributions, and a consideration of Newton and Leibniz.

Synopsis:

Origins in antiquity, medieval contributions, work of Newton, Leibniz, rigorous formulation. Treatment is verbal.

Synopsis:

Fluent description of the development of both the integral and differential calculus. Early beginnings in antiquity, medieval contributions, and a century of anticipation lead up to a consideration of Newton and Leibniz, the period of indecison that followed them, and the final rigorous formulation that we know today.

Description:

Includes bibliographical references (p. [311]-335) and index.

Table of Contents

I. INTRODUCTION

II. CONCEPTIONS IN ANTIQUITY

III. MEDIEVAL CONTRIBUTIONS

IV. A CENTURY OF ANTICIPATION

V. NEWTON AND LEIBNIZ

VI. THE PERIOD OF INDECISION

VII. THE RIGOROUS FORMULATION

VIII. CONCLUSION

  BIBLIOGRAPHY

  INDEX

Product Details

ISBN:
9780486605098
Author:
Boyer, Carl B.
Publisher:
Dover Publications
Author:
Mathematics
Location:
New York
Subject:
History
Subject:
Mathematics
Subject:
Calculus
Subject:
Mathematics -- Philosophy.
Subject:
Historia Da Ciencia
Subject:
General Mathematics
Subject:
Mathematics-Calculus
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Series Volume:
102-1003
Publication Date:
19590631
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
368
Dimensions:
8.5 x 5.38 in 0.88 lb

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Related Subjects


Science and Mathematics » History of Science » General
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » History
Science and Mathematics » Physics » Optics

The History of the Calculus and Its Conceptual Development New Trade Paper
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Product details 368 pages Dover Publications - English 9780486605098 Reviews:
"Synopsis" by ,
Fluent description of the development of both the integral and differential calculus — its early beginnings in antiquity, medieval contributions, and a consideration of Newton and Leibniz.
"Synopsis" by , Origins in antiquity, medieval contributions, work of Newton, Leibniz, rigorous formulation. Treatment is verbal.

"Synopsis" by ,
Fluent description of the development of both the integral and differential calculus. Early beginnings in antiquity, medieval contributions, and a century of anticipation lead up to a consideration of Newton and Leibniz, the period of indecison that followed them, and the final rigorous formulation that we know today.

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