Conflicts Between Generalization, Rigor, and Intuition: Number Concepts Underlying the Development of Analysis in 17th-19th Century France and Germany / Edition 1

Conflicts Between Generalization, Rigor, and Intuition: Number Concepts Underlying the Development of Analysis in 17th-19th Century France and Germany / Edition 1

by Gert Schubring
     
 

ISBN-10: 1441919872

ISBN-13: 9781441919878

Pub. Date: 12/01/2010

Publisher: Springer New York

This book deals with the development of the terms of analysis in the 18th and 19th centuries, the two main concepts being negative numbers and infinitesimals. Schubring studies often overlooked texts, in particular German and French textbooks, and reveals a much richer history than previously thought while throwing new light on major figures, such as Cauchy.

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Overview

This book deals with the development of the terms of analysis in the 18th and 19th centuries, the two main concepts being negative numbers and infinitesimals. Schubring studies often overlooked texts, in particular German and French textbooks, and reveals a much richer history than previously thought while throwing new light on major figures, such as Cauchy.

Product Details

ISBN-13:
9781441919878
Publisher:
Springer New York
Publication date:
12/01/2010
Series:
Sources and Studies in the History of Mathematics and Physical Sciences Series
Edition description:
Softcover reprint of hardcover 1st ed. 2005
Pages:
678
Product dimensions:
1.39(w) x 6.14(h) x 9.21(d)

Table of Contents

* Question and Method
• Paths Towards Algebraization – Development until the 18th Century. The Number Field
• The development of negative numbers
• Paths towards algebraization—The field of limits: The development of infinitely small quantities
• Culmination of Algebraization and retour du refoulé
• Le Retour du Refoulé: From the Perspective of Mathematical Concepts
• Cauchy’s Compromise Concept
• Development of Pure Mathematics in Prussia/Germany
• Conflicts Between Confinement to Geometry and Algebraization in France
• Summary and Outlook
• References
• Appendix

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