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Original Essays | September 17, 2014

Merritt Tierce: IMG Has My Husband Read It?



My first novel, Love Me Back, was published on September 16. Writing the book took seven years, and along the way three chapters were published in... Continue »
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    Love Me Back

    Merritt Tierce 9780385538077

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This title in other editions

Other titles in the Sources and Studies in the History of Mathematics and Physic series:

Conflicts Between Generalization, Rigor, and Intuition: Number Concepts Underlying the Development of Analysis in 17th-19th Century France and Germany (Sources and Studies in the History of Mathematic

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Conflicts Between Generalization, Rigor, and Intuition: Number Concepts Underlying the Development of Analysis in 17th-19th Century France and Germany (Sources and Studies in the History of Mathematic Cover

 

Synopses & Reviews

Publisher Comments:

Conflicts Between Generalization, Rigor, and Intuition undertakes a historical analysis of the development of two mathematical concepts -negative numbers and infinitely small quantities, mainly in France and Germany, but also in Britain, and the different paths taken there. This book not only discusses the history of the two concepts, but it also introduces a wealth of new knowledge and insights regarding their interrelation as necessary foundations for the emergence of the 19th century concept of analysis. The historical investigation unravels several processes underlying and motivating conceptual change: generalization (in particular, algebraization as an agent for generalizing) and a continued effort of intuitive accessibility which often conflicted with likewise desired rigor. The study focuses on the 18th and the 19th centuries, with a detailed analysis of Lazare Carnot's and A. L. Cauchy's foundational ideas. By researching the development of the concept of negative and infinitely small numbers, the book provides a productive unity to a large number of historical sources. This approach permits a nuanced analysis of the meaning of mathematical ideas as conceived of by 18th and 19th century scientists, while illustrating the authors' actions within the context of their respective cultural and scientific communities. The result is a highly readable study of conceptual history and a new model for the cultural history of mathematics.

Synopsis:

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.

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

Product Details

ISBN:
9781441919878
Author:
Schubring, Gert
Publisher:
Springer
Location:
New York, NY
Subject:
Mathematics-Calculus
Subject:
History
Subject:
History of Mathematical Sciences
Subject:
Analysis
Subject:
Mathematics
Subject:
B
Subject:
mathematics and statistics
Subject:
Global analysis (Mathematics)
Copyright:
Edition Description:
Softcover reprint of hardcover 1st ed. 2005
Series:
Sources and Studies in the History of Mathematics and Physical Sciences
Publication Date:
20101201
Binding:
TRADE PAPER
Language:
English
Pages:
692
Dimensions:
235 x 155 mm 1029 gr

Related Subjects

Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » History

Conflicts Between Generalization, Rigor, and Intuition: Number Concepts Underlying the Development of Analysis in 17th-19th Century France and Germany (Sources and Studies in the History of Mathematic New Trade Paper
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Product details 692 pages Springer - English 9781441919878 Reviews:
"Synopsis" by , 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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