Conflicts Between Generalization, Rigor, and Intuition: Number Concepts Underlying the Development of Analysis in 17th-19th Century France and Germany ... History of Mathematics and Physical Sciences) - Tapa dura

Schubring, Gert

 
9780387228365: Conflicts Between Generalization, Rigor, and Intuition: Number Concepts Underlying the Development of Analysis in 17th-19th Century France and Germany ... History of Mathematics and Physical Sciences)
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ISBN 10: 0387228365 ISBN 13: 9780387228365
Editorial: Springer, 2005

Sinopsis

This volume is, as may be readily apparent, the fruit of many years’ labor in archives and libraries, unearthing rare books, researching Nachlässe, and above all, systematic comparative analysis of fecund sources. The work not only demanded much time in preparation, but was also interrupted by other duties, such as time spent as a guest professor at universities abroad, which of course provided welcome opportunities to present and discuss the work, and in particular, the organizing of the 1994 International Graßmann Conference and the subsequent editing of its proceedings. If it is not possible to be precise about the amount of time spent on this work, it is possible to be precise about the date of its inception. In 1984, during research in the archive of the École polytechnique, my attention was drawn to the way in which the massive rupture that took place in 1811-precipitating the change back to the synthetic method and replacing the limit method by the method of the quantités infiniment petites-significantly altered the teaching of analysis at this first modern institution of higher education, an institution originally founded as a citadel of the analytic method.

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De la contraportada

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.

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Editorial
Springer
Año de publicación
2005
Idioma
Inglés
ISBN 10 
0387228365
ISBN 13 
9780387228365
Encuadernación
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Número de páginas
696
Contacto del fabricante
no disponible
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Otras ediciones populares con el mismo título

9781441919878: Conflicts Between Generalization, Rigor, and Intuition: Number Concepts Underlying the Development of Analysis in 17th-19th Century France and Germany ... History of Mathematics and Physical Sciences)

Edición Destacada

ISBN 10:  1441919872 ISBN 13:  9781441919878
Editorial: Springer, 2010
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