Conflicts Between Generalization, Rigor, and Intuition Number Concepts Underlying the Development of Analysis in 17th-19th Century France and Germany
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 discus...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer New York
2005, 2005
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| Edition: | 1st ed. 2005 |
| Series: | Sources and Studies in the History of Mathematics and Physical Sciences
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| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- Question and Method
- Paths Toward Algebraization — Development to the Eighteenth Century. The Number Field
- Paths toward 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