Conflicts between Generalization, Rigor, and Intuition : Number Concepts Underlying the Development of Analysis in 17 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...
Enregistré dans:
| Auteur principal: | |
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| Format: | Livre numérique |
| Langue: | Anglais |
| Publié: |
New York, NY :
Springer New York
[20..].
Cham : Springer Nature |
| Édition: | 1st ed. 2005. |
| Collection: | Sources and Studies in the History of Mathematics and Physical Sciences
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| Accès en ligne: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Note: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Conflicts between generalization, rigor, and intuition, number concepts underlying the development of analysis in 17th-19th century France and Germany, Gert Schubring, 2005, New York, Springer, 1 vol. (XIV- 678 p.), Sources and studies in the history of mathematics and physical sciences, 0-387-22836-5 • Conflicts Between Generalization, Rigor, and Intuition, Texte imprimé, 9780387501956 • Conflicts between generalization, rigor, and intuition, number concepts underlying the development of analysis in 17th-19th century France and Germany, Gert Schubring, 2005, New York, Springer, 1 vol. (XIV- 678 p.), Sources and studies in the history of mathematics and physical sciences, 0-387-22836-5 |
| Résumé: | 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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| Description: | Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| ISBN: | 9780387282732 |
| ISSN: | 2196-8829 |
| Accès: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |