Conflicts between generalization, rigor, and intuition : number concepts underlying the development of analysis in 17-19th century France and Germany
著者
書誌事項
Conflicts between generalization, rigor, and intuition : number concepts underlying the development of analysis in 17-19th century France and Germany
（Sources and studies in the history of mathematics and physical sciences）
Springer, c2005
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注記
Includes bibliographical references (p. [631]-670) and index
内容説明・目次
内容説明
This volume is, as may be readily apparent, the fruit of many years' labor in archives and libraries, unearthing rare books, researching Nachlasse, 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 Ecole 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 quantites 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.
目次
* 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 refoule * Le Retour du Refoule: 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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