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
大学図書館所蔵 全11件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
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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