The Resource Conflicts Between Generalization, Rigor, and Intuition : Number Concepts Underlying the Development of Analysis in 17th-19th Century France and Germany, by Gert Schubring, (electronic resource)

Conflicts Between Generalization, Rigor, and Intuition : Number Concepts Underlying the Development of Analysis in 17th-19th Century France and Germany, by Gert Schubring, (electronic resource)

Label
Conflicts Between Generalization, Rigor, and Intuition : Number Concepts Underlying the Development of Analysis in 17th-19th Century France and Germany
Title
Conflicts Between Generalization, Rigor, and Intuition
Title remainder
Number Concepts Underlying the Development of Analysis in 17th-19th Century France and Germany
Statement of responsibility
by Gert Schubring
Creator
Author
Author
Subject
Language
  • eng
  • eng
Summary
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
Member of
http://library.link/vocab/creatorName
Schubring, Gert
Dewey number
  • 515.09
  • 515/.09
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
o0I_yrzwzyc
Language note
English
LC call number
QA21-27
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Sources and Studies in the History of Mathematics and Physical Sciences,
http://library.link/vocab/subjectName
  • Global analysis (Mathematics)
  • History of Mathematical Sciences
  • Analysis
Label
Conflicts Between Generalization, Rigor, and Intuition : Number Concepts Underlying the Development of Analysis in 17th-19th Century France and Germany, by Gert Schubring, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. [631]-670) and index
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
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
Dimensions
unknown
Edition
1st ed. 2005.
Extent
1 online resource (690 p.)
Form of item
online
Isbn
9780387282732
Media category
computer
Media type code
  • c
Other control number
10.1007/0-387-28273-4
Specific material designation
remote
System control number
  • (CKB)1000000000227519
  • (EBL)302622
  • (OCoLC)76822576
  • (SSID)ssj0000128654
  • (PQKBManifestationID)11138743
  • (PQKBTitleCode)TC0000128654
  • (PQKBWorkID)10070279
  • (PQKB)10698048
  • (SSID)ssj0000769021
  • (PQKBManifestationID)12281038
  • (PQKBTitleCode)TC0000769021
  • (PQKBWorkID)10769128
  • (PQKB)10929418
  • (DE-He213)978-0-387-28273-2
  • (MiAaPQ)EBC302622
  • (EXLCZ)991000000000227519
Label
Conflicts Between Generalization, Rigor, and Intuition : Number Concepts Underlying the Development of Analysis in 17th-19th Century France and Germany, by Gert Schubring, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. [631]-670) and index
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
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
Dimensions
unknown
Edition
1st ed. 2005.
Extent
1 online resource (690 p.)
Form of item
online
Isbn
9780387282732
Media category
computer
Media type code
  • c
Other control number
10.1007/0-387-28273-4
Specific material designation
remote
System control number
  • (CKB)1000000000227519
  • (EBL)302622
  • (OCoLC)76822576
  • (SSID)ssj0000128654
  • (PQKBManifestationID)11138743
  • (PQKBTitleCode)TC0000128654
  • (PQKBWorkID)10070279
  • (PQKB)10698048
  • (SSID)ssj0000769021
  • (PQKBManifestationID)12281038
  • (PQKBTitleCode)TC0000769021
  • (PQKBWorkID)10769128
  • (PQKB)10929418
  • (DE-He213)978-0-387-28273-2
  • (MiAaPQ)EBC302622
  • (EXLCZ)991000000000227519

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