000			03652nam a22004695i 4500
001			978-0-387-28273-2
003			DE-He213
005			20161121230925.0
007			cr nn 008mamaa
008			100301s2005 xxu| s |||| 0|eng d
020			_a9780387282732 _9978-0-387-28273-2
024	7		_a10.1007/0-387-28273-4 _2doi
050		4	_aQA21-27
072		7	_aPBX _2bicssc
072		7	_aMAT015000 _2bisacsh
082	0	4	_a510.9 _223
100	1		_aSchubring, Gert. _eauthor.
245	1	0	_aConflicts between Generalization, Rigor, and Intuition _h[electronic resource] : _bNumber Concepts Underlying the Development of Analysis in 17–19th Century France and Germany / _cby Gert Schubring.
264		1	_aNew York, NY : _bSpringer New York, _c2005.
300			_aXIV, 678 p. 22 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aSources and Studies in the History of Mathematics and Physical Sciences
505	0		_aQuestion 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.
520			_aConflicts 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.
650		0	_aMathematics.
650		0	_aMathematical analysis.
650		0	_aAnalysis (Mathematics).
650		0	_aHistory.
650	1	4	_aMathematics.
650	2	4	_aHistory of Mathematical Sciences.
650	2	4	_aAnalysis.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387228365
830		0	_aSources and Studies in the History of Mathematics and Physical Sciences
856	4	0	_uhttp://dx.doi.org/10.1007/0-387-28273-4
912			_aZDB-2-SMA
950			_aMathematics and Statistics (Springer-11649)
999			_c506003 _d506003