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008			240724s2007 xx o ||||0 eng d
020			_a9781470418083 _q(electronic bk.)
020			_z9780821843437
035			_a(MiAaPQ)EBC4908542
035			_a(Au-PeEL)EBL4908542
035			_a(CaPaEBR)ebr11410083
035			_a(OCoLC)993774793
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA151.E657 2007
082	0		_a512.00900000000001
100	1		_aGray, Jeremy J.
245	1	0	_aEpisodes in the History of Modern Algebra (1800–1950).
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2007.
264		4	_c©2007.
300			_a1 online resource (346 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aHistory of Mathematics ; _vv.32
505	0		_aCover -- Half Title -- Title Page -- Contents -- Acknowledgments -- Introduction -- Babbage and French Idéologie: Functional equations, language, and the analytical method -- "Very full of symbols": Duncan F. Gregory, the calculus of operations, and the Cambridge Mathematical Journal -- Divisibility theories in the early history of commutative algebra and the foundations of algebraic geometry -- Kronecker's fundamental theorem of general arithmetic -- Developments in the theory of algebras over number fields: A new foundation for the Hasse norm residue symbol and new approaches to both the Artin reciprocity law and class field theory -- Minkowski, Hensel, and Hasse: On the beginnings of the local-global principle -- Research in algebra at the University of Chicago: Leonard Eugene Dickson and A. Adrian Albert -- Emmy Noether's 1932 ICM lecture on noncommutative methods in algebraic number theory -- From Algebra (1895) to Moderne Algebra (1930): Changing conceptions of a discipline-A guided tour using the Jahrbuch über die Fortschritte der Mathematik -- A historical sketch of B. L. van der Waerden's work in algebraic geometry: 1926-1946 -- On the arithmetization of algebraic geometry -- The rising sea: Grothendieck on simplicity and generality -- Back Cover.
520			_aAlgebra, as a subdiscipline of mathematics, arguably has a history going back some 4000 years to ancient Mesopotamia. The history, however, of what is recognized today as high school algebra is much shorter, extending back to the sixteenth century, while the history of what practicing mathematicians call "modern algebra" is even shorter still. The present volume provides a glimpse into the complicated and often convoluted history of this latter conception of algebra by juxtaposing twelve episodes in the evolution of modern algebra from the early nineteenth-century work of Charles Babbage on functional equations to Alexandre Grothendieck's mid-twentieth-century metaphor of a "rising sea" in his categorical approach to algebraic geometry. In addition to considering the technical development of various aspects of algebraic thought, the historians of modern algebra whose work is united in this volume explore such themes as the changing aims and organization of the subject as well as the often complex lines of mathematical communication within and across national boundaries. Among the specific algebraic ideas considered are the concept of divisibility and the introduction of non-commutative algebras into the study of number theory and the emergence of algebraic geometry in the twentieth century. The resulting volume is essential reading for anyone interested in the history of modern mathematics in general and modern algebra in particular. It will be of particular interest to mathematicians and historians of mathematics.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aAlgebra--History.
655		4	_aElectronic books.
700	1		_aParshall, Karen Hunger.
776	0	8	_iPrint version: _aGray, Jeremy J. _tEpisodes in the History of Modern Algebra (1800–1950) _dProvidence : American Mathematical Society,c2007 _z9780821843437
797	2		_aProQuest (Firm)
830		0	_aHistory of Mathematics
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4908542 _zClick to View
999			_c128051 _d128051