000			03953nam a22003735i 4500
001			280973
003			MX-SnUAN
005			20160429154045.0
007			cr nn 008mamaa
008			150903s2006 xxu| o |||| 0|eng d
020			_a9780817644758 _99780817644758
024	7		_a10.1007/081764475-X _2doi
035			_avtls000333514
039		9	_a201509030722 _bVLOAD _c201404120638 _dVLOAD _c201404090418 _dVLOAD _y201402041113 _zstaff
040			_aMX-SnUAN _bspa _cMX-SnUAN _erda
050		4	_aQA21-27
100	1		_aSteffens, Karl-Georg. _eautor _9306262
245	1	4	_aThe History of Approximation Theory : _bFrom Euler to Bernstein / _cby Karl-Georg Steffens ; edited by George A. Anastassiou.
264		1	_aBoston, MA : _bBirkhäuser Boston, _c2006.
300			_axIx, 219 páginas 22 ilustraciones _brecurso en línea.
336			_atexto _btxt _2rdacontent
337			_acomputadora _bc _2rdamedia
338			_arecurso en línea _bcr _2rdacarrier
347			_aarchivo de texto _bPDF _2rda
500			_aSpringer eBooks
505	0		_aForerunners -- Pafnuti Lvovich Chebyshev -- The Saint Petersburg Mathematical School -- Development Outside Russia -- Constructive Function Theory: Kharkiv.
520			_aThe problem of approximating a given quantity is one of the oldest challenges faced by mathematicians. Its increasing importance in contemporary mathematics has created an entirely new area known as Approximation Theory. The modern theory was initially developed along two divergent schools of thought: the Eastern or Russian group, employing almost exclusively algebraic methods, was headed by Chebyshev together with his coterie at the Saint Petersburg Mathematical School, while the Western mathematicians, adopting a more analytical approach, included Weierstrass, Hilbert, Klein, and others. This work traces the history of approximation theory from Leonhard Euler's cartographic investigations at the end of the 18th century to the early 20th century contributions of Sergei Bernstein in defining a new branch of function theory. One of the key strengths of this book is the narrative itself. The author combines a mathematical analysis of the subject with an engaging discussion of the differing philosophical underpinnings in approach as demonstrated by the various mathematicians. This exciting exposition integrates history, philosophy, and mathematics. While demonstrating excellent technical control of the underlying mathematics, the work is focused on essential results for the development of the theory. The exposition begins with a history of the forerunners of modern approximation theory, i.e., Euler, Laplace, and Fourier. The treatment then shifts to Chebyshev, his overall philosophy of mathematics, and the Saint Petersburg Mathematical School, stressing in particular the roles played by Zolotarev and the Markov brothers. A philosophical dialectic then unfolds, contrasting East vs. West, detailing the work of Weierstrass as well as that of the Goettingen school led by Hilbert and Klein. The final chapter emphasizes the important work of the Russian Jewish mathematician Sergei Bernstein, whose constructive proof of the Weierstrass theorem and extension of Chebyshev's work serve to unify East and West in their approaches to approximation theory. Appendices containing biographical data on numerous eminent mathematicians, explanations of Russian nomenclature and academic degrees, and an excellent index round out the presentation.
590			_aPara consulta fuera de la UANL se requiere clave de acceso remoto.
700	1		_aAnastassiou, George A. _eeditor. _9305487
710	2		_aSpringerLink (Servicio en línea) _9299170
776	0	8	_iEdición impresa: _z9780817643539
856	4	0	_uhttp://remoto.dgb.uanl.mx/login?url=http://dx.doi.org/10.1007/0-8176-4475-X _zConectar a Springer E-Books (Para consulta externa se requiere previa autentificación en Biblioteca Digital UANL)
942			_c14
999			_c280973 _d280973