| 查看: 241 | 回复: 1 | ||
| 【奖励】 本帖被评价1次，作者wangye增加金币 0.5 个 | ||
| 当前主题已经存档。 | ||
[资源]
【转贴】The History of Approximation Theory【已搜无重复】
|
||
|
By Karl-Georg Steffens Publisher: Birkhäuser Boston Number Of Pages: 219 Publication Date: 2005-12-16 Sales Rank: 1550848 ISBN / ASIN: 0817643532 EAN: 9780817643539 Binding: Paperback Manufacturer: Birkhäuser Boston Studio: Birkhäuser Boston pass: gigapedia.org The 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 http://mihd.net/21jqon http://rapidshare.com/files/64481067/ebc_xuw8eqai.rar http://rapidshare.com/files/6442 ... ximation_Theory.pdf [ Last edited by wangye on 2007-10-23 at 23:46 ] |
回复此楼» 猜你喜欢
建议基金发布提前给出明确的时间点
已经有10人回复
-
科研孤儿太难了
已经有17人回复
-
今日不放榜？网传国自然预计 8 月 27 日可查结果
已经有19人回复
-
看来今天不会放榜了？
已经有11人回复
-
时间戳又变了
已经有19人回复
-
filecode，4个jtjc了
已经有14人回复
-
让我中一个面上吧！
已经有13人回复
-
人气不行了
已经有7人回复
-
感觉是下周放榜了
已经有12人回复
-
我面上完蛋了
已经有8人回复
2楼2007-12-13 04:48:27
40