| 查看: 167 | 回复: 0 | |||
| 当前主题已经存档。 | |||
[交流]
【转贴】Fundamentals of Mathematics, Volume III: Analysis (Geometry)
|
|||
|
Fundamentals of Mathematics, Volume III: Analysis (Geometry) Publisher: The MIT Press Number Of Pages: 545 Publication Date: 1984-02-05 Sales Rank: 2432384 ISBN / ASIN: 0262520958 EAN: 9780262520959 Binding: Paperback Manufacturer: The MIT Press Studio: The MIT Press Fundamentals of Mathematics represents a new kind of mathematical publication. While excellent technical treatises have been written about specialized fields, they provide little help for the nonspecialist; and other books, some of them semipopular in nature, give an overview of mathematics while omitting some necessary details. Fundamentals of Mathematics strikes a unique balance, presenting an irreproachable treatment of specialized fields and at the same time providing a very clear view of their interrelations, a feature of great value to students, instructors, and those who use mathematics in applied and scientific endeavors. Moreover, as noted in a review of the German edition in Mathematical Reviews, the work is "designed to acquaint [the student] with modern viewpoints and developments. The articles are well illustrated and supplied with references to the literature, both current and 'classical.'" The outstanding pedagogical quality of this work was made possible only by the unique method by which it was written. There are, in general, two authors for each chapter: one a university researcher, the other a teacher of long experience in the German educational system. (In a few cases, more than two authors have collaborated.) And the whole book has been coordinated in repeated conferences, involving altogether about 150 authors and coordinators. Volume I opens with a section on mathematical foundations. It covers such topics as axiomatization, the concept of an algorithm, proofs, the theory of sets, the theory of relations, Boolean algebra, and antinomies. The closing section, on the real number system and algebra, takes up natural numbers, groups, linear algebra, polynomials, rings and ideals, the theory of numbers, algebraic extensions of a fields, complex numbers and quaternions, lattices, the theory of structure, and Zorn's lemma. Volume II begins with eight chapters on the foundations of geometry, followed by eight others on its analytic treatment. The latter include discussions of affine and Euclidean geometry, algebraic geometry, the Erlanger Program and higher geometry, group theory approaches, differential geometry, convex figures, and aspects of topology. Volume III, on analysis, covers convergence, functions, integral and measure, fundamental concepts of probability theory, alternating differential forms, complex numbers and variables, points at infinity, ordinary and partial differential equations, difference equations and definite integrals, functional analysis, real functions, and analytic number theory. An important concluding chapter examines "The Changing Structure of Modern Mathematics."Password: gigapedia.org Type: djvu Size: 3.66 MB MD5: 5fcb4ac5ea0210b83090146076d54666 http://rapidshare.com/files/41670221/0262520958.zip.html http://mihd.net/ejzbw7 [ Last edited by laizuliang on 2007-10-31 at 16:29 ] |
回复此楼» 猜你喜欢
拟解决的关键科学问题还要不要写
已经有8人回复
-
最失望的一年
已经有10人回复
-
求推荐英文EI期刊
已经有5人回复
-
存款400万可以在学校里躺平吗
已经有27人回复
-
请教限项目规定
已经有4人回复
-
国自然申请面上模板最新2026版出了吗？
已经有20人回复
-
26申博
已经有3人回复
-
基金委咋了？2026年的指南还没有出来？
已经有10人回复
-
基金申报
已经有6人回复
-
疑惑？
已经有5人回复