One of the most cited books in mathematics, John Milnor's exposition of Morse theory has been the most important book on the subject for more than forty years. Morse theory was developed in the 1920s by mathematician Marston Morse. (Morse was on the faculty of the Institute for Advanced Study, and Princeton published his "Topological Methods in the Theory of Functions of a Complex Variable" in the "Annals of Mathematics Studies" series in 1947.) One classical application of Morse theory includes the attempt to understand, with only limited information, the large-scale structure of an object. This kind of problem occurs in mathematical physics, dynamic systems, and mechanical engineering. Morse theory has received much attention in the last two decades as a result of a famous paper in which theoretical physicist Edward Witten relates Morse theory to quantum field theory. Milnor was awarded the Fields Medal (the mathematical equivalent of a Nobel Prize) in 1962 for his work in differential topology. He has since received the National Medal of Science (1967) and the Steele Prize from the American Mathematical Society twice (1982 and 2004) in recognition of his explanations of mathematical concepts across a wide range of scientific.c disciplines. The citation reads, "The phrase sublime elegance is rarely associated with mathematical exposition, but it applies to all of Milnor's writings. Reading his books, one is struck with the ease with which the subject is unfolding and it only becomes apparent after re.ection that this ease is the mark of a master." Milnor has published five books with Princeton University Press.
1 有用 翡翠 2012-04-10 23:42:07
怕是没几个人写书可以入Milnor这般清明如水
0 有用 hakusai 2023-04-16 15:29:28 加拿大
这么好的书,居然没有人用latex重排一遍!
1 有用 Herbertzou 2013-02-06 22:44:13
传说中的零基础书吧……基本selfcontained,milnor真是大神啊
0 有用 ahun 2021-09-07 02:07:21
第一部分和最后一部分在李群上的应用实在太精彩了。一泻千里的畅快感。
0 有用 丁白 2023-08-08 17:14:47 安徽
chapter1是理论介绍(分别从同伦和morse不等式两个方向来谈),chapter3则是理论高潮。虽然这个方向已经成熟了,但感觉临界点和大范围几何的关系非常值得关注…尤其是在光滑动力系统里
0 有用 Renart Effendi 2024-05-14 15:22:00 北京
我从约翰·米尔诺的书《莫尔斯理论》学到很多关于这理论的内容。很惊讶莫尔斯本人非常讨厌这本书和它的书名,说它应该叫《极限点理论》才对。传说莫尔斯收到这本书后,随即把它撕烂并扔进垃圾箱,他认为只有自己才配写这题目的书。这种反应好像过激了一点。但我个人对莫尔斯倒没有什么看法,他和他的夫人都挺和善。为了保持良好的关系,以免他发怒,我小心翼翼地不让他知道,我是多么喜爱米尔诺的书,并且从那儿学到不少几何知识呢... 我从约翰·米尔诺的书《莫尔斯理论》学到很多关于这理论的内容。很惊讶莫尔斯本人非常讨厌这本书和它的书名,说它应该叫《极限点理论》才对。传说莫尔斯收到这本书后,随即把它撕烂并扔进垃圾箱,他认为只有自己才配写这题目的书。这种反应好像过激了一点。但我个人对莫尔斯倒没有什么看法,他和他的夫人都挺和善。为了保持良好的关系,以免他发怒,我小心翼翼地不让他知道,我是多么喜爱米尔诺的书,并且从那儿学到不少几何知识呢。 (展开)
1 有用 JeanChristophe 2023-12-31 04:38:52 法国
常读常新,现已有TeX重排版
0 有用 丁白 2023-08-08 17:14:47 安徽
chapter1是理论介绍(分别从同伦和morse不等式两个方向来谈),chapter3则是理论高潮。虽然这个方向已经成熟了,但感觉临界点和大范围几何的关系非常值得关注…尤其是在光滑动力系统里
0 有用 北方火柴 2023-05-23 10:44:48 上海
看1/4 pinch的时候翻了翻,奇妙。 排版让人心累。 实的bott periodicity没有看懂证明,晕乎乎。
0 有用 hakusai 2023-04-16 15:29:28 加拿大
这么好的书,居然没有人用latex重排一遍!