发表于2024-11-04
Morse Theory 2024 pdf epub mobi 电子书
图书标签: 数学 morse_theory 拓扑学 米尔诺 几何 几何与拓扑 流形上的分析 拓扑
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.
可以看出milnor对几何的理解,其它书中可能只是定理的一步步推导,但milnor能把一些直觉性的理解写出来(当然是有严格推导作为基础的)。(不过他图省事的地方也很多)
评分挺适合复习黎曼几何的书
评分写得很流畅,读最后一章效率出奇的高呀
评分Milnor的书都是值得细细地读的。前面貌似不难,但是能完全读通后面的Bott周期性定理也不是一件容易的事。
评分真神作也!为什么我没有早点读这本书!后面的Bott Periodicity部分回味无穷啊。
Morse Theory 2024 pdf epub mobi 电子书