Terence "Terry" Chi-Shen Tao, FAA FRS, is an Australian mathematician. His areas of interests are in harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, compressed sensing and analytic number theory. As of 2015, he holds the James and Carol Collins chair in mathematics at the University of California, Los Angeles. Professor Tao is a co-recipient of the 2006 Fields Medal and the 2014 Breakthrough Prize in Mathematics. He maintains a personal mathematics blog, which has been described by Timothy Gowers as the undisputed king of all mathematics blogs ."
This is part one of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25-30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.
首先向陶致敬!不仅仅出于对陶过人的能力,也出于他治学严谨并且从学生角度出发写书的良苦用心。但是对这本书,我想说明另一种观点。 这是一本读起来相当令人愉快的书,我感受到的主要由以下三点: 1.文笔是面向学生的,对于种种数学处理都会不厌其烦地说明其思想,出发点等等...
評分该书第22页命题2.2.12(c)的内容是:若a≥b且 b≥a,则a=b. 同页命题2.2.13(自然数的序的三岐性)的论证中,有如下内容:若a>b且a<b则根据命题2.2.12必有a=b,这是矛盾的。 笔者以为,命题2.2.12(c)之所以成立,是由于a≥b与 b≥a均含等号的缘故。具体理由是...
評分前5章和2个附录其实完全适合一般公众或者对数学有兴趣的中学生。 另外这本书其实是一本数学分析教材,本来大可不必给它加一个看上去更高级一点的新名字。
評分这本书可以说是对我帮助最大的书,从我接触大学数学一来,我花的最多时间的书就是这本。另外百度贴吧“陶哲轩实分析吧”就是我建的,那里人不多,不过希望大家有空去逛逛,有啥问题问出来,大家互相交流。 言归正传,在我刚学数学分析半年的时候,我对实数的严格定义特别感兴趣...
陶的迷人不僅在其天纔,更在慈悲。
评分看瞭前五章和附錄,可能是這本書最有特色的地方,因為這種書真的很少有從頭做起來構建自然數、整數、有理數和實數的。跟著陶哲軒就像真的一步一步把曾經那些習以為常的結論重新建構齣來,不過也很纍,要不斷挑戰自己的直覺。實數構建完瞭似乎可以暫時放下,估計微積分那一套弄起來和彆人是差不多的,可以去看看彆的書瞭。
评分陶的迷人不僅在其天纔,更在慈悲。
评分看瞭前五章和附錄,可能是這本書最有特色的地方,因為這種書真的很少有從頭做起來構建自然數、整數、有理數和實數的。跟著陶哲軒就像真的一步一步把曾經那些習以為常的結論重新建構齣來,不過也很纍,要不斷挑戰自己的直覺。實數構建完瞭似乎可以暫時放下,估計微積分那一套弄起來和彆人是差不多的,可以去看看彆的書瞭。
评分陶的迷人不僅在其天纔,更在慈悲。
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