具體描述
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.
著者簡介
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 ."
圖書目錄
讀後感
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。
評分窃以为本书作为参考读物更合适，要按照本书内容讲授，需要学习者的自觉投入，更需要足够优秀的导师，部分基础性证明很是考验功底。
評分首先向陶致敬！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...
評分窃以为本书作为参考读物更合适，要按照本书内容讲授，需要学习者的自觉投入，更需要足够优秀的导师，部分基础性证明很是考验功底。
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。
用戶評價
陶的迷人不僅在其天纔，更在慈悲。
评分陶的迷人不僅在其天纔，更在慈悲。
评分工科生一枚，覺得學的高等數學不爽，並且受不瞭中文版的“陶哲軒實分析”翻譯。欣賞作者一步步構建分析的大廈。第三版終於可以在springer下載瞭，爽歪歪
评分Excellent exposition and very rigorous approach. 用這本書輔助實分析課程很有用，很多概念都說得很清楚。
评分工科生一枚，覺得學的高等數學不爽，並且受不瞭中文版的“陶哲軒實分析”翻譯。欣賞作者一步步構建分析的大廈。第三版終於可以在springer下載瞭，爽歪歪
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