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I did not read through the whole book, I must confess, since I picked it up for the purpose of finding interesting homework problems for my students. I believes it gives a good general impression of things, but it would not be my main choice for learning real analysis.
Terence "Terry" Tao FAA FRS (simplified Chinese: 陶哲轩; traditional Chinese: 陶哲軒; pinyin: Táo Zhéxuān) is an Australian-American mathematician who has worked in various areas of mathematics. He currently focuses on harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, compressed sensing and analytic number theory. As of 2015, ...more