Analysis II

by Terence Tao

This is part two 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.   

Genres: Mathematics, Textbooks, Science, Nonfiction

220 pages, Kindle Edition

First published January 31, 2006

About the author

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, he holds the James and Carol Collins chair in mathematics at the University of California, Los Angeles. Tao was a co-recipient of the 2006 Fields Medal and the 2014 Breakthrough Prize in Mathematics.

Reviews

[Sabrina · Rating 5 out of 5]

a nice sequel to the absolutely wonderful analysis 1. this book has some of my favorite topics in real analysis and made me love it. it has the readability of the first book and even more intriguing topics!

[Tommy Pett · Rating 5 out of 5]

used it to self study some of the topics my real analysis class didn't get to, and it's pretty good. I think some sections could have a few more problems but otherwise really no complaints.