Analysis II

by Terence Tao

This two-volume introduction to real analysis is intended for honours undergraduates, who have already been exposed to calculus. The emphasis is on rigour and on foundations. The material starts at the very beginning - the construction of the number systems and set theory, then to the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and finally to 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. There are also appendices on mathematical logic and the decimal system. The course material is deeply intertwined with the exercises, as it is intended for the student to actively learn the material and to practice thinking and writing rigorously.

Genres: Mathematics, Textbooks, Science, Nonfiction

218 pages, Hardcover

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.