By Terence Tao - Analysis II (Texts and Readings in Mathematics 38) (3rd Edition) (2014-10-30) Corrected Reprint [Hardcover]

by Terence Tao

This is part two of a two-volume introduction to real analysis and 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 goes on 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 entire text (omitting some less central topics) can be taught in two quarters of twenty-five to thirty 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. In the third edition, several typos and other errors have been corrected and few new exercises have been added. Reviews From a review of the first "... it would be an error not to stick very close to the text -- its very well crafted indeed and deviating from the score would mean an unacceptable dissonance. "I hope to use Analysis I, II in an honors course myself, when the opportunity arises." -- Michael Berg, for MAA Reviews Contents Volume 2 1. Metric spaces 2. Continuous functions on metric spaces 3. Uniform convergence 4. Power series 5. Fourier series 6. Several variable differential calculus 7. Lebesgue measure 8. Lebesgue integration

Genres: Mathematics

Hardcover

Published January 1, 2017

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.