# Analysis II: Third Edition

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*Terence Tao*

A publication of Hindustan Book Agency

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 a few new exercises have been added.

A publication of Hindustan Book Agency; distributed within the Americas by the American Mathematical Society. Maximum discount of 20% for all commercial channels.

#### Readership

Undergraduate and graduate students interested in analysis.

#### Reviews & Endorsements

…it would be an error not to stick very close to the text — it's 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