# Analysis I: Third Edition

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*Terence Tao*

A publication of Hindustan Book Agency

This is part one 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