# Analysis I: Fourth 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.

The fourth edition incorporates a large number of
corrections reported since the release of the third edition, as well
as some new exercises.

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.