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Additive combinatorics is the theory of counting
additive structures in sets. This theory has seen
exciting developments and dramatic changes in
direction in recent years thanks to its connections
with areas such as number theory, ergodic theory
and graph theory. This graduate level text will allow
students and researchers easy entry into this
fascinating field. Here, for the first time, the authors
bring together in a self-contained and systematic
manner the many different tools and ideas that are
used in the modern theory, presenting them in an
accessible, coherent, and intuitively clear manner,
and providing immediate applications to problems in
additive combinatorics. The power of these tools is
well demonstrated in the presentation of recent
advances such as Szemerédi`s theorem on
arithmetic progressions, the Kakeya conjecture and
Erdos distance problems, and the developing field of
sum-product estimates. The text is supplemented by
a large number of exercises and new results.
ISBN - 9780521170123
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Pages : 536
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