Prologue; 1. The probabilistic method; 2. Sum set estimates; 3. Additive geometry; 4. Fourier-analytic methods; 5. Inverse sum set theorems; 6. Graph-theoretic methods; 7. The Littlewood–Offord problem; 8. Incidence geometry; 9. Algebraic methods; 10. Szemerédi's theorem for k = 3; 11. Szemerédi's theorem for k > 3; 12. Long arithmetic progressions in sum sets; Bibliography; Index.
A graduate-level 2006 text bringing together the tools from different fields used in additive combinatorics.
Terence Tao is a Professor in the Department of Mathematics at the University of California, Los Angeles. He was awarded the Fields Medal in 2006 for his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory. Van H. Vu is a Professor in the Department of Mathematics at Rutgers University, New Jersey.
'The book under review is a vital contribution to the literature,
and it has already become required reading for a new generation of
students as well as for experts in adjacent areas looking to learn
about additive combinatorics. … This was very much a book that
needed to be written at the time it was, and the authors are to be
highly commended for having done so in such an effective way.'
Bulletin of the American Mathematical Society
'The book gathers diverse important techniques used in additive
combinatorics, and its main advantage is that it is written in a
very readable and easy to understand style. The authors try very
successfully to develop all the necessary background material …
[which] makes the book useful not only to graduate students, but
also to researchers who are interested to learn more about the
variety of diverse tools and ideas applied in this fascinating
subject.' Zentralblatt MATH
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