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.

• 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.

'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