Bibliographic Information

Additive combinatorics

Terence Tao, Van H. Vu

(Cambridge studies in advanced mathematics, 105)

Cambridge University Press, 2010

  • : pbk

Available at  / 22 libraries

Search this Book/Journal

Note

Includes bibliographical references (p. 488-504) and index

Paperback edition

Description and Table of Contents

Description

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 2006 text will allow students and researchers easy entry into this fascinating field. Here, 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 Szemeredi'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.

Table of Contents

  • 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. Szemeredi's theorem for k = 3
  • 11. Szemeredi's theorem for k > 3
  • 12. Long arithmetic progressions in sum sets
  • Bibliography
  • Index.

by "Nielsen BookData"

Related Books: 1-1 of 1

Details

  • NCID
    BB00526085
  • ISBN
    • 9780521136563
  • Country Code
    uk
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Cambridge
  • Pages/Volumes
    xviii, 512 p.
  • Size
    23 cm
  • Parent Bibliography ID
Page Top