Terence Tao: Additive Combinatorics

Cover: 9780521136563 | Additive Combinatorics | Terence Tao (u. a.) | Taschenbuch | Englisch

Rückseite: 9780521136563 | Additive Combinatorics | Terence Tao (u. a.) | Taschenbuch | Englisch

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Sprache: Englisch

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Beschreibung

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 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.

Über den Autor

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.

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2010
Fachbereich:	Allgemeines
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	Kartoniert / Broschiert
ISBN-13:	9780521136563
ISBN-10:	0521136563
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Tao, Terence Vu, Van H.
Hersteller:	Cambridge University Press
Verantwortliche Person für die EU:	Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de
Maße:	229 x 152 x 32 mm
Von/Mit:	Terence Tao (u. a.)
Erscheinungsdatum:	01.11.2010
Gewicht:	0,854 kg