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Graph Theory and Additive Combinatorics: Exploring Structure and Randomness - Couverture rigide

Zhao, Yufei

 
9781009310949: Graph Theory and Additive Combinatorics: Exploring Structure and Randomness
Couverture rigide
ISBN 10 : 1009310941 ISBN 13 : 9781009310949
Editeur : Cambridge University Press, 2023

Synopsis

Using the dichotomy of structure and pseudorandomness as a central theme, this accessible text provides a modern introduction to extremal graph theory and additive combinatorics. Readers will explore central results in additive combinatorics-notably the cornerstone theorems of Roth, Szemerédi, Freiman, and Green-Tao-and will gain additional insights into these ideas through graph theoretic perspectives. Topics discussed include the Turán problem, Szemerédi's graph regularity method, pseudorandom graphs, graph limits, graph homomorphism inequalities, Fourier analysis in additive combinatorics, the structure of set addition, and the sum-product problem. Important combinatorial, graph theoretic, analytic, Fourier, algebraic, and geometric methods are highlighted. Students will appreciate the chapter summaries, many figures and exercises, and freely available lecture videos on MIT OpenCourseWare. Meant as an introduction for students and researchers studying combinatorics, theoretical computer science, analysis, probability, and number theory, the text assumes only basic familiarity with abstract algebra, analysis, and linear algebra.

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À propos de l'auteur

Yufei Zhao is Associate Professor of Mathematics at the Massachusetts Institute of Technology. His research tackles a broad range of problems in discrete mathematics, including extremal, probabilistic, and additive combinatorics, graph theory, and discrete geometry, as well as applications to computer science. His honors include the SIAM Dénes Kőnig prize (2018), the Sloan Research Fellowship (2019), and the NSF CAREER Award (2021). This book is based on an MIT graduate course, which he has taught and developed over the last five years.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Cambridge University Press
Date d'édition
2023
Langue
anglais
ISBN 10 
1009310941
ISBN 13 
9781009310949
Reliure
Relié
Numéro d'édition
1
Nombre de pages
338
Coordonnées du fabricant
Cambridge University Press
https://www.cambridge.org/

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