Graph Theory and Additive Combinatorics: Exploring Structure and Randomness
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Description
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. Read more
Publisher : Cambridge University Press
Publication date : August 31, 2023
Edition : 1st
Language : English
Print length : 338 pages
ISBN-10 : 1009310941
ISBN-13 : 49
Item Weight : 1.68 pounds
Dimensions : 7.01 x 0.94 x 10 inches
Best Sellers Rank: #1,381,197 in Books (See Top 100 in Books) #113 in Graph Theory (Books) #217 in Discrete Mathematics (Books) #6,421 in Mathematics (Books)
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