000			01643 a2200169 4500
005			20251011163506.0
008			251011b |||||||| |||| 00| 0 eng d
020			_a9781009310949
082			_a511.5 _bZhaG
100			_aZhao, Yufei
245			_aGraph Theory and Additive Combinatorics : _bExploring Structure and Randomness / _cYufei Zhao
260			_bCambridge University Press : _aNew York , _c©2023.
300			_axvii, 316p.
520			_aUsing 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.
650			_aGraph Theory
942			_cBK
999			_c7424 _d7424