000			02033cam a22002538i 4500
001			23087665
005			20250609123612.0
008			230429s2023 enk b 001 0 eng
020			_a9781009310949
040			_aCSL _cCSL
041			_2eng _aeng
084			_aB44 R3 NBHM _qCSL
100	1		_aZhao, Yufei, _eauthor. _9812199
245	1	0	_aGraph theory and additive combinatorics : _bexploring structure and randomness
264		1	_aCambridge ; _bCambridge University Press, _c2023.
300			_axvii, 316 p. _c24 cm.
504			_aIncludes bibliographical references and index.
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		0	_aGraph theory. _9812200
650		0	_aDiscrete Mathematics Information Theory and Coding. _9812201
650		0	_aAdditive combinatorics. _9812202
650		0	_a, Computational Geometry. _9812203
942			_2CC _n0 _cTEXL _hB44 R3 NBHM
999			_c1431509 _d1431509