图论与加性组合学：探索结构与随机性 MIT未来科学奖、斯隆奖得主 华裔数学家赵宇飞 Graph Theory and Additive Combinatorics： Exploring Structure and Randomness

基本信息

Publisher：Cambridge University Press; 1st edition (August 31, 2023)

Language：English

Hardcover：338 pages

ISBN-10：1009310941

ISBN-13：978-1009310949

Item Weight：1.74 pounds

页面参数仅供参考，具体以实物为准

书籍简介

本书以结构和伪随机性的二分法为中心主题，提供了极端图论和加法组合学的现代介绍。读者将探索加法组合学的核心结果--特别是Roth、Szemerédi、Freiman和Green-Tao的基石定理--并将通过图论的视角获得对这些想法的额外见解。讨论的主题包括图兰问题、Szemerédi的图规律性方法、伪随机图、图极限、图同构不等式、加法组合学中的傅里叶分析、集合加法的结构以及和积问题。重要的组合学、图论、分析、傅里叶、代数和几何方法被强调。学生会喜欢本章的摘要、许多数字和练习，以及在MIT OpenCourseWare上免费提供的讲课视频。作为学习组合学、理论计算机科学、分析、概率和数论的学生和研究人员的入门教材，该书只假定对抽象代数、分析和线性代数有基本的熟悉。

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.

作者简介

赵宇飞是美国麻省理工学院的数学副教授。他的研究涉及离散数学的广泛问题，包括极值、概率和加法组合学、图论和离散几何学，以及在计算机科学中的应用。他的荣誉包括SIAM Dénes Kőnig奖（2018年）、斯隆研究奖学金（2019年）和NSF CAREER奖（2021年）。本书以麻省理工学院的研究生课程为基础，是他在过去五年中教授和开发的。

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.