Additive Combinatorics

出版者:Cambridge University Press

作者:Terence Tao

页数:532

出版时间:2009-12-21

价格:USD 60.00

装帧:Paperback

isbn号码:9780521136563

丛书系列:Cambridge Studies in Advanced Mathematics

图书标签:组合Tao计算机科学数理逻辑7数学与我有关CUP2009

Additive combinatorics is the theory of counting additive structures in sets. This theory has seen exciting developments and dramatic changes in direction in recent years thanks to its connections with areas such as number theory, ergodic theory and graph theory. This graduate-level 2006 text will allow students and researchers easy entry into this fascinating field. Here, the authors bring together in a self-contained and systematic manner the many different tools and ideas that are used in the modern theory, presenting them in an accessible, coherent, and intuitively clear manner, and providing immediate applications to problems in additive combinatorics. The power of these tools is well demonstrated in the presentation of recent advances such as Szemeredi's theorem on arithmetic progressions, the Kakeya conjecture and Erdos distance problems, and the developing field of sum-product estimates. The text is supplemented by a large number of exercises and new results.