Additive Combinatorics

Author: Terence Tao
Publisher: Cambridge University Press
ISBN: 1139458345
Format: PDF, Mobi
Download Now
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 Szemerédi'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.

Additive Combinatorics

Author: Bela Bajnok
Publisher: CRC Press
ISBN: 1351137603
Format: PDF, ePub, Docs
Download Now
Additive Combinatorics: A Menu of Research Problems is the first book of its kind to provide readers with an opportunity to actively explore the relatively new field of additive combinatorics. The author has written the book specifically for students of any background and proficiency level, from beginners to advanced researchers. It features an extensive menu of research projects that are challenging and engaging at many different levels. The questions are new and unsolved, incrementally attainable, and designed to be approachable with various methods.

Mathematics

Author: Ida Kantor
Publisher: American Mathematical Soc.
ISBN: 1470422611
Format: PDF, ePub, Mobi
Download Now
Mathematics++ is a concise introduction to six selected areas of 20th century mathematics providing numerous modern mathematical tools used in contemporary research in computer science, engineering, and other fields. The areas are: measure theory, high-dimensional geometry, Fourier analysis, representations of groups, multivariate polynomials, and topology. For each of the areas, the authors introduce basic notions, examples, and results. The presentation is clear and accessible, stressing intuitive understanding, and it includes carefully selected exercises as an integral part. Theory is complemented by applications--some quite surprising--in theoretical computer science and discrete mathematics. The chapters are independent of one another and can be studied in any order. It is assumed that the reader has gone through the basic mathematics courses. Although the book was conceived while the authors were teaching Ph.D. students in theoretical computer science and discrete mathematics, it will be useful for a much wider audience, such as mathematicians specializing in other areas, mathematics students deciding what specialization to pursue, or experts in engineering or other fields.

Combinatorial Number Theory and Additive Group Theory

Author: Alfred Geroldinger
Publisher: Springer Science & Business Media
ISBN: 3764389613
Format: PDF, ePub, Mobi
Download Now
Additive combinatorics is a relatively recent term coined to comprehend the developments of the more classical additive number theory, mainly focussed on problems related to the addition of integers. Some classical problems like the Waring problem on the sum of k-th powers or the Goldbach conjecture are genuine examples of the original questions addressed in the area. One of the features of contemporary additive combinatorics is the interplay of a great variety of mathematical techniques, including combinatorics, harmonic analysis, convex geometry, graph theory, probability theory, algebraic geometry or ergodic theory. This book gathers the contributions of many of the leading researchers in the area and is divided into three parts. The two first parts correspond to the material of the main courses delivered, Additive combinatorics and non-unique factorizations, by Alfred Geroldinger, and Sumsets and structure, by Imre Z. Ruzsa. The third part collects the notes of most of the seminars which accompanied the main courses, and which cover a reasonably large part of the methods, techniques and problems of contemporary additive combinatorics.

Geometric Analysis

Author: Peter Li
Publisher: Cambridge University Press
ISBN: 1107020646
Format: PDF, Mobi
Download Now
Basic techniques for researchers interested in the field of geometric analysis.

Surveys in Combinatorics 2017

Author: Anders Claesson
Publisher: Cambridge University Press
ISBN: 1108350356
Format: PDF, ePub, Mobi
Download Now
This volume contains nine survey articles which provide expanded accounts of plenary seminars given at the British Combinatorial Conference at the University of Strathclyde in July 2017. This biennial conference is a well-established international event attracting speakers from around the world. Written by internationally recognised experts in the field, these articles represent a timely snapshot of the state of the art in the different areas of combinatorics. Topics covered include the robustness of graph properties, the spt-function of Andrews, switching techniques for edge decompositions of graphs, monotone cellular automata, and applications of relative entropy in additive combinatorics. The book will be useful to researchers and advanced graduate students, primarily in mathematics but also in computer science and statistics.