Ramsey Theory
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Ramsey Theory
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Author : Ronald L. Graham
language : en
Publisher: John Wiley & Sons
Release Date : 1991-01-16
Ramsey Theory written by Ronald L. Graham and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-01-16 with Mathematics categories.
Praise for the First Edition "Anyone interested in getting an introduction to Ramsey theorywill find this illuminating..." --MAA Reviews Covering all the major concepts, proofs, and theorems, theSecond Edition of Ramsey Theory is the ultimate guideto understanding every aspect of Shelah's proof, as well asthe original proof of van der Waerden. The book offers a historicalperspective of Ramsey's fundamental paper from 1930 andErdos' and Szekeres' article from 1935, while placingthe various theorems in the context of T. S. Motzkin'sthought on the subject of "Complete Disorder isImpossible." Ramsey Theory, Second Edition includes new and excitingcoverage of Graph Ramsey Theory and Euclidean Ramsey Theory andalso relates Ramsey Theory to other areas in discrete mathematics.In addition, the book features the unprovability results of Parisand Harrington and the methods from topological dynamics pioneeredby Furstenburg. Featuring worked proofs and outside applications, RamseyTheory, Second Edition addresses: * Ramsey and density theorems on both broad and meticulousscales * Extentions and implications of van der Waerden's Theorem,the Hales-Jewett Theorem, Roth's Theorem, Rado'sTheorem, Szemeredi's Theorem, and the Shelah Proof * Regular homogeneous and nonhomogeneous systems andequations * Special cases and broader interdisciplinary applications ofRamsey Theory principles An invaluable reference for professional mathematicians workingin discrete mathematics, combinatorics, and algorithms, RamseyTheory, Second Edition is the definitive work on thesubject.
Fundamentals Of Ramsey Theory
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Author : Aaron Robertson
language : en
Publisher: CRC Press
Release Date : 2021-06-18
Fundamentals Of Ramsey Theory written by Aaron Robertson and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-18 with Mathematics categories.
Ramsey theory is a fascinating topic. The author shares his view of the topic in this contemporary overview of Ramsey theory. He presents from several points of view, adding intuition and detailed proofs, in an accessible manner unique among most books on the topic. This book covers all of the main results in Ramsey theory along with results that have not appeared in a book before. The presentation is comprehensive and reader friendly. The book covers integer, graph, and Euclidean Ramsey theory with many proofs being combinatorial in nature. The author motivates topics and discussion, rather than just a list of theorems and proofs. In order to engage the reader, each chapter has a section of exercises. This up-to-date book introduces the field of Ramsey theory from several different viewpoints so that the reader can decide which flavor of Ramsey theory best suits them. Additionally, the book offers: A chapter providing different approaches to Ramsey theory, e.g., using topological dynamics, ergodic systems, and algebra in the Stone-Čech compactification of the integers. A chapter on the probabilistic method since it is quite central to Ramsey-type numbers. A unique chapter presenting some applications of Ramsey theory. Exercises in every chapter The intended audience consists of students and mathematicians desiring to learn about Ramsey theory. An undergraduate degree in mathematics (or its equivalent for advanced undergraduates) and a combinatorics course is assumed. TABLE OF CONENTS Preface List of Figures List of Tables Symbols 1. Introduction 2. Integer Ramsey Theory 3. Graph Ramsey Theory 4. Euclidean Ramsey Theory 5. Other Approaches to Ramsey Theory 6. The Probabilistic Method 7. Applications Bibliography Index Biography Aaron Robertson received his Ph.D. in mathematics from Temple University under the guidance of his advisor Doron Zeilberger. Upon finishing his Ph.D. he started at Colgate University in upstate New York where he is currently Professor of Mathematics. He also serves as Associate Managing editor of the journal Integers. After a brief detour into the world of permutation patterns, he has focused most of his research on Ramsey theory.
Mathematics Of Ramsey Theory
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Author : Jaroslav Nesetril
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mathematics Of Ramsey Theory written by Jaroslav Nesetril and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
One of the important areas of contemporary combinatorics is Ramsey theory. Ramsey theory is basically the study of structure preserved under partitions. The general philosophy is reflected by its interdisciplinary character. The ideas of Ramsey theory are shared by logicians, set theorists and combinatorists, and have been successfully applied in other branches of mathematics. The whole subject is quickly developing and has some new and unexpected applications in areas as remote as functional analysis and theoretical computer science. This book is a homogeneous collection of research and survey articles by leading specialists. It surveys recent activity in this diverse subject and brings the reader up to the boundary of present knowledge. It covers virtually all main approaches to the subject and suggests various problems for individual research.
Rudiments Of Ramsey Theory
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Author : Ronald L. Graham
language : en
Publisher: American Mathematical Soc.
Release Date : 1981-12-31
Rudiments Of Ramsey Theory written by Ronald L. Graham and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981-12-31 with Mathematics categories.
It is no exaggeration to say that over the past several decades there has been a veritable explosion of activity in the general field of combinatorics. Ramsey theory, in particular, has shown remarkable growth. This book gives a picture of the state of the art of Ramsey theory at the time of Graham's CBMS lectures. In keeping with the style of the lectures, the exposition is informal. However, complete proofs are given for most of the basic results presented. In addition, many useful results may be found in the exercises and problems. Loosely speaking, Ramsey theory is the branch of combinatorics that deals with structures that are preserved under partitions. Typically, one looks at the following kind of question: If a particular structure (e.g., algebraic, combinatorial or geometric) is arbitrarily partitioned into finitely many classes, what kinds of substructures must always remain intact in at least one of the classes? At the time of these lectures, a number of spectacular advances had been made in the field of Ramsey theory. These include: the work of Szemeredi and Furstenberg settling the venerable conjecture of Erdos and Turan, the Nesetril-Rodl theorems on induced Ramsey properties, the results of Paris and Harrington on ``large'' Ramsey numbers and undecidability in first-order Peano arithmetic, Deuber's solution to the old partition regularity conjecture of Rado, Hindman's surprising generalization of Schur's theorem, and the resolution of Rota's conjecture on Ramsey's theorem for vector spaces by Graham, Leeb and Rothschild. It has also become apparent that the ideas and techniques of Ramsey theory span a rather broad range of mathematical areas, interacting in essential ways with parts of set theory, graph theory, combinatorial number theory, probability theory, analysis and even theoretical computer science. These lecture notes lay out the foundation on which much of this work is based. Relatively little specialized mathematical background is required for this book. It should be accessible to upper division students.
Rudiments Of Ramsey Theory
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Author : Ron Graham
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-10-01
Rudiments Of Ramsey Theory written by Ron Graham and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-01 with Combinatorial analysis categories.
In every sufficiently large structure which has been partitioned there will always be some well-behaved structure in one of the parts. This takes many forms. For example, colorings of the integers by finitely many colors must have long monochromatic arithmetic progressions (van der Waerden's theorem); and colorings of the edges of large graphs must have monochromatic subgraphs of a specified type (Ramsey's theorem). This book explores many of the basic results and variations of this theory. Since the first edition of this book there have been many advances in this field. In the second edition the authors update the exposition to reflect the current state of the art. They also include many pointers to modern results. A co-publication of the AMS and CBMS.
An Introduction To Ramsey Theory Fast Functions Infinity And Metamathematics
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Author : Matthew Katz
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-10-03
An Introduction To Ramsey Theory Fast Functions Infinity And Metamathematics written by Matthew Katz and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-03 with Combinatorial analysis categories.
This book takes the reader on a journey through Ramsey theory, from graph theory and combinatorics to set theory to logic and metamathematics. Written in an informal style with few requisites, it develops two basic principles of Ramsey theory: many combinatorial properties persist under partitions, but to witness this persistence, one has to start with very large objects. The interplay between those two principles not only produces beautiful theorems but also touches the very foundations of mathematics. In the course of this book, the reader will learn about both aspects. Among the topics explored are Ramsey's theorem for graphs and hypergraphs, van der Waerden's theorem on arithmetic progressions, infinite ordinals and cardinals, fast growing functions, logic and provability, Gödel incompleteness, and the Paris-Harrington theorem. Quoting from the book, “There seems to be a murky abyss lurking at the bottom of mathematics. While in many ways we cannot hope to reach solid ground, mathematicians have built impressive ladders that let us explore the depths of this abyss and marvel at the limits and at the power of mathematical reasoning at the same time. Ramsey theory is one of those ladders.”
Ramsey Theory On The Integers
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Author : Bruce M. Landman
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-11-10
Ramsey Theory On The Integers written by Bruce M. Landman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-10 with Mathematics categories.
Ramsey theory is the study of the structure of mathematical objects that is preserved under partitions. In its full generality, Ramsey theory is quite powerful, but can quickly become complicated. By limiting the focus of this book to Ramsey theory applied to the set of integers, the authors have produced a gentle, but meaningful, introduction to an important and enticing branch of modern mathematics. Ramsey Theory on the Integers offers students a glimpse into the world of mathematical research and the opportunity for them to begin pondering unsolved problems. For this new edition, several sections have been added and others have been significantly updated. Among the newly introduced topics are: rainbow Ramsey theory, an "inequality" version of Schur's theorem, monochromatic solutions of recurrence relations, Ramsey results involving both sums and products, monochromatic sets avoiding certain differences, Ramsey properties for polynomial progressions, generalizations of the Erdős-Ginzberg-Ziv theorem, and the number of arithmetic progressions under arbitrary colorings. Many new results and proofs have been added, most of which were not known when the first edition was published. Furthermore, the book's tables, exercises, lists of open research problems, and bibliography have all been significantly updated. This innovative book also provides the first cohesive study of Ramsey theory on the integers. It contains perhaps the most substantial account of solved and unsolved problems in this blossoming subject. This breakthrough book will engage students, teachers, and researchers alike.
Introduction To Ramsey Spaces Am 174
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Author : Stevo Todorcevic
language : en
Publisher: Princeton University Press
Release Date : 2010-07-01
Introduction To Ramsey Spaces Am 174 written by Stevo Todorcevic and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-01 with Mathematics categories.
Ramsey theory is a fast-growing area of combinatorics with deep connections to other fields of mathematics such as topological dynamics, ergodic theory, mathematical logic, and algebra. The area of Ramsey theory dealing with Ramsey-type phenomena in higher dimensions is particularly useful. Introduction to Ramsey Spaces presents in a systematic way a method for building higher-dimensional Ramsey spaces from basic one-dimensional principles. It is the first book-length treatment of this area of Ramsey theory, and emphasizes applications for related and surrounding fields of mathematics, such as set theory, combinatorics, real and functional analysis, and topology. In order to facilitate accessibility, the book gives the method in its axiomatic form with examples that cover many important parts of Ramsey theory both finite and infinite. An exciting new direction for combinatorics, this book will interest graduate students and researchers working in mathematical subdisciplines requiring the mastery and practice of high-dimensional Ramsey theory.
Ramsey Theory
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Author : Alexander Soifer
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-29
Ramsey Theory written by Alexander Soifer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-29 with Mathematics categories.
This book explores the theory’s history, recent developments, and some promising future directions through invited surveys written by prominent researchers in the field. The first three surveys provide historical background on the subject; the last three address Euclidean Ramsey theory and related coloring problems. In addition, open problems posed throughout the volume and in the concluding open problem chapter will appeal to graduate students and mathematicians alike.
Ramsey Theory For Product Spaces
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Author : Pandelis Dodos
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-05-16
Ramsey Theory For Product Spaces written by Pandelis Dodos and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-16 with Combinatorial analysis categories.
Ramsey theory is a dynamic area of combinatorics that has various applications in analysis, ergodic theory, logic, number theory, probability theory, theoretical computer science, and topological dynamics. This book is devoted to one of the most important areas of Ramsey theory—the Ramsey theory of product spaces. It is a culmination of a series of recent breakthroughs by the two authors and their students who were able to lift this theory to the infinite-dimensional case. The book presents many major results and methods in the area, such as Szemerédi's regularity method, the hypergraph removal lemma, and the density Hales–Jewett theorem. This book addresses researchers in combinatorics but also working mathematicians and advanced graduate students who are interested in Ramsey theory. The prerequisites for reading this book are rather minimal: it only requires familiarity, at the graduate level, with probability theory and real analysis. Some familiarity with the basics of Ramsey theory would be beneficial, though not necessary.