About this product

Product Identifiers

PublisherCRC Press LLC

ISBN-101138364339

ISBN-139781138364332

eBay Product ID (ePID)18050093171

Product Key Features

Number of Pages241 Pages

Publication NameIntroduction to Ramsey Theory

LanguageEnglish

Publication Year2021

SubjectGeneral, Algebra / General, Discrete Mathematics

TypeTextbook

Subject AreaMathematics

AuthorAaron Robertson

SeriesDiscrete Mathematics and Its Applications Ser.

FormatHardcover

Dimensions

Item Weight22.3 Oz

Item Length9.2 in

Item Width6.1 in

Additional Product Features

LCCN2021-000970

TitleLeadingAn

Dewey Edition23

IllustratedYes

Dewey Decimal511.5

Table Of Content1. Introduction. 1.1. What is Ramsey Theory? 1.2. Notations and Conventions. 1.3. Prerequisites. 1.4. Compactness Principle. 1.5. Set Theoretic Considerations. 1.6. Exercises. 2. Integer Ramsey Theory. 2.1. Van der Waerden's Theorem. 2.2. Equations. 2.3. Hales-Jewett Theorem. 2.4. Finite Sums. 2.5. Density Results. 2.6. Exercises. 3. Graph Ramsey Theory. 3.1. Complete Graphs. 3.2. Other Graphs. 3.3. Hypergraphs. 3.4. Infinite Graphs. 3.5. Comparing Ramsey and van der Waerden Results. 3.6. Exercises. 4. Euclidean Ramsey Theory. 4.1. Polygons. 4.2. Chromatic Number of the Plane. 4.3. Four Color Map Theorem. 4.4. Exercises. 5. Other Approaches to Ramsey Theory. 5.1. Topological Approaches. 5.2. Ergodic Theory. 5.3. Stone-cech Compactification. 5.4. Additive Combinatorics Methods. 5.5. Exercises. 6. The Probabilistic Method. 6.1. Lower Bounds on Ramsey, van der Waerden, and Hales-Jewett Numbers. 6.2. Turán's Theorem. 6.3. Almost-surely van der Waerden and Ramsey Numbers. 6.4. Lovász Local Lemma. 6.5. Exercises. 7. Applications. 7.1. Fermat's Last Theorem. 7.2. Encoding Information. 7.3. Data Mining. 7.4. Exercises. Bibliography. Index.

SynopsisThis up-to-date book introduces the field of Ramsey theory from several different viewpoints. 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., 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-cech 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., 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-cech 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 permutationpatterns, he has focused most of his research on Ramsey theory.

LC Classification NumberQA166.R57 2021