Softcover ISBN:  9780821841563 
Product Code:  CBMS/123 
82 pp 
List Price:  $31.00 
MAA Member Price:  $27.90 
AMS Member Price:  $24.80 
Electronic ISBN:  9781470426675 
Product Code:  CBMS/123.E 
82 pp 
List Price:  $29.00 
MAA Member Price:  $26.10 
AMS Member Price:  $23.20 

Book DetailsCBMS Regional Conference Series in MathematicsVolume: 123; 2015MSC: Primary 05;
In every sufficiently large structure which has been partitioned there will always be some wellbehaved 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 copublication of the AMS and CBMS.
ReadershipGraduate students and researchers interested in combinatorics, in particular, Ramsey theory.

Table of Contents

Chapters

Introduction

Chapter 1. Three views of Ramsey theory

Chapter 2. Ramsey’s theorem

Chapter 3. van der Waerden’s theorem

Chapter 4. The HalesJewett theorem

Chapter 5. Szemerédi’s theorem

Chapter 6. Graph Ramsey theory

Chapter 7. Euclidean Ramsey theory

Chapter 8. A general Ramsey product theorem

Chapter 9. The theorems of Schur, Folkman, and Hindman

Chapter 10. Rado’s theorem

Chapter 11. Current trends


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In every sufficiently large structure which has been partitioned there will always be some wellbehaved 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 copublication of the AMS and CBMS.
Graduate students and researchers interested in combinatorics, in particular, Ramsey theory.

Chapters

Introduction

Chapter 1. Three views of Ramsey theory

Chapter 2. Ramsey’s theorem

Chapter 3. van der Waerden’s theorem

Chapter 4. The HalesJewett theorem

Chapter 5. Szemerédi’s theorem

Chapter 6. Graph Ramsey theory

Chapter 7. Euclidean Ramsey theory

Chapter 8. A general Ramsey product theorem

Chapter 9. The theorems of Schur, Folkman, and Hindman

Chapter 10. Rado’s theorem

Chapter 11. Current trends