Softcover ISBN:  9781470442903 
Product Code:  STML/87 
List Price:  $59.00 
Individual Price:  $47.20 
MAA Member Price:  $47.20 
eBook ISBN:  9781470449940 
Product Code:  STML/87.E 
List Price:  $49.00 
Individual Price:  $39.20 
MAA Member Price:  $39.20 
Softcover ISBN:  9781470442903 
eBook: ISBN:  9781470449940 
Product Code:  STML/87.B 
List Price:  $108.00 $83.50 
MAA Member Price:  $86.40 $66.80 
Softcover ISBN:  9781470442903 
Product Code:  STML/87 
List Price:  $59.00 
Individual Price:  $47.20 
MAA Member Price:  $47.20 
eBook ISBN:  9781470449940 
Product Code:  STML/87.E 
List Price:  $49.00 
Individual Price:  $39.20 
MAA Member Price:  $39.20 
Softcover ISBN:  9781470442903 
eBook ISBN:  9781470449940 
Product Code:  STML/87.B 
List Price:  $108.00 $83.50 
MAA Member Price:  $86.40 $66.80 

Book DetailsStudent Mathematical LibraryVolume: 87; 2018; 207 ppMSC: Primary 05; 03;
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 ParisHarrington 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.”
This book is published in cooperation with Mathematics Advanced Study Semesters.ReadershipUndergraduate and graduate students and researchers interested in combinatorics and mathematical logic.

Table of Contents

Chapters

Graph Ramsey theory

Infinite Ramsey theory

Growth of Ramsey functions

Metamathematics


Additional Material

Reviews

This little book is a gem. It is advertised as having minimal prerequisites. Such statements are often made but less often accurate, but the claim seems entirely truthful here. The authors have taken pains to develop, as necessary, what background material is used in the book...and have written this book in a clear, conversational tone that is certain to engage student interest.
Mark Hunacek, MAA Reviews


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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 ParisHarrington 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.”
Undergraduate and graduate students and researchers interested in combinatorics and mathematical logic.

Chapters

Graph Ramsey theory

Infinite Ramsey theory

Growth of Ramsey functions

Metamathematics

This little book is a gem. It is advertised as having minimal prerequisites. Such statements are often made but less often accurate, but the claim seems entirely truthful here. The authors have taken pains to develop, as necessary, what background material is used in the book...and have written this book in a clear, conversational tone that is certain to engage student interest.
Mark Hunacek, MAA Reviews