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An Introduction to Ramsey Theory: Fast Functions, Infinity, and Metamathematics
 
Matthew Katz Pennsylvania State University, University Park, PA
Jan Reimann Pennsylvania State University, University Park, PA
An Introduction to Ramsey Theory
Softcover ISBN:  978-1-4704-4290-3
Product Code:  STML/87
List Price: $59.00
Individual Price: $47.20
MAA Member Price: $47.20
eBook ISBN:  978-1-4704-4994-0
Product Code:  STML/87.E
List Price: $49.00
Individual Price: $39.20
MAA Member Price: $39.20
Softcover ISBN:  978-1-4704-4290-3
eBook: ISBN:  978-1-4704-4994-0
Product Code:  STML/87.B
List Price: $108.00 $83.50
MAA Member Price: $86.40 $66.80
An Introduction to Ramsey Theory
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An Introduction to Ramsey Theory: Fast Functions, Infinity, and Metamathematics
Matthew Katz Pennsylvania State University, University Park, PA
Jan Reimann Pennsylvania State University, University Park, PA
Softcover ISBN:  978-1-4704-4290-3
Product Code:  STML/87
List Price: $59.00
Individual Price: $47.20
MAA Member Price: $47.20
eBook ISBN:  978-1-4704-4994-0
Product Code:  STML/87.E
List Price: $49.00
Individual Price: $39.20
MAA Member Price: $39.20
Softcover ISBN:  978-1-4704-4290-3
eBook ISBN:  978-1-4704-4994-0
Product Code:  STML/87.B
List Price: $108.00 $83.50
MAA Member Price: $86.40 $66.80
  • Book Details
     
     
    Student Mathematical Library
    Volume: 872018; 207 pp
    MSC: 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 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.”

    This book is published in cooperation with Mathematics Advanced Study Semesters.
    Readership

    Undergraduate 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
  • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 872018; 207 pp
MSC: 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 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.”

This book is published in cooperation with Mathematics Advanced Study Semesters.
Readership

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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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