An Introduction to Ramsey Theory: Fast Functions, Infinity, and Metamathematics (Student Mathematical Library) (Student Mathematical Library, 87) - Softcover

Matthew Katz; Jan Reimann

Softcover

ISBN 10: 1470442906 ISBN 13: 9781470442903

Publisher: American Mathematical Society, 2018

Synopsis

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.

About this title

About the Author

Matthew Katz: Pennsylvania State University, University Park, PA, Jan Reimann: Pennsylvania State University, University Park, PA

Review

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

Edition details

• Publisher: American Mathematical Society
• Publication date: 2018
• ISBN 10: 1470442906
• ISBN 13: 9781470442903
• Binding: Paperback
• Language: English
• Number of pages: 207