Basics of Ramsey Theory
Veselin Jungić, Basics of Ramsey Theory, Routledge, 2023
The purpose of this book is to serve as a gentle introduction to Ramsey theory for those interested in becoming familiar with this dynamic segment of contemporary mathematics that combines, among others, ideas from number theory and combinatorics.
This book is intended to be accessible to undergraduate students, mathematicians, and educators curious to learn more about Ramsey theory.
I had three major motivations for writing it:
Mathematical: The fundamental Ramsey theory results, like Ramsey's theorem or van der Waerden's theorem, for example, are self-contained.
Educational: The story about the beginnings and the development of Ramsey theory and people involved in those processes, like Frank Ramsey and Paul Erdős, for instance, supports the view of mathematics as a living organism and a deeply human endeavour.
Personal: I was privileged to witness how Ramsey theory served as a portal into the world of mathematical research to some extraordinarily talented young mathematicians. My hope is that this book might open this portal to some of its readers.