Basics of Ramsey Theory
Veselin Jungić, , 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.
The only real prerequisites to fully grasp the material presented in the book, to paraphrase Fikret Vajzović, a Bosnian mathematician, 1928-2017, are knowing how to read and write and possessing a certain level of mathematical maturity. In other words, my presentation of the material is based on an assumption of the reader's maximum intelligence and minimum background.
Any undergraduate student who has successfully completed the standard calculus sequence of courses and a standard entry level linear algebra course and has a genuine interest in learning mathematics should be able to master the main ideas presented in this book.
The Ramsey Theory Podcast: No Strangers At This Party
The "Ramsey Theory Podcast: No Strangers at This Party" is created by a group of students from ¶¡ÏãÔ°AV under the supervision of Veselin Jungic.
This podcast celebrates Ramsey theory and the people working in this dynamic field of modern mathematics.
Through their conversations with undergraduate students, some of today's most notable Ramsey theorists talk about their first experiences with mathematics, their times as undergraduate and graduate students, their views about Ramsey theory and mathematics in general, and about their research interests.
The podcast is available on , , , and .
