Preface Preface
The purpose of these lecture notes is to serve as a gentle introduction to Ramsey theory for those undergraduate students interested in becoming familiar with this dynamic segment of contemporary mathematics that combines, among others, ideas from number theory and combinatorics.
Since this booklet contains the class lecture notes, the reader will occasionally need the help of a more knowledgeable other: an instructor, a peer, a book, or Google. In addition to the bibliography, links with the relevant freely available online resources are provided at the end of each section.
The only real prerequisites to fully grasp the material presented in these lecture notes, to paraphrase Professor Fikret Vajzović (1928 — 2017), is knowing how to read and write and possessing a certain level of mathematical maturity.
Any undergraduate student who has successfully completed the standard calculus sequence of courses and a standard first (or second) year linear algebra course and has a genuine interest in learning mathematics should be able to master the main ideas presented here.
My wish is to give to the reader both challenging and enjoyable experiences in learning some of the basic facts about Ramsey theory, a relatively new mathematical field.
But what is Ramsey theory?
Probably the best-known description of Ramsey theory is provided by Theodore S. Motzkin:
Complete disorder is impossible.
Here are a few more:
Ramsey theory studies the mathematics of colouring. — Alexander Soifer
Ramsey theory is the study of the preservation of properties under set partitions. — Bruce Landman and Aaron Robertson
The fundamental kind of question Ramsey theory asks is: can one always find order in chaos? If so, how much? Just how large a slice of chaos do we need to be sure to find a particular amount of order in it? — Imre Leader
If mathematics is a science of patterns, then Ramsey theory is a science of the stubbornness of patterns. – V. Jungic
No project such as this can be free from errors and incompleteness. I would be grateful to anyone who points out any typos, errors, or provides any other suggestion on how to improve this manuscript.
Veselin Jungic
Department of Mathematics, Simon Fraser University
Contact address: vjungic@sfu.ca
In Burnaby, B.C., August 2020