In the words of Imre Leader, a Professor at the Cambridge University: "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?"

Frank Plumpton Ramsey (1903–1930) was a British mathematician, philosopher, and economist who made major contributions to all three fields.

The theorem that Ramsey established in 1930, now known as Ramsey's theorem, turned out to be a source of inspiration for generations of mathematicians.

"Ramsey Theory" by Bethani L'Heureux. The Coast Salish people use welcome figures as markers to welcome people to their territories. Can you recognize the colour pattern?

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.

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.

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-ontained.

Veselin Jungić, Basics of Ramsey Theory, Routledge, 2023

• 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 "Ramsey Theory Podcast: No Strangers At This Party" was created by a group of students from Simon Fraser University in Fall 2021: Knute Hardin, Harleen Kaur, Wassim Khelifi, Brian Krammer, Connor Marriam, Stephen Ng, Payal Payal, Amritha Raj Kizhakkeputhukulathil Ramanan, Anmol Anmol Singh, and Manan Sood.

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 podcasts are available on the following podcast services: Spotify, Anchor, Apple Podcasts, and Google Podcasts.

The episodes were edited by Aidan Wright. The background music was composed and performed by Nina Djokić. Both Aidan and Nina were students in the Fall 2020 “Introduction to Ramsey Theory” class taught by Veselin Jungić.

All podcast covers were created by Manan Sood.

All photos were courtesy of the interviewees. The photo of Dr. Joel Spencer is by Mary Ann Spencer. The drawing of Frank Ramsey was created by Veselin Jungić and Simon Roy.

The producer of the series was Veselin Jungić.

This collection contains 25 group projects completed by students enrolled in three different "Introduction To Ramsey Theory" courses offered by the Department of Mathematics, Simon Fraser University. 

The purpose of the projects was to give each student an opportunity to understand a segment of Ramsey theory in a deeper way by working on a Ramsey theory related theme in a group setting.

The diversity of the presented projects reflects the diversity of the students' academic backgrounds, their levels of mathematical knowledge, and their plans for their future careers. Still, all students shared their joy of doing mathematics.

A collection of students' group projects: PreTeXt HTML Link

• Jungić, V., Basics of Ramsey Theory, Routledge, 2023
• Jungić, V., An introduction of the Hales-Jewett theorem through examples and exercises, Part I, Crux Mathematicorum, v 49 n 4, 2023, pp. 206-212
• Jungić, V., The Never-ending Happiness of Erdős's Mathematics, The Mathematical Intelligencer, 2023
• Jungić, V., Still Spinning: The Moser Spindle at Sixty, Mathematics Magazine, DOI: 10.1080/0025570X.2023.2176684, 2023
• Jungić, V., An introduction of van der Waerden's theorem through examples and exercises, Part II, Crux Mathematicorum, v 48 n 8, 2022, pp. 468-474
• Jungić, V., The Problem, Crux Mathematicorum, v 48 n 8, 2022, p. 475-476
• Jungić, V.  An introduction of van der Waerden's theorem through examples and exercises, Part I, Crux Mathematicorum, v 48 n 7, 2022, pp. 412-420
• Brian Krammer, No Strangers at this Party: The Story of the Ramsey Theory Podcast, U(t) - Mathazine, Issue 7, Summer 2022, pages 30-31
• Jungić, V., On density of planar sets avoiding unit distance, U(t) - Mathazine, Issue 7, Summer 2022, pages 2-5

• Singh, K., Mei, J.B., and Jungić, V., Life of a Working Ramsey Theorist: Conversation With Tom C. Brown, Journal of Humanistic Mathematics, Volume 12 Issue 1 (January 2022), pages 399-407.
• Jungić, V. An introduction of the problem of finding the chromatic number of the plane, Part I, Crux Mathematicorum, Vol. 45(8), October 2020
• Jungić, V., An introduction of the problem of finding the chromatic number of the plane, Part II, Crux Mathematicorum Vol. 47(8), October 2021
• Jungić, V., Ramsey's Theorem Through Examples, Exercises, and Problems, Part I, Crux Mathematicorum, v 40 n 2, 2014
• Jungić, V., Ramsey's Theorem Through Examples, Exercises, and Problems, Part II, Crux Mathematicorum, v 40 n 4, 2014
• Jungić, O., Jungić. V., Frank P. Ramsey: The Theory, The Myth, and The Mirror, The Mathematical Intelligencer, 2015
• Jungić, V., An introduction of the Hales-Jewett theorem through examples and exercises, Part II, To appear in Crux Mathematicorum
• Brown, T., Freedman, A., and Jungić, V., Problem, To appear in the American Mathematical Monthly
• Jungić, V., Problem, To appear in the American Mathematical Monthly

Here are several drawings inspired by Ramsey theory and people involved in Ramsey theory.

For example, the image on the Math Catcher Program logo, created by Ms. Bethani L'Heuruex of the Cree First Nation, was inspired by an edge-colouring of the complete graph on 14 vertices by 23 colours that avoids both monochromatic and rainbow complete subgraphs on four vertices. The colouring was constructed by Veselin Jungić, Tomas Kaiser, and Daniel Král in A note on edge-colourings avoiding rainbow K₄ and monochromatic K_m, The Electronic Journal Of Combinatorics 16 (2009), #N19.

The art presented here is the outcome of the collaboration between Veselin Jungić and Bethani L'Heureux, Listiarini Listiarini, Nicole Oishi, Kyra Pukanich, and Simon Roy.

© 2022. All copyrights belong to the Math Catcher Outreach Program.