## Preface Preface

This collection contains term projects completed by students enrolled in the course Math 301/302/303 - Mathematical Journeys offered by the Department of Mathematics, Simon Fraser University. The calendar description of this course is as follows:

A focused exploration of a special topic (varying from term to term) that builds on mathematical ideas from lower division courses and provides further challenges in quantitative and deductive reasoning. Each Journeys course is designed to appeal particularly to mathematics minor students and others with a broad interest in mathematics.

In the spring 2014, the fall 2020, the fall 2021, and the spring 2024 semesters the topic of the course was “Ramsey Theory: Complete Chaos is Impossible”. The main goal of the course was to give students a very gentle introduction to the basic ideas and problems in Ramsey theory, their history and their place in contemporary mathematics. The only real pre–requisites to fully grasp the material presented in this course was to know how to read and write and to possess a certain level of mathematical common sense.

My wish was to give to my students both challenging and enjoyable experiences in learning some of the basic facts about Ramsey theory.

The purpose of the term–project 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.

This approach was inspired by Kieran Egan (1942 – 2022), an Irish educational philosopher. In my notes, that I had taken during one of Eagan's presentations on the topic of “Learning in Depth”, I wrote:

Learning in Depth (LiD) is a simple though radical innovation in curriculum and instruction designed to ensure that all students become experts about something during their school years. To the surprise of many, children usually take to the program with great enthusiasm, and within a few months LiD begins to transform their experience as learners.

Consequently, my expectations included the following:

that every student would wholeheartedly participate in the chosen project;

that each student would understand and know the Ramsey theory part of the project to the best of their abilities;

that each student would relish their imagination and use their familiarity with the contemporary technology and both high- and pop-culture to create a product that they would be proud of for years to come.

My advice to the class was: “The more you are sincerely curious about your project, the more enjoyable it will be for you, and the better your final product will be.”

It should be mentioned that because of the global pandemic the fall 2020 class was offered online. This meant that only a few groups of students were able to physically get together. The majority of the groups collaborated across multiple time zones.

I am happy to report that all projects were completed on time. In my opinion each of the projects is an excellent example both how much talent there is among this generation of students and how mathematics can trigger students' creativity in sometimes unpredictable ways.

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

This collection contains an essay by a student who was enrolled in a four–week long non–credit course that I taught in SFU's Liberal Arts and 55+ Program in October 2020. The title of the course was “LIB 225 - Ramsey Theory: Complete Chaos is Impossible”.

Veselin Jungic

Math 301, Math 302, Math 303, and LIB 225 Instructor

Department of Mathematics, Simon Fraser University

Contact address: vjungic@sfu.ca

In Burnaby, B.C., July, 2024