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Introduction to Ramsey Theory:
Students' Projects
Veselin Jungic
Contents
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Contents
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Front Matter
Colophon
Dedication
Acknowledgements
Preface
1
Life of Ramsey - 26 Year Long Story
2
Ramsey and Friends: A Story of Ramsey Theory
3
Order to Chaos: The Evolution of Ramsey Theory
Script
References
4
Ramsey Theory – An Introduction
5
A Fun Video of the Happy Ending Problem–Ramsey's Theory in Multimedia
6
Ramsey Theory and Art
7
Ramsey Theory Website
8
Three Ramsey Theorists
Transcript
Maria Axenovich
Steve Butler
Julian Sahasrabudhe
9
The Ramsey Theory Podcast
10
Tom Brown's Wikipage
Interview with Professor Tom Brown
11
Hosting Guest Speakers
12
Aaron Robertson's Wikipedia Page
13
Neil Hindman and Julian Sahasrabudhe's Wikipedia Pages
14
Collection of professors's favourite Ramsey theory proofs
Introduction
Steve Butler
Jay Cummings
David Conlon
Jacob Fox
William Ian Gasarch
David Gunderson
Daniel Král
Imre Leader
Dhruv Mubayi
Joel Spencer
15
Life as Ramsey Theory Students
16
Model of \(R(3,3)\)
17
Search for Monochromatic \(\{a,b,a+b,ab\}\)
Environment
Algorithm
Implementation
Result
Reflection
18
van der Waerden Computations
Introduction
Historical Background and Importance
Method of Computing van der Waerden Numbers
Results
Conclusion
References
19
“Deadly-Trio” - A Ramsey's Game
20
Ramsey Colouring Games
21
Complete a Complete Graph: A Game
22
Applet: Games we always win
23
\(R(3,3,3) = 17\text{:}\) Before Your Eyes
24
\(R(4,4) = 18\text{:}\) Before Your Eyes
25
A proof without words that \(R(a,b,c)\) exists
26
Happy Ending Problem Applet
27
How Big are Ramsey Numbers?
28
Quad-Tac-Toe Game
29
Schur's Theorem: A Game
30
Ramsey's Nocturne
31
Music on the Theme of van der Waerden's Theorem
32
A Song for Ramsey
Introduction
Presentation Sides
33
Animation of the Proof of van der Waerden's Theorem
34
Mission Impossible
35
The Happy Ending Problem
36
A Graphic Novel About the creation of the proof of van der Waerden's Theorem
37
Ramsey's Main Coure – A Comic
38
The Rise and Fall of Chaos – Comic
39
Canonical Form of van der Waerden's Theorem
40
Graham's Number
41
Moser's Spindle
42
“The Moser Spindle” – A Graphic Novel
43
The Hidden Order: A Painting
44
Happy Ending Problem: A Play
45
Roth's Theorem in Ten Minutes
46
Solutions to Combinatorial Problems and Exercises
Problems: Ramsey's Theorem and Graphs
Combinatorial Geometry
Ramsey Property
Various Problems
47
Enhancement of the Course Notes
Exercises
Fractional Chromatic Number
Density of planar sets avoiding unit distance
48
Accessibility of Fibonacci numbers
Introduction
Preliminaries
Degree of Accessibility of Even Fibonacci Numbers
More About Even Fibonacci Numbers
Accessibility and divisibility
Reflection
References
49
Polynomial van der Waerden Theorem
The Theorem
History of the Proof
The Proof
Current Events and References
50
A Ramsey Theory Essay: The Dinner Party
51
Ramsey Theory: “Complete Chaos Is Impossible” Course Essay
Authored in PreTeXt
Introduction to Ramsey Theory:
Students' Projects
Veselin Jungic
Department of Mathematics
Simon Fraser University
Colophon
Dedication
Acknowledgements
Preface