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Introduction to Ramsey Theory:
Lecture notes for undergraduate course
Veselin Jungic
Contents
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Contents
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Front Matter
Colophon
Dedication
Acknowledgements
Preface
1
Introduction: Pioneers and Trailblazers
Complete Chaos is Impossible
Paul Erdős
Frank Plumpton Ramsey
2
Ramsey's Theorem
The Pigeonhole Principle
Ramsey's Theorem: Friends and Strangers
Ramsey's Theorem: Two Colours
Ramsey's Theorem, Infinite Case
Exercises
3
van der Waerden's Theorem
Bartel van der Waerden
van der Waerden's Theorem:
3
-term APs
Proof of van der Waerden's Theorem
van der Waerden's Theorem: How Far and Where?
van der Waerden's Theorem: A Few Related Questions
Exercises
4
Schur's Theorem and Rado's Theorem
Issai Schur
Schur's Theorem
Richard Rado
Rado's Theorem
Exercises
5
The Hales-Jewett Theorem
Combinatorial Lines
The Hales-Jewett Theorem
Exercises
6
Colourings of the Plane
Erdős-Szekeres Problem of Convex Polygons
Erdős-Szekeres Problem of Convex Polygons - Part Two
The Chromatic Number of the Plane
The Polychromatic Number of the Plane
Exercises
Back Matter
Bibliography
Authored in PreTeXt
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Introduction to Ramsey Theory:
Lecture notes for undergraduate course
Veselin Jungic
Department of Mathematics
Simon Fraser University
Colophon
Dedication
Acknowledgements
Preface