List of Tables
Preface to the Second Edition
Acknowledgements
Preface to the First Edition
Chapter 1.Preliminaries
1.1.The Pigeonhole Principle
1.2.Ramsey's Theorem
1.3.Some Notation
1.4.Three Classical Theorems
1.5.A Little More Notation
1.6.Exercises
1.7.Research Problems
1.8.References
Chapter 2.Van der Waerden's Theorem
2.1.The Compactness Principle
2.2.Alternate Forms of van der Waerden's Theorem
2.3.Computing van der Waerden Numbers
2.4.Bounds on van der Waerden Numbers
2.5.The Erd?s and Turán Function
2.6.On the Number of Monochromatic Arithmetic Progressions
2.7.Proof of van der Waerden's Theorem
2.8.Exercises
2.9.Research Problems
2.10.References
Chapter 3.Supersets of AP
3.1.Quasi-Progressions
3.2.Generalized Quasi-Progressions
3.3.Descending Waves
3.4.Semi-Progressions
3.5.Iterated Polynomials
3.6.Arithmetic Progressions as Recurrence Solutions
3.7.Exercises
3.8.Research Problems
3.9.References
Chapter 4.Subsets of AP
4.1.Finite Gap Sets
4.2.Infinite Gap Sets
4.3.Exercises
4.4.Research Problems
4.5.References
Chapter 5.Other Generalizations of w(k;r)
5.1.Sequences of Type x,ax+d,bx+2d
5.2.Homothetic Copies of Sequences
5.3.Sequences of Type x,x+d,x+2d+b
5.4.Polynomial Progressions
5.5.Exercises
5.6.Research Problems
5.7.References
Chapter 6.Arithmetic Progressions (mod m)
6.1.The Family of Arithmetic Progressions (mod m)
