About the authors RONALD L. GRAHAM is Adjunct Director for Researchat AT&T Bell Laboratories, and University Professor of theMathematical Sciences at Rutgers University. He is coauthor ofConcrete Mathematics and of Old and New Problems in CombinatorialNumber Theory, and serves on the editorial boards of more than 25technical journals. He received his PhD in mathematics from theUniversity of California, Berkeley. BRUCE L. ROTHSCHILD isProfessor of Mathematics at the University of California, LosAngeles. He is Managing Editor of the Journal of CombinatorialTheory. He received his PhD in mathematics from Yale University.JOEL H. SPENCER is a professor of mathematics and computer scienceat the Courant Institute. He is the author of Ten Lectures on theProbabilistic Method and the editor of Random Structures andAlgorithms. He received his PhD in mathematics from HarvardUniversity.

"Anyone interested in getting an introduction to Ramsey theory will find this illuminating…" (MAA Reviews, December 17, 2006)

• Sets.Progressions.Equations.Numbers.Particulars.Beyond Combinatorics.References.Index.

About the authors RONALD L. GRAHAM is Adjunct Director for Researchat AT&T Bell Laboratories, and University Professor of theMathematical Sciences at Rutgers University. He is coauthor ofConcrete Mathematics and of Old and New Problems in CombinatorialNumber Theory, and serves on the editorial boards of more than 25technical journals. He received his PhD in mathematics from theUniversity of California, Berkeley. BRUCE L. ROTHSCHILD isProfessor of Mathematics at the University of California, LosAngeles. He is Managing Editor of the Journal of CombinatorialTheory. He received his PhD in mathematics from Yale University.JOEL H. SPENCER is a professor of mathematics and computer scienceat the Courant Institute. He is the author of Ten Lectures on theProbabilistic Method and the editor of Random Structures andAlgorithms. He received his PhD in mathematics from HarvardUniversity.

"Anyone interested in getting an introduction to Ramsey theory will find this illuminating…" (MAA Reviews, December 17, 2006)

• Sets.Progressions.Equations.Numbers.Particulars.Beyond Combinatorics.References.Index.

About the authors RONALD L. GRAHAM is Adjunct Director for Researchat AT&T Bell Laboratories, and University Professor of theMathematical Sciences at Rutgers University. He is coauthor ofConcrete Mathematics and of Old and New Problems in CombinatorialNumber Theory, and serves on the editorial boards of more than 25technical journals. He received his PhD in mathematics from theUniversity of California, Berkeley. BRUCE L. ROTHSCHILD isProfessor of Mathematics at the University of California, LosAngeles. He is Managing Editor of the Journal of CombinatorialTheory. He received his PhD in mathematics from Yale University.JOEL H. SPENCER is a professor of mathematics and computer scienceat the Courant Institute. He is the author of Ten Lectures on theProbabilistic Method and the editor of Random Structures andAlgorithms. He received his PhD in mathematics from HarvardUniversity.

"Anyone interested in getting an introduction to Ramsey theory will find this illuminating…" (MAA Reviews, December 17, 2006)

• Sets.Progressions.Equations.Numbers.Particulars.Beyond Combinatorics.References.Index.