Ramsey Theory, 2nd Edition Hardcover - 1990

In 1987 Saharon Shelah was shown van der Waerden's Theorem, a cornerstone of Ramsey Theory, and within several days found an entirely new proof that resolves one of the central questions of the theory. In this second edition of Ramsey Theory, three leading experts in the field give a complete treatment of Shelah's proof as well as the original proof of van der Waerden. The text covers all the major concepts and theorems of Ramsey theory. The authors give full proofs, in many cases more than one proof of the major theorems. These include Ramsey's Theorem, van der Waerden's Theorem, the Hales-Jewett Theorem and Rado's Theorem. A historical perspective is included of the fundamental papers of Ramsey in 1930, and of Erdos and Szekeres in 1935. The theme of Ramsey Theory, as stated by the late T.S. Motzkin, is "Complete Disorder Is Impossible." Inside any large structure, no matter how chaotic, will lie a smaller substructure with great regularity. Throughout the authors place the different theorems in this context. This second edition deals with several other more detailed areas, including Graph Ramsey Theory and Euclidean Ramsey Theory, which have received substantial attention in recent years. The final chapter relates Ramsey Theory to areas other than discrete mathematics, including the unprovability results of Jeff Paris and Leo Harrington and the use of methods from topological dynamics pioneered by H. Furstenburg. Ramsey Theory, Second Edition is the definitive work on Ramsey Theory. It is an invaluable reference for professional mathematicians working in discrete mathematics, combinatorics, and algorithms. It also serves as an excellent introductory text for students taking graduate courses in these areas.