Wiley-Interscience Series in Discrete Mathematics
2 total works
This a a guide to the probabilistic method, an extremely powerful tool for solving complex problems in discrete mathematics which is recognized as a primary methodology in theoretical computer science. Improved techniques and classical methods are discussed, with applications to discrete maths, theoretical computer science, circuit complexity, coding theory and computational geometry. The book also presents the probabilistic method in action and provides a section giving new insights into already known theorems and results.
Ramsey Theory
by Ronald L. Graham, Bruce L. Rothschild, Joel H. Spencer, and Jozsef Solymosi
Published 1 January 1980
Ramsey Theory has become the reference book its field as it contains most of the results and techniques in classical Ramsey Theory and remains the only book to cover the broad spectrum of the subject area. It provides both full proofs (in many cases more than one proof to give different vantage points) and a leisurely discussion of the major theorems, such as Ramsey's Theorem, van der Waerden's Theorem, the Hales-Jewett Theorem, and Rado's Theorem. A new chapter on Graph Ramsey has been added in light of recent emphasis on the topic within the mathematics community, and numerous new exercises have been added to help make the book more classroom friendly. This book also includes a complete treatment of Saharon Shelah's proof, which avoids double induction, involves fast growing functions, and is elementary in nature. A historical perspective is included and discusses the fundamental papers of Ramsey in 1930, and of Erdos and Szekeres in 1935.