Synopses & Reviews
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Wiley-Interscience Series in Discrete Mathematics and Optimization AdvisoryEditors: Ronald L. Graham, Jan Karel Lenstra, and Robert E. Tarjan
Discrete mathematics, the study of finite structures, is one of the fastest-growing areas in mathematics. The wide applicability of its evolving techniques points to the rapidity with which the field is moving from its beginnings to its maturity, and reflects the ever-increasing interaction between discrete mathematics and computer science. This Series provides broad coverage of discrete mathematics and optimization, ranging over such fields as combinatorics, graph theory, enumeration, and the analysis of algorithms. The Wiley-Interscience Series in Discrete Mathematics and Optimizationwill be a substantial part of the record of the extraordinary development of this field. A complete listing of the titles in the Series appears on the inside front cover of this book.
\"[Integer and Combinatorial Optimization] is a major contribution to the literature of discrete programming. This text should be required reading for anybody who intends to research this area or even just to keep abreast of developments.\"
—Times Higher Education Supplement, London
\"An extensive but extremely well-written graduate text covering integer programming.\"
—American Mathematical Monthly
Recent titles in the Series include:
Integer and Combinatorial OptimizationGeorge L. Nemhauser and Laurence A. Wolsey 1988 (0 471-82819-X) 763 pp.
Introduction to the Theory of Error-Correcting CodesSecond Edition Vera Pless
For mathematicians, engineers, and computer scientists, here is an introduction to the theory of error-correcting codes, focusing on linear block codes. The book considers such codes as Hamming and Golay codes, correction of double errors, use of finite fields, cyclic codes, B.C.H. codes, weight distributions, and design of codes. In a second edition of the book, Pless offers thoroughly expanded coverage of nonbinary and cyclic codes. Some proofs have been simplified, and there are many more examples and problems. 1989 (0 471-61884-5) 224 pp. '
Review
"Anyone interested in getting an introduction to Ramsey theory will find this illuminating…" (MAA Reviews, December 17, 2006)
Synopsis
Wiley-Interscience Series in Discrete Mathematics and Optimization AdvisoryEditors: Ronald L. Graham, Jan Karel Lenstra, and Robert E. Tarjan
Discrete mathematics, the study of finite structures, is one of the fastest-growing areas in mathematics. The wide applicability of its evolving techniques points to the rapidity with which the field is moving from its beginnings to its maturity, and reflects the ever-increasing interaction between discrete mathematics and computer science. This Series provides broad coverage of discrete mathematics and optimization, ranging over such fields as combinatorics, graph theory, enumeration, and the analysis of algorithms. The Wiley-Interscience Series in Discrete Mathematics and Optimizationwill be a substantial part of the record of the extraordinary development of this field. A complete listing of the titles in the Series appears on the inside front cover of this book.
"[Integer and Combinatorial Optimization] is a major contribution to the literature of discrete programming. This text should be required reading for anybody who intends to research this area or even just to keep abreast of developments."
—Times Higher Education Supplement, London
"An extensive but extremely well-written graduate text covering integer programming."
—American Mathematical Monthly
Recent titles in the Series include:
Integer and Combinatorial OptimizationGeorge L. Nemhauser and Laurence A. Wolsey 1988 (0 471-82819-X) 763 pp.
Introduction to the Theory of Error-Correcting CodesSecond Edition Vera Pless
For mathematicians, engineers, and computer scientists, here is an introduction to the theory of error-correcting codes, focusing on linear block codes. The book considers such codes as Hamming and Golay codes, correction of double errors, use of finite fields, cyclic codes, B.C.H. codes, weight distributions, and design of codes. In a second edition of the book, Pless offers thoroughly expanded coverage of nonbinary and cyclic codes. Some proofs have been simplified, and there are many more examples and problems. 1989 (0 471-61884-5) 224 pp.
Synopsis
'In 1987 Saharon Shelah was shown van der Waerdens 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 Shelahs 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 Ramseys Theorem, van der Waerdens Theorem, the Hales-Jewett Theorem and Rados 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. '
Table of Contents
Sets.
Progressions.
Equations.
Numbers.
Particulars.
Beyond Combinatorics.
References.
Index.