Wiley-Interscience Series in Discrete Mathematics and Optimization Advisory
Editors: 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 Optimization" will 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 Optimization" George L. Nemhauser and Laurence A. Wolsey 1988 (0 471-82819-X) 763 pp.

"Introduction to the Theory of Error-Correcting Codes" Second Edition Vera Pless
For mathematicians, engineers, and computer scientists, here is an introduction to the theory of error-correctingcodes, 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.

The ship was doomed before it ever left port. His fate was sealed before he ever stepped on board. From R. L. Graham, Death on the Lusitania is an immersive WW1 historical novel set aboard the ill-fated ocean liner.

Welcome on board the Lusitania’s final voyage . . .

New York, 1915. RMS Lusitania, one of the world’s most luxurious ocean liners, departs for war-torn Europe. Among those on board is Patrick Gallagher, a civil servant in Her Majesty’s government tasked with escorting a British diplomat back to England.

When a fellow passenger is believed to have shot himself in his cabin, Gallagher is asked by the captain to investigate the scene but one crucial detail doesn’t fit. The man’s body was discovered in a locked cabin with the key inside and no gun to be found. Was it really suicide? Or murder?

Gallagher believes one of the passengers is a deadly killer - one who could strike again at any moment. And all the while, the ship sails on towards Europe, where enemy submarines patrol dark waters . . .

Death on the Lusitania by R. L. Graham is an atmospheric and immersive historical fiction novel set on board the doomed RMS Lusitania ocean liner. New York, 1915. RMS Lusitania, one of the world’s most luxurious trans-Atlantic liners, departs for Liverpool and war-torn Europe. Among those on board is Patrick Gallagher, a civil servant in Her Majesty’s government tasked with discreetly escorting a British diplomat back to England in relation to charges of suspected treason. When a fellow passenger, Jimmy Dowrich, is found shot to death in his cabin, the captain asks Gallagher to investigate. Knowing something of the man’s past, Gallagher realizes that the problem will not be simple; and also, the body was discovered in a locked cabin with the key inside and no gun to be found. Gallagher believes that one of his fellow passengers is a deadly killer. But many of those on board are harbouring secrets of their own, and his questioning reveals that several had a motive for ending Dowrich’s life. He fears that the killer could strike again to protect their true reasons for being on board and all the while, the ship sails on towards Europe, where deadly submarines patrol the war zone . . .

Praise for the First Edition "Anyone interested in getting an introduction to Ramsey theory will find this illuminating..." MAA Reviews Covering all the major concepts, proofs, and theorems, the Second Edition of Ramsey Theory is the ultimate guide to understanding every aspect of Shelah s proof, as well as the original proof of van der Waerden. The book offers a historical perspective of Ramsey s fundamental paper from 1930 and Erdos and Szekeres article from 1935, while placing the various theorems in the context of T. S. Motzkin s thought on the subject of Complete Disorder is Impossible. Ramsey Theory, Second Edition includes new and exciting coverage of Graph Ramsey Theory and Euclidean Ramsey Theory and also relates Ramsey Theory to other areas in discrete mathematics. In addition, the book features the unprovability results of Paris and Harrington and the methods from topological dynamics pioneered by Furstenburg. Featuring worked proofs and outside applications, Ramsey Theory, Second Edition addresses: * Ramsey and density theorems on both broad and meticulous scales * Extentions and implications of van der Waerden s Theorem, the Hales-Jewett Theorem, Roth s Theorem, Rado s Theorem, Szemeredi s Theorem, and the Shelah Proof * Regular homogeneous and nonhomogeneous systems and equations * Special cases and broader interdisciplinary applications of Ramsey Theory principles An invaluable reference for professional mathematicians working in discrete mathematics, combinatorics, and algorithms, Ramsey Theory, Second Edition is the definitive work on the subject.

This book discusses various problems in elementary number theory, most of which have a combinatorial flavor. In general classical problems are avoided and almost no proofs are given for the presented problems. Both the difficulty and importance of the problems discussed are very variable in some are only exercises while others are very difficult or even hopeless and may have important consequences or their eventual solution may lead to important advances and the discovery of new methods. This new edition is the joint work of the late Paul Erdys, Ron Graham, and as new co-authors, Melvin Nathanson and Xingde Jia.