Selected Papers of Alan J Hoffman

Download or read book Selected Papers of Alan J Hoffman written by Charles A Micchelli and published by World Scientific. This book was released on 2003-08-25 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dr Alan J Hoffman is a pioneer in linear programming, combinatorial optimization, and the study of graph spectra. In his principal research interests, which include the fields of linear inequalities, combinatorics, and matrix theory, he and his collaborators have contributed fundamental concepts and theorems, many of which bear their names. This volume of Dr Hoffman's selected papers is divided into seven sections: geometry; combinatorics; matrix inequalities and eigenvalues; linear inequalities and linear programming; combinatorial optimization; greedy algorithms; graph spectra. Dr Hoffman has supplied background commentary and anecdotal remarks for each of the selected papers. He has also provided autobiographical notes showing how he chose mathematics as his profession, and the influences and motivations which shaped his career. Contents:The Variation of the Spectrum of a Normal Matrix (with H W Wielandt)Integral Boundary Points of Convex Polyhedra (with J Kruskal)On Moore Graphs with Diameters 2 and 3 (with R R Singleton)Cycling in the Simplex AlgorithmOn Approximate Solutions of Systems of Linear InequalitiesOn the Polynomial of a GraphSome Recent Applications of the Theory of Linear Inequalities of Extremal Combinatorial AnalysisOn Simple Linear Programming ProblemsSelf-Orthogonal Latin Squares (with R K Brayton & D Coppersmith)On the Nonsingularity of Complex Matrices (with P Camion)A Generalization of Max Flow-Min CutA Characterization of Comparability Graphs and of Interval Graphs (with P C Gilmore)and 33 other papers Readership: Researchers in linear programming and inequalities, combinatorics, combinatorial optimization, graph theory, matrix theory and operations research. Keywords:Linear Programming;Combinatorial Optimization;Graph Spectra;Matrix TheoryReviews:“The papers themselves are the heart of the book, and each one has a brief introduction that explains its origins and motivation … The whole is rounded off by a twenty-page autobiography, notable for its insights into the diverse aspects of the life of a professional mathematician, and anecdotes about the many interesting people whom Hoffman encountered.” The London Mathematical Society “Each section is well edited along with editorial comment. The book is well written and is helpful to the younger generation.”Zentralblatt MATH “Alan's ‘Autobiographical notes’ are worthwhile by themselves and should be required reading for any prospective PhD student in a mathematical discipline … The introduction of this book is entertaining and thought provoking for anyone in mathematics. The papers and commentaries form a worthwhile sourcebook for anyone from PhD students to professors who is interested in the delightful mathematics at the intersection of combinatorics, linear algebra, and linear programming.”Interfaces “These papers are annotated in such a way that the reader learns something about Hoffman's motivation for working on the problems they discuss. We also learn a good deal about Hoffman and his collaborators, and the academic climate in which the papers were written … This is a fun book to read. Hoffman is a good storyteller and he has many stories. His writing style is fluent and lively … The book gives a whirlwind tour through a very fascinating career. It shows what a career in mathematics can be if one is both lucky and talented.”Mathematical Reviews