Handbook of Discrete and Combinatorial Mathematics

Citation

Hutton, D.M. (2001), "Handbook of Discrete and Combinatorial Mathematics", Kybernetes, Vol. 30 No. 1, pp. 103-115. https://doi.org/10.1108/k.2001.30.1.103.8

For a handbook to live up to systemists’ and cyberneticians’ expectations it has to be structured with the potential reader very much in mind. A handbook of this size, of well over 1,000 pages, is not meant to be read from cover to cover, although this text is sufficiently readable and has such attractive chapter titles that it could well be much more than a reference handbook. The book aims to provide a wide‐ranging and comprehensive reference within this area, not just for mathematicians, who would obviously be attracted by its title, but by those who have applications in mind and require a well‐organised reference text. Potential readers could include anyone who believes that their approach to their discipline would be improved by the use of the more precise language of mathematics and its theoretical techniques. Such a potential readership would include scientists who are involved with physical or social studies, and quite obviously those who are theoretical computer scientists. It should also appeal to enlightened engineers who are more likely to demand such a comprehensive reference tome.

The editor‐in‐chief is to be congratulated in marshalling his compilers who have had the daunting task of choosing the material from the mass of literature covering the book’s remit. Some idea of the range is given by simply looking at titles of chapters. They are: “Foundations”; “Counting methods”; “Sequences”; “Number theory”; “Algebraic structures”; “Linear algebra”; “Discrete probability graph theory”; “Trees”; “Networks and flows”; “Partially ordered sets”; “Combinatorial designs”; “Discrete and computational geometry”; “Coding theory and cryptology”; “Discrete optimisation”; “Theoretical computer science”; and “Information structures”.

The headings themselves indicate the handbook’s relevance to systems and cybernetics and, indeed, might encourage many of the researchers in these disciplines to seek new approaches.

To be useful the handbook needed to be well‐organised and provide easy access to its contents. This has been achieved in large measure with each chapter starting with a list of contents, followed by a summary of what it contains. In addition, unlike so many reference texts, it includes a glossary of terms and terminology used in the chapter. Each chapter also includes its references for the printed as well as online references. The actual chapter content is set out clearly, with emphasis on definitions, the relevant facts and also examples where they are needed. A great deal more information is featured, together with important theorems, tables and algorithms (in easily‐read pseudo code).

A final chapter in the handbook is reserved for biographies of the people who had brought the fields to their present state. Finally, a most comprehensive index is provided.

There should be no shortage of readers for this large volume which contains such a variety of carefully chosen material presented in a clear, structured fashion.

Not all “handbooks” reviewed in this journal have reached the high standards of this one. It meets an obvious need and it will bring to cybernetics researchers, and to many others in widely differing areas of endeavour, an authoritative and highly desirable reference text.