All things with some omissions

Since there are many textbooks titled Discrete Mathematics , and even more dealing with that part of mathematics, authors often feel the need to express what makes theirs so different. The preface of this one claims it is unique: "fully adequate for all discrete mathematics courses" with "an unusually wide set of topics", "historical material is fully integrated in our text", "graduated level of difficulty of exercises", using "exercises, advanced exercises and computer exercises" and so on. In other words, it tries to be all things for all people.

Unfortunately, this approach means that the material becomes a muddle in which it is hard to find the appropriate pieces. Apart from a mixture in the level of the material, many parts also contain a strange combination of topics. For instance, section 3.1, "Functions and relations", discusses subjects ranging from the definitions of functions and relations, graph isomorphisms and Hasse diagrams, to the Prufer correspondence (the one-one correspondence between labelled spanning trees on n vertices and n -1 tuples of integers from 1,... n ) - and all this before graphs are properly defined in chapter four. Additionally, there are are historic notes and lines from Lewis Carroll's The Hunting of the Snark , making a total hardly manageable for most courses.

The book indeed covers an unusually wide set of topics, from basic set theory and logic to models of computation. There are also many exercises, which are sometimes quite repetitive.

The variation in topics and levels will, I feel, make the book hard to adapt for most courses in discrete mathematics. A lecturer would have to make a detailed selection as to what to cover from the book, even deciding which parts of which sections will be useful for a particular group of students. The book may, however, be useful as secondary reading for a more advanced course.

Jan van den Heuvel is lecturer in mathematics, London School of Economics.