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A Beginner's Guide to Discrete Mathematics

W. D. Wallis
Publisher: 
Birkhäuser
Publication Date: 
2012
Number of Pages: 
427
Format: 
Hardcover
Edition: 
2
Price: 
74.95
ISBN: 
9780817682859
Category: 
Textbook
[Reviewed by
Miklós Bóna
, on
02/16/2012
]

The title is certainly very true. The book can be a good choice for your class if and only if your students are indeed truly beginners in the following strong sense. First, they did not have a “bridge course,” that is, a course on “Transition into Higher Mathematics.” This is very important since four of the book’s ten chapters covers material (proof techniques, formal logic, sets), that are often discussed in such a course. Second, if your students had linear algebra, then one additional chapter will mostly be old news to them.

The rest of the book consists of chapters that will be enjoyable for your students no matter their background — but if the students did not need the introductory chapters, then the chapters on core combinatorics will not be deep enough for them. There are three core chapters, on counting arguments, graph theory, and probability, and two more specialized chapters, on number theory and cryptography, and on voting theory. The latter is a first for a book of this kind, and is certainly well-written. As one would expect, the exercises are easier than those in most undergraduate discrete mathematics textbook.

On the whole, the book is certainly unique in the sense that it teaches a transition to higher mathematics course, a discrete mathematics course, and even some linear algebra, and does so on a relatively short 427 pages. This breadth is achieved, of course, at the expense of depth. However, if your class is designed to teach all those things at once, then the book is a good choice, since it does so in a clear and reader-friendly way.


Miklós Bóna is Professor of Mathematics at the University of Florida.

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