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3.0 out of 5 stars
Pretty Good, But Contains Errors
June 1, 2005

For a discrete math book, this one is pretty good (it's far better than the last one I read). From the Preface on, the author states exactly what he's going to do (and why), does it, and then summarizes it. This gives the book good structure and is an excellent teaching methodology. There are oodles of examples and tons of exercises (odd numbers answered). Each section has its own exercises as do the chapters themselves. There are also more challenging "Supplementary Exercises" following the chapter exercises. Right up front, the author states that "the book has been designed for students in computer science, electrical engineering, and mathematics as a one- or two-semester course in discrete mathematics at the sophomore/junior level." He got that exactly right. To emphasize the applications orientation, he also provides "Computer Assignments" at the end of each chapter (and computer algorithmic examples within each chapter). In what I consider to be an odd twist, he also includes a set of writing projects at the end of each chapter.

Unfortunately, there's one big negative to the book: it contains a lot of errors. These range from inconsequential typos through errors in mathematical definitions and proofs to wrong answers for exercises. For instance, the first serious contextual error I found is on page 78: the definitions of set union and intersection are wrong. Both read "...x such that x is an element of A OR x is an element of B." Obviously, the intersection is supposed to be AND, but they both read OR. Usually, these types of errors are easy to spot from the surrounding, correct, material. For errors in exercises, the first several I found are: Exercises 1.2, #63; Exercises 1.4, #21; Exercises 1.5, #37; Exercises 2.2, #15; Exercises 2.4, #33, #45, #47; Chapter 3 Review Exercises, #33, #37; and Chapter 5 Review Exercises, #5 (after this, I stopped keeping track).

To add a bit more information to the raw data of these reviews, I've mapped the universe of all possible readers of this book onto a set of x-y axes. Let the x-axis run from "non-Math-types" up through "Math-types." Let they y-axis go from "non-geniuses" up through "geniuses:"

- Quadrant I: genius Math-types. This group will probably not appreciate the book. It's definitely aimed at the application of discrete math instead of at the proving of it. There are many proofs in the book, but there are also a lot missing. There doesn't seem to be any pattern to this. At a guess, I'd say that if a proof isn't easy, the author just leaves it out. Regarding the intellectual level of the text, Quadrant Is might be OK with it. Some of the material is fairly easy, but other parts are pretty challenging: it's a good mix. Overall, this group could probably get by with the book, they would just complain a lot :) .

- Quadrant II: genius non-Math-types. The intellectual level of the book follows the same pattern for this group as for the Quadrant Is, above. The application focus would please the Quadrant IIs more, though. Like the Quadrant Is, the Quadrant IIs would probably find the book acceptable (probably a little more so than the Quadrant Is).

- Quadrant III: non-genius non-Math-types (i.e., "normal" people). This is the group that should get the most out of the book. The book is well-structured and complete and leads the reader through a reasonable sequence from basics to advanced topics. For the most part, the author is careful to keep the intellectual and theoretical levels reasonable (though I'm still lost regarding Relations, Graphs, Digraphs, and Formal Languages and Finite-State Machines -- and his recurring motif of Fibonacci-related stuff is tough). Assuming most people will use the book in a classroom setting, the errors in it shouldn't be a problem since the instructor should be able to point them out.

- Quadrant IV: non-genius Math-types. This group can be lumped in with the Quadrant Is: the intellectual level of the book isn't the problem -- it's the application orientation that would bother them. Quadrant IVs could get by with the book, but would complain a bit.

Regardless of its errors, this is a pretty good book. The potential audience covers the entire universe of readers with the best target being Quadrant III ("normal" people). It's written well enough to be good for university use as well as for personal reading (mostly). Without the number of errors, I would have given this a rating of 4 stars out of 5. Because of them, I'm reducing my rating to 3 stars out of 5.

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