A Logical Approach to Discrete Math (Monographs in Computer Science)

Discrete math is usually taught as a fairly motley collection of ideas and techniques, none of which really relate to each other. When you've read a book or taken a course on the stuff, you're left thinking "so what?". In contrast, this book begins by showing you how to USE propositional and predicate logic to a) model things, and then b) reason (i.e. prove theorems) about your models by simple algebraic calculation (the kind of stuff you did in high-school). They then show that this logic is "the glue" that binds together all the other notions by using it to define and prove properties of sets, relations, functions, sequences, numbers and induction, and so on.

The logic alone is worth buying the book for. Instead of skating over the material, throwing in a few truth tables to define the operators, and then getting you to check a couple of laws by making your own truth tables (boring and ultimately useless), they take the time to show you how to prove logical theorems by calculation. What's really good is that they give lots of practical heuristics to guide you though these calculations, and demonstrate them on loads of examples. Do the exercises and your view of mathematics will be changed forever (for the better!). I promise.

Recently, the late Yehudi Menuhin said that learning a musical instrument can be a worthwhile experience even if you don't want to be a performer, because mastering a skill empowers you as a human being. It builds your self-confidence and raises your standards. What I get from this book is that the authors seem to hold to a similar philosophy: that by mastering these skills (early in the curriculum), you'll be able to tackle other technical material with greater confidence than before. You get the feeling that they really want to empower you with this stuff and believe you can master it. The writing style is immediately accessible: you feel like they're there in person, taking you through the calculations. All you have to do is practice. Every teacher of math (and programming) should read this book.

My only quibble actually holds for many of the books in this (Springer-Verlag) series: it's a bit pricey (or, at least, in Ireland). If you want undergrads to learn this stuff, you've got to bring it within their price range. The book should be available in paperback, with larger length/width dimensions, to make it thinner and less formal-looking (no pun intended).

Ah, if only every math/computer science book was like this! If you think this review is OTT, check out your college library and see for yourself. If the library aint got it, demand a refund of your fees and study somewhere else.


That's the point.   March 4, 2001
reader (Portland, OR)
12 out of 13 found this review helpful

The previous reviewer knows not of what they speak. Yes, the book does teach calculation independent of meaning (equational logic), and this is so that one may arrive at results, at insights, at meaning, which one would _not_ have otherwise, or at least not with such great ease. To wit, solving Portia's suitor's dilemma is reduced to a trivial two step manipulation, rather than, for example a 21-step formal natural-deduction solution. I cannot overemphasize the astounding increase in problem solving power available to you when you can manipulate a problem without having to keep the meaning of everything in your head.... I searched for quite some time before finally finding this book, and I will be forever happy that I've been able to read it. Can't say that about too many math books. :-) Contains excellent reference summaries too, including card stock tear out duplicates of same.


A unique and very effective approach   January 12, 1999
13 out of 16 found this review helpful

This is a fantastic text on discrete math. I have looked at many different texts dealing with this subject and this is without question the best one I have come across. There are tons of examples and exercises. This book clearly has the student in mind and progresses slowly and clearly. A tremendous effort and truly a great success.


A great and successful effort!   January 16, 1999
8 out of 10 found this review helpful

This without question the best book on this subject to date. The authors begin with an eqational logic which is very elegent and easy to understand. In doing so they introduce various concepts effortlessly and when they finally introduce the traditional Hilbert style of proof the reader has a very firm grasp of the matrial that makes it easy to follow. A brilliant book!!


An Incredible Mathematics Tool for Young and Old   February 12, 2000
11 out of 15 found this review helpful

I studied with this book in college. My professor wouldn't teach the course unless he was allowed to use this text. After working with it I agree with him.

This book has such incredible potential for the future. It is so easy to learn that a student old enough to learn algebra could learn this material. A person armmed with the knowlege in this book could learn to write flawless (bug free) computer code in real time. The material in this book is not limited to computer science -- it could be applied to any type of complex organizational system. The proof techniques in this book are priceless.