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

David Gries (Author), Fred B. Schneider (Author)

Book Description

ISBN-10: 0387941150 | ISBN-13: 978-0387941158 | Publication Date: October 22, 1993 | Edition: 1

Here, the authors strive to change the way logic and discrete math are taught in computer science and mathematics: while many books treat logic simply as another topic of study, this one is unique in its willingness to go one step further. The book traets logic as a basic tool which may be applied in essentially every other area.

Editorial Reviews

Review

"This is a rather extraordinary book, and deserves to be read by everyone involved in computer science and - perhaps more importantly - software engineering. I recommend it highly... If the book is taken seriously, the rigor that it unfolds and the clarity of its concepts could have a significant impact on the way in which software is conceived and developed." - Peter G. Neumann

Product Details

• Hardcover: 497 pages
• Publisher: Springer; 1 edition (October 22, 1993)
• Language: English
• ISBN-10: 0387941150
• ISBN-13: 978-0387941158
• Product Dimensions: 9.3 x 6.2 x 1.2 inches
• Shipping Weight: 1.9 pounds (View shipping rates and policies)
• Average Customer Review: 3.8 out of 5 stars  See all reviews (16 customer reviews)
• Amazon Best Sellers Rank: #737,479 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

40 of 42 people found the following review helpful:

5.0 out of 5 stars This book is a must-buy!, July 18, 2000

By 

KH "Irish fella..." (Dublin, Ireland) - See all my reviews

This review is from: A Logical Approach to Discrete Math (Monographs in Computer Science) (Hardcover)

The other reviewers don't spill the beans! Basically, this book is wonderful. It teaches the kind of undergrad discrete math that underlies any good computer science course. (In fact, I think this material should be the first math topic encountered by any student taking math courses.) What makes the experience of this book different from the mortal tedium normally associated with textbooks on this subject, is that these guys really teach you HOW TO DO MATH.

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.

14 of 15 people found the following review helpful:

5.0 out of 5 stars That's the point., March 4, 2001

By 

reader (Portland, OR) - See all my reviews

This review is from: A Logical Approach to Discrete Math (Monographs in Computer Science) (Hardcover)

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.

13 of 16 people found the following review helpful:

5.0 out of 5 stars A unique and very effective approach, January 11, 1999

By A Customer

This review is from: A Logical Approach to Discrete Math (Monographs in Computer Science) (Hardcover)

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.