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Rating: 
Summary: There is more to math than syntax!
Review: By the end of chapter 3, students will be comfortable writing formal proofs in a propositional logic. It is a great experience for beginning undergraduates to work through the theorems in chapter 3. There are some annoying typos, but on the whole the first four chapters are well written (4-5 stars).
Chapter 8 (necessary for predicate logic in chapter 9) is neat, but in my opinion it is a bit too abstract for beginning undergraduates. The next chapter on predicate logic is too hard and concise, even for upperclassmen. (2-3 stars)
There is some material on applications, but the main focus in the book is on derivations that involve manipulating strings of abstract, uninterpreted symbols. Students won't become more adept at using logic to represent knowledge because they don't "understand". For human beings(who knows about machines!), there is more to math than syntax. The later chapters are not as well written, and in my opinion are not a good choice for classroom use.(1 star)
Rating:
Summary: Not for independent study, questionable otherwise
Review: For the right kind of reader - namely, one with a competent instructor - this book probably does a lot of things well. It starts off by requiring you to get a firm grip on concepts that are used throughout the remainder of the book; you'll be doing proofs right off the bat. Unfortunately, I couldn't understand the content of the first four chapters until after a month of study. I was genuinely applying myself, but I just had a difficult time understanding this material. You may struggle unless you've previously had an introduction to proofs of this kind, like in an Abstract Math course. The proofs from high school Geometry class are nothing like those seen here! I can only recommend this book if a really good instructor comes with it. If you know you'll have a good professor who can explain things well, I think this book can take you into some tougher, more complex tasks relatively quickly. If not, you're going to have a devil of a time penetrating this thing: the author's words seem to trip over themselves all the time. It's somewhat of a difficult read, at least at the beginning; once I got my bearings, the later chapters seemed to get a little easier. If only these concepts could be taught better... but I can't see a better method than what's done here, and that method is initially horribly difficult. I do not recommend this book for independent study, but it may work when paired with a knowledgeable, helpful instructor. The fact that there are no answers in the back of the book limit the book's use.
Rating:
Summary: Not for independent study, questionable otherwise
Review: For the right kind of reader - namely, one with a competent instructor - this book probably does a lot of things well. It starts off by requiring you to get a firm grip on concepts that are used throughout the remainder of the book; you'll be doing proofs right off the bat. Unfortunately, I couldn't understand the content of the first four chapters until after a month of study. I was genuinely applying myself, but I just had a difficult time understanding this material. You may struggle unless you've previously had an introduction to proofs of this kind, like in an Abstract Math course. The proofs from high school Geometry class are nothing like those seen here! I can only recommend this book if a really good instructor comes with it. If you know you'll have a good professor who can explain things well, I think this book can take you into some tougher, more complex tasks relatively quickly. If not, you're going to have a devil of a time penetrating this thing: the author's words seem to trip over themselves all the time. It's somewhat of a difficult read, at least at the beginning; once I got my bearings, the later chapters seemed to get a little easier. If only these concepts could be taught better... but I can't see a better method than what's done here, and that method is initially horribly difficult. I do not recommend this book for independent study, but it may work when paired with a knowledgeable, helpful instructor. The fact that there are no answers in the back of the book limit the book's use.
Rating: 
Summary: This book here...
Review: I have just taken a programming theory which used this book. This book has very poor descriptions and basically I had to peice things together from other students. Honestly, if you're going to buy a book for your own personal enrichment this is definetly not the way to go. No answers. Bad Descriptions. akward proofs. nuff said
Rating:
Summary: This book is awful!
Review: 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.
Rating: 
Summary: This book is a must-buy!
Review: 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.
Rating:
Summary: That's the point.
Review: 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.
Rating:
Summary: That's the point.
Review: 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.
Rating:
Summary: There is more to math than syntax!
Review: Those who wrote positve stuff about this book, please tell me why nobody even mentioned that the authors did not give the answers to all the excises in the book? I just can not believe this, am I missing something here? Is this a math book? What am I supposed to do now with those questions?
Rating:
Summary: 5 Stars, of course!
Review: We have used this book as a text for discrete math courses in our undergraduate Computing Engineering and Systems program (University of los Andes, Colombia). There are a lot of advantages using this approach instead of the classical one (e.g., people really learn to prove and learn to write correct proofs).
However, to grasp these ideas you have to be patient and open minded. When other reviewers give 1 star to the book it is clear for me that perhaps they were expecting something magical that did not occur. This presentation of logic and its applications to informatics provides an excellent way to learn and really use the knowledge in the praxis.
In Chapter 8 you go seamlessly from propositional to higher order logic. Sums and logical quantifications are, for example, treated in an uniform way. Maybe the type concept is not so fine explained, but one has to remember that this is an introductory book.
5 stars, of course.
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