Reviews (13)

5 Stars, of course!
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.

Not for independent study, questionable otherwise
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.

Isbn: 0521631076
Sales Rank: 585882
Subjects:  1. Aquatic mammals    2. Behavior    3. Congresses    4. Ecology    5. Foundations Of Mathematics    6. General    7. Mathematics    8. Philosophy Of Mathematics    9. Riparian animals    10. Science/Mathematics    11. Mathematical foundations    12. Mathematics / General   

Reviews (24)

A pourry of combinatorics
I want to start saying that this is a book designed for Engineers, not for Mathematicians. It focuses on the tecniques, not on the arguments. This is not a book about combinatorics, it is a wide raging introduction (it lacks on definitions, and his proofs are a lot far away from mathematical ones). The Enegineers can use this book as a good reference. The Mathematicians can improve their lateral thinking, for them (well: us) it is book about problem-solving strategies.
I will never use this book as a textbook for a graduate/undergraduate course, it can be helpful if used with another book about combinatorics: when you study a combinatorial object, you can read from this book the techniques it involves.
The exercises are extremely exciting, when I read this book I spent a lot of time about its exercises (proportion read:solve = 1:3), and they led me to interesting results.

Steep learning curve, the definitive prerequisite for TAOCP.
Why I got this book:
It's a great feeling to know how computers work, when I decided that I want to make a career and a life out of computers, as its truly a passion for me, I delved deeper, discovering the true beauty in the Science part of Computer Science, so I decided to get Donald Knuth' "The Art of Computer Programming" - to describe that seminal, huge work, it's like biting more than you can chew while trying to drink from a fire hose, moreover, the technical and mathematical prerequisites for the work are sometimes too demanding, they require a huge amount of experience with discrete mathematics, although I had some lectures and read some books, none came close "Concrete Mathematics", it covers, from ground up (though with a dangerously steep learning curve) a lot of discrete mathematics topics, it is by far the most extensive work I've read about Sums and really teaches the algorithmic problem solving thinking skill the authors preach so much about, with small amusing comments written by actual students of this course, a comfortable format, and very good writing skills, you can feel these guys are great professors who enjoy this material and are passionate about teaching it.

Recommended, though some better, less steep, introductionary text books are probably out there.

Enjoy.

Only one problem with this textbook
Basically, I like this textbook. The material is interesting, the way the authors presented the material is inspiring, and they provided a lot of jokes to make even studying for exams not that boring. But there is one big problem which made me decided to rate this book only 3 stars instead of 5 stars: the authors like to use non-standard notations. For example: m\n means "m>0 and n=mk for some integer k". One of the worst thing in scientific world is writing things others cannot read, and the authors did this by introducing many strange notations. These things makes the good work sometimes almost unreadable. This is not computer systems in which we use "cp" for the copy command and "cd" for change directory command.

Reviews (4)

Good.
I liked this book. After taking a discrete math course some time ago then promptly and deliberately forgetting as much as humanly possible about it. I am going on to get a masters degree in computer science. The professors love discrete math so some work involves writing things out mathematically. I am not a math oriented person unless that math pertains to what I am currently working on, 3D graphics, Neural networks, etc.I was able to fly through this book feeling like I picked up a lot of useful information and it will serve as a simple reference.This isn't the 'be all end all' of discrete math it's a simple intro/refresher, of the core topics, which my discrete math professor must have glossed straight over to get to the "fun stuff".Fun for math nerds maybe, but when I was called on to reproduce this knowledge outside of that class most of what must be demonstrated is the basic core stuff.

So I am happy to say this book helped me refresh my skills up to the point I am confident I will be able to slide under the radar during that work to do well in the courses I am taking.

I was tempted to give this book 4 stars because it is still a math book, but what the heck.5/5

Too Brief and Too Simple
From reading the above reviews, I assumed the book was a good source of information to help me understand the materials being covered in class.There are some useful information in the book but it didn't cover 50% of the topics that were went over in class.
A few topics that the book didn't cover was:
* Big O concept
* Modular Arithmetic

Isbn: 0201544296
Sales Rank: 859804
Subjects:  1. Computer Bks - General Information    2. Logic, Symbolic and mathematical    3. Programming - Systems Analysis & Design    4. Reference    5. Reference - General    6. Set theory    7. System design   

Isbn: 0471571806
Sales Rank: 1959574
Subjects:  1. Algebra    2. Algebra - General    3. Discrete Mathematics    4. Mathematics    5. Reference    6. Science/Mathematics    7. Applied mathematics    8. Mathematics / Algebra / Abstract   

Isbn: 0130131512
Sales Rank: 1566227
Subjects:  1. Applied    2. Computer Mathematics    3. Computer Science    4. Computers    5. Discrete Mathematics    6. Mathematics    7. Science/Mathematics   

Reviews (6)

Avoid this book, droogs
I've taken a first semester Discrete Math course, and am currently taking the second semester of it. I bought this book on a whim, hoping it might supplement my text, or at least clarify a few points. It fails at both of those things. Here's why:

1) Abundant errors: I read the first 15 pages and found at least one *serious* typo per page (i.e. a typo that could impede learning). Plus, the grammar ranges from illegal to ambiguous. Thankfully, I was familiar with all of the material that I was reading -- were I not, severe confusion and discouragement would have been the result.

2) Poor examples: They're too abstract or too simple -- and there aren't even very many of them. Oftentimes, he contradicts what he's trying to illustrate due to a small oversight or typo. It's truly bad.

3) Gratuitous brevity (yes I know that may sound paradoxical): The author uses compound sentences in his definitions; sometimes going as far as to define two or three concepts IN THE SAME SENTENCE! It's infuriating.

4) Chapter Zero: This deserves its own rant section. Chapter zero contains nearly all of the material from the first four chapters of my current textbook: Logic, Set theory, Induction, Relations, etc. Somehow the author crams all of it into about 24 pages (plus 4 or 5 pages of exercises). He fails at clarity or lucidity. It's an ambomination -- it reads like lecture notes (you know, the ones only the professor looks at).

OK -- I WANTED to like this book. It's kind of cute, I'll admit it. And the price is sweet. But friends, you get what you pay for. Even after I came across the first 5 or so serious typos I was willing to forgive. Eventually, the sheer amount of contradictory examples and ambiguous sentences riled me up so much that I considered tearing the book in half. Really. I doubt I'll ever open the thing again.

Excellent Text
As with any Dover text, it is important to remember that this text is designed to teach the material, not to coddle the reader.This text provides broad and deep coverage of the various topics that fall under discrete mathematics (set theory, boolean logic, graph theory, etc.) with clarity and simplicity.This book is not designed to help you pass a test, but is instead designed to help you grasp and understand the topic, which it does very well.Easily the best book I own on this topic (I often joke that the author covered my first semester course on discrete math in the first chapter!).

Too succinct for the discrete novice
I learned much more from the Schaum's Outline (ISBN: 0070380457 -Schaum'sOutline of Theory and Problems of Discrete Mathematics (Schaum's OutlineSeries) by Seymour Lipschutz, Marc Lipson (Contributor), Seymour Lipschultz).

That book overcomes the two shortcomings of this one: for aself-proclaimed introductory work on discrete mathematics, this textcontains too few worked out in-chapter examples, and too many omitted stepsin the reasoning.On this latter point, there were many times my readingbrought me to the phrase "It follows from the definition that..."or "obviously..." when, for me, it didn't follow, or it wasn'tobvious. Contrary to another reviewer's assessment, I found quite a lot oftypos, but none too serious.To its credit, the book does contain a lot ofend-of-chapter problems with solutions, and it is inexpensive.

Reviews (3)

Catches the Misconceptions Before They Happen
This book not only covers discrete mathematics well, but shows real professionalism in education.I have over twenty years of software experience and this book was arranged to allow me to refresh or learn for the first time precisely the material I wanted.

Not only this, but Dr Nissanke is well aware of common misconceptions and misunderstandings that students may have in learning discrete mathematics.Examples are the differences between bound and free variables, unknowns and genuine variables, what to guard against in building proofs, and more.For me, I had missed in my education the material from the entire chapters on Interpretation of Formulae and Proofs in Predicate Logic, and never had the time and patience to piece this together from textbooks where this material was learned by osmosis or "between-the-lines".

Another big plus for me was the introductory material to Z, formal specification, functional programming, and lambda calculus.These were done very straightforwardly and user-friendly.

The book also spends more than a tenth of its 400 pages on giving solutions to its exercises.

Finally, it is reasonably priced, especially considering that other introductory textbooks in discrete mathematics run $100 to $125 but are still short on the educational know-how.

My only regrets are that it does not cover posets and graphs.However, this may be a good division of labor between this and a follow-on course.

a good sophomore-level book
a nice sophomore-level book. it introduces basic set theory and logic concepts, but at "gentle" pace. the type of book that would be used at a liberal arts college, but not at a "real" engineering school. has a nice examples and does a decent job in explaining the basics.

Reviews (5)

Please, stay away from this book.
You will not learn anything from this book. The author twists simple material into cabalistic abstractions by adding ramification where not needed and the converse of course holds for formidable notions; as to why this is, one might reason for of the sake of original presentation of well established mathematical concepts, moreover the result: unworthy compilation of simple ideas, presented in an amateurish way - arduous to understand. Hence, summing up: A WASTE OF TIME.

Terrible Book .
There is just nothing lower than one star, that's too bad. This is thus far the most lousy and unavailing text on mathematics that I have ever confronted; the data is alleged in the most juvenile and inverted fashion - obvious self-explanatory concepts are reiterated abundantly and pointlessly, when notions of key precedence are not at all explained in an unambiguous way; the exercizes are scarcely associated with the author's presentation of the topics and to add, the "Answer(s) Appendix", titled "Lots of Hints and Comments; some Answers" is all-pervasive with sarcastic remarks for answers and SHOULD be reported as "There are NO ANSWERS in This 'Book' !". This book, in its entirety, is written in an austere and arrogant manner - akin to the "Answer(s) Appendix"; that is - irrelavant comments (togething with ones of the author's personal life! - WHO CARES, right?), "bufoonery" back talk(s) which are NOT funny nor amusing and come about in the most perplexing components of this contorted presentation , etc . Profuse examples of the same, routinely just one type, are provided; yet, in the exercizes one is asked to do something entirely dissimilar - namely, answer a question of a problem that is all but unconnected to virtually everything just read!The aforesaid commentary is just a prelude to what should be avouched about this "Mathematics Book"; it does not even merit such a prestigious denomination, namely - "Mathematics Book". If you are a serious mathematics student, you will throw this book in the trash can, if it didn't cost so much money! I already did.

This book is sabotage for university students
This book was a required textbook for a discrete mathematics course I am taking in school. Be warned, this book is terrible and is filled with logic holes and gaps!

There are COUNTLESS times in the book where there will be a large proof about a major concept that will take you hours to wrap your head around, only to discover that afterwards it tells you that it is incorrect and suggests that you try to figure it out for yourself!!

From page 372, following a large proof: "Nice proof, huh? Not really. The above proof is incorrect! What went wrong? Try to figure out the difficulty for yourself."

From page 464, following a proof: "Read this proof carefully. When you spot the error, you will know how to answer this problem." A smiley face follows.

Isbn: 0132347172
Sales Rank: 1667583
Subjects:  1. Computer Books: General    2. Computer Mathematics    3. Computer science    4. Discrete Mathematics    5. General    6. Mathematics    7. Mathematics (General)