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Concrete Mathematics: A Foundation for Computer Science (2nd Edition) 2nd Edition

by Ronald L. Graham (Author),
Donald E. Knuth (Author)
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Donald E. Knuth (Author), Oren Patashnik (Author)
4.5 out of 5 stars 54 customer reviews
ISBN-13: 078-5342558029
ISBN-10: 0201558025
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Product Details

  • Hardcover: 672 pages
  • Publisher: Addison-Wesley Professional; 2 edition (March 10, 1994)
  • Language: English
  • ISBN-10: 0201558025
  • ISBN-13: 978-0201558029
  • Product Dimensions: 7.6 x 1.4 x 9.4 inches
  • Shipping Weight: 3 pounds (View shipping rates and policies)
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (54 customer reviews)
  • Amazon Best Sellers Rank: #59,721 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

130 of 130 people found the following review helpful
Great book... some reviewers simply don't get it.
By Wayne Folta on June 20, 2007
Format: Hardcover
I have the First Edition and came here to look into the Second Edition. There are several negative reviews and basically those folks have fundamental misunderstandings. So I'll add my review.

First, what kind of book is it? It is not an introductory-level math book with lots and lots of repetition. It is a book on hard math, done in a concise manner by brilliant teachers who assume students are very comfortable with calculus, probability, etc. You really cannot afford to skip around and dabble as if this were an introductory algebra course or something. (I'm not being elitist. I did not attend Stanford and don't consider myself a math genius and am not making this a "we versus the unwashed masses" issue, as I have really struggled with the material myself.)

Second, what is the book about? Several reviewers have theories on where the "Concrete" part of the title comes from, but the bottom line is that it's a book on the discrete math that you need to know for theoretical computer science. (For example, discrete calculus versus the continuous calculus we all learned in school.) Any Analysis of Algorithms course, for example, will confront you with recurrence equations and lots of discrete math.

Third, how is the book organized? At first, it appears rather disjoint. The authors have a sort of, "Hey, look at that flower," and "hey, look under this rock" kind of approach as you walk down a path but the path itself isn't really spelled out. None-the-less, the book does build step-by-step from examples of recurrence equations (Towers of Hanooi, Josephus) in Chapter 1, to Generating Functions in Chapter 7.

Perhaps they could have made the path more explicit, but I can't see how they'd organize it much differently.Read more ›
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262 of 271 people found the following review helpful
Please Be Discrete
By Mary P. Campbell on July 13, 2001
Format: Hardcover
What is "concrete" math, as opposed to other types of math? The authors explain that the title comes from the blending of CONtinuous and disCRETE math, two branches of math that many seem to like to keep asunder, though each occurs in the foundation of the other. The topics in the book, such as sums, generating functions, and number theory, are actually standard discrete math topics; however, the treatment in this text shows the inherent continuous (read: calculus) undergirding of the topics. Without calculus, generating functions would not have come to mind and their tremendous power could not be put to use in figuring out series.

The smart-aleck marginal notes notwithstanding, this is a serious math book for those who are willing to dot every i and cross every t. Unlike most math texts (esp. graduate math texts), nothing is omitted along the way. Notation is explained (=very= important), common pitfalls are pointed out (as opposed to the usual way students come across them -- by getting back bleeding exams), and what is important and what is =not= as important are indicated.

Still, I cannot leave the marginal notes unremarked; some are serious warnings to the reader. For example, in the introduction, one note remarks "I would advise the casual student to stay away from this course." Notes that advise one to skim, and there are a few, should be taken seriously. All the marginal notes come from the TAs who had to help with the text, and thus have a more nitty-gritty understanding of the difficulties students are likely to face. Still, there are plenty of puns and bad jokes to amuse the text-reader for hours: "The empty set is pointless," "But not Imbesselian," and "John .Read more ›
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228 of 236 people found the following review helpful
Beware of great books
By James Street on October 3, 2005
Format: Hardcover
This book is excellent (5 stars) if you have the mathematical "maturity" that it assumes. If not, it will vary from 4 stars to 0 stars.

The problem is, the book looks as if it might be an entry level text and it is tempting to think that with a little extra hard work any intelligent, reasonably well-grounded mathematics undergraduate student could prove that he is a genius by mastering the content. A fair number, of course, will do just that. But many more will unnecessarily bloody their noses and egos.

Most people skip prefaces but this one shouldn't be skipped. The preface says that most of the people who have taken the course that the book is based on have been graduate students and alumni and (some) have been juniors and seniors.

To give an example of the difficulty an unwary student might find: The chapter on probability looks straightforward and well-written and it is! But it is truly useful only to students who have already studied probability theory and mastered the basic theory. The trap is that the book does, in fact, provide introductions to most of the topics covered. But in reality, they are reviews, introductions to the symbols and notation to be used and repositories for results that will be referenced throughout the book.

The prerequisites for having a profitable encounter with this book are : a good understanding of elementary number theory, probability theory and linear algebra and two years of calculus with a very good understanding of infinite series. A good knowledge of generating functions and recursive functions is also necessary. A few juniors and seniors will always be dedicated and smart enough to achieve this level of maturity but it usually takes more than four years.Read more ›
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Most Recent Customer Reviews

This is fun stuff. It's an interesting take on discrete math

This is fun stuff. It's an interesting take on discrete math. In fact, it's really not discrete math; in includes discrete math but also includes other elements. Read more

Published 28 days ago by DAF
other than this it's good

now obviously this is Knuth, so lots of information there, im still going through the book but sometimes i feel im lost at certain points which needs me to do some search somewhere... Read more

Published 2 months ago by A.Mellice
this is a very nice intermediate material to this must to know subject

Not that I've seen many discrete math books, nonetheless, this is a very nice intermediate material to this must to know subject.

Published 2 months ago by José Vinícius de Miranda Cardoso
Classic Reference that's Fun!

This book is an expansion of the Preliminary Mathematics section of Book 1 of TAOCP by Knuth. Unlike TAOCP, the tone is much less dense, very relaxed and actually fun to read. Read more

Published 2 months ago by Indranath Mitra
must read

Anyone interest in understanding how to evaluate algorithms must read this book.

Published 2 months ago by Amazon Customer
Fun to read.

Yet another classic. Concrete Mathematics is the second most accessible book by Knuth as one of the co-authors. Read more

Published 5 months ago by Peteris Krumins
Four Stars

great!

Published 5 months ago by Christopher M Ford
Five Stars

Great book for studying math

Published 6 months ago by Smeha
This is a very good collegiate level book

This is a very good collegiate level book, but not so great at explaining concepts to the high school level. Read more

Published 10 months ago by J. Kelly
Five Stars

Development seems not too deep but problems and exercises make it an extremely interesting book.

Published 11 months ago by teclado

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