- 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 1.6 x 9.4 inches
- Shipping Weight: 3 pounds (View shipping rates and policies)
- Average Customer Review: 4.6 out of 5 stars See all reviews (63 customer reviews)
- Amazon Best Sellers Rank: #293,520 in Books (See Top 100 in Books)
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Concrete Mathematics: A Foundation for Computer Science (2nd Edition) 2nd Edition
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From the Back Cover
This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline.
Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems." The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study.
Major topics include:
- Integer functions
- Elementary number theory
- Binomial coefficients
- Generating functions
- Discrete probability
- Asymptotic methods
This second edition includes important new material about mechanical summation. In response to the widespread use of the first edition as a reference book, the bibliography and index have also been expanded, and additional nontrivial improvements can be found on almost every page. Readers will appreciate the informal style of Concrete Mathematics. Particularly enjoyable are the marginal graffiti contributed by students who have taken courses based on this material. The authors want to convey not only the importance of the techniques presented, but some of the fun in learning and using them.
About the Author
Donald E. Knuth is known throughout the world for his pioneering work on algorithms and programming techniques, for his invention of the Tex and Metafont systems for computer typesetting, and for his prolific and influential writing. Professor Emeritus of The Art of Computer Programming at Stanford University, he currently devotes full time to the completion of these fascicles and the seven volumes to which they belong.
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Top Customer Reviews
Take-Aways (As of Ch 3):
There are many aspects of summations, integer functions, and proofing that: I never saw covered in my CS degree, are unforgettable, and can be immediately applied to most algorithm research. Those alone make this book worth every penny. Further, the problems posed by this book are more than just repeated mechanics, as I have seen in books like those mentioned below. Each problem is carefully chosen, thorough, and exposes multiple aspects of each topic. They really do weed out many faults that I wasn't really exposed to- as a small example: the importance of ensuring validity of n-1 and n-2 hypothesis & base cases during an induction proof.
Students educated through a contemporary CS track at most American uni's, I believe, (e.g. Rosen Discrete Math, Cormen Algorithms) will find this book both terrifyingly terse and frustratingly paced. In many cases, examples are given without derivation. In many cases, important points are made without obvious connection to previous topics. This is not without a solution however, and getting through this book is often an acquired technique of paper noting things as-you-go, as well as a learned hyper-literacy. The terseness is also a double-edged sword, as sometimes I found it useful as an extra opportunity to practice the taught methods to see if I could come to the same result. Further, the reader should be prepared to go back and review propositional logic & university calculus theorems (atleast FTC, definite vs indefinite integrals). For example, the description of sum by parts in the section on finite calculus assumes _much_ from the reader, and being able to use university calc. as a point of reference to get through that is helpful.
A lot of exercises are tersely explained in both problem and solution. Further, many solutions are totally left-field (having little to do with material in the book). This isn't necessarily bad, as even taking the wrong path to a solution is very educational. However, at some point the reader has to make a judgment as to how long to commit to a certain problem. Many terse problems & left-field solutions instill the wrong judgment: quitting too early.
Attention to detail & extra work is necessary to overcome the terseness of this particular beast, but it's worth it. I recommend this book for developers confronted with algorithm optimization problems, as a well as for a different take on parts of discrete math, and definitely for students coming out of a US state school CS program, the last which this book complements very well. Having worked through some of V1 TAOCP, I would also say that the book is effective in expanding upon its math underpinnings (V1 at-least), and incidentally, does give one confidence to tackle Knuth's other works.
It gets 4 instead of 5 stars because despite having, as advertised, complete coverage of the mathematical topics needed for Computer Science, it is NOT a math book designed to teach you how to *conceptualize* the content it covers. It is heavy on examples and light on theory, and so is not particularly apt for developing one's math schemas. Let me reiterate this point: "Concrete Mathematics" will NOT teach you Pre-Calculus, Discrete Mathematics, or Calculus concepts. If you don't already have a robust mathematical repertoire, this book will not instill a sense of confidence that you're doing things correctly when working on your own. In the Introduction, it says it was written based on an undergraduate class the authors routinely taught... but what seems missing from this book is the *teaching part* of their lecture series. One gets the impression reading it that students who took the course must have all been math aces prior to setting foot in the lecture hall, that they needed only to learn how to apply their considerable math talents to the Computer Science problem domain. I was fine reading and applying the content in this book, but I felt I should warn people looking for math instruction that they will need to supplement this volume with additional "pure math instruction" textbooks (Brief Applied Calculus, Discrete Math, etc.).
The book is great for self -study. As with TAOCP, problems are graded. Solutions exist to all problems - except research ones- but trying to solve them yourself will be the best way to use this book.
Overall, worth every penny. A classic reference and must have.
Graham, Patashnik and Knuth have done great job. Thank you guys!
Most Recent Customer Reviews
This book is for entertainment.
Very good book.
It's extremely dense, which is great for me because I will keep learning from it for months or years to come.Read more