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Concrete Mathematics: Foundation for Computer Science [Hardcover]

Ronald L. Graham , Donald E. Knuth , Oren Patashnik
5.0 out of 5 stars  See all reviews (5 customer reviews)
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Book Description

28 Feb 1994 0201558025 978-0201558029 2
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: *Sums *Recurrences *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. 0201558025B04062001

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Concrete Mathematics: Foundation for Computer Science + Introduction to Algorithms + The Algorithm Design Manual
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Product details

  • Hardcover: 672 pages
  • Publisher: Addison Wesley; 2 edition (28 Feb 1994)
  • Language: English
  • ISBN-10: 0201558025
  • ISBN-13: 978-0201558029
  • Product Dimensions: 18.8 x 3.6 x 23.6 cm
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (5 customer reviews)
  • Amazon Bestsellers Rank: 59,792 in Books (See Top 100 in Books)
  • See Complete Table of Contents

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Product Description

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:

  • Sums
  • Recurrences
  • 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.



0201558025B04062001

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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Most Helpful Customer Reviews
24 of 24 people found the following review helpful
5.0 out of 5 stars Fills in some crucial gaps, for sure 23 Jun 2007
Format:Hardcover
So you've done an undergraduate degree course in maths. So you want to take it further. But all the books you can find either go at light speed or are written like koans.

Not this one - goes for some really heavy and contemporary maths and does it completely accessibly. I never thought I'd be studying hypergeometric functions this side of 90 - but here they are in all their glory.

Yes it's tough, goodness it's tough, but nowhere near as tough as I'd expected it to be for the concepts being covered.

Oh, and it covers the Stern-Brocot tree which I thought I'd invented, took it to my Number Theory tutor and she'd (a) never heard of it and (b) didn't believe it. They take a handful of pages over it, and that's it, done and dusted.

*This* is the way to write a maths book.
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16 of 16 people found the following review helpful
5.0 out of 5 stars Well worth the effort 20 Oct 2004
Format:Hardcover
Unless you're very used to this type of mathematics, this book will, as other reviewers comment, prove hard work. However, even someone with little formal maths background like myself can get a lot out of it. It's beautifully written and well-presented, and on the whole the pacing is OK, although sometimes it goes much too fast for casual reading.
Once I've made my way through it, I suspect it will make a very useful reference book too; it's full of useful techniques for solving real-world problems, at least if you work in a field that sometimes requires you to solve recurrences and work with tricky integer functions.
Although often corny, the marginalia do give you something of the feeling of being on a course, rather than just reading a textbook. As well as daft jokes, there are hints as to the relative importance of some sections (including "skip this bit on first reading" as well as "this is the critical part" -- both kinds very helpful).
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20 of 21 people found the following review helpful
5.0 out of 5 stars Excellent 8 Dec 2001
By A Customer
Format:Hardcover
This book is not light reading, but it's worth it. It has most value as a reference tool, and covers well some areas of maths which are important to CS. Moreover, the information is presented in a light-hearted way, with lots of inline jokes (mainly very corny) and margin notes from students who took the lecture course behind the book. The examples tend to help, and there are plenty of exercises with worked solutions. Also lots of references to the primary literature.
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1 of 1 people found the following review helpful
5.0 out of 5 stars Very well written, in a friendly style. 14 Sep 2013
Format:Hardcover|Verified Purchase
I am greatly enjoying working through this book although it is not easy. The last time i studied maths was A Level 6 years ago but it is probably the right level.
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12 of 20 people found the following review helpful
5.0 out of 5 stars It's a hard ONE!!! 10 Jan 2000
By A Customer
Format:Hardcover
Well, I love Knuth, I think he is a genius... Anyway, the problem is that he is a hard genius. I have High School Mathematics Knowledge because I'm in the first year of college studying Software Enginneering. Anyway, this book is just great, with examples, jokes (when appropriate) and alot of Mathematical tricks but do not think it's easy to read it (well, at least I didn't found it easy to read...). But the money I paid for it is worthy. I liked the book and advise you it if you want a some good problems to solve (or not...)... Good luck!!! ;)
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