Product Description

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

Product Details

• Amazon Sales Rank: #135137 in Books
• Published on: 1994-03-31
• Original language: English
• Number of items: 1
• Binding: Hardcover
• 672 pages

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.

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.

Customer Reviews

Well worth the effort
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).

Fills in some crucial gaps, for sure
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.

Excellent
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.