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Art of Computer Programming, Volume 2: Seminumerical Algorithms (3rd Edition) 3rd Edition

4.8 out of 5 stars 14 customer reviews
ISBN-13: 078-5342896848
ISBN-10: 0201896842
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Editorial Reviews

Amazon.com Review

Volume 2 of Donald Knuth's classic series The Art of Computer Programming covers seminumerical algorithms, with topics ranging from random number generators to floating point operations and other optimized arithmetic algorithms. Truly comprehensive and meticulously written, this book (and series) is that rarest of all creatures--a work of authoritative scholarship in classical computer science, but one that can be read and used profitably by virtually all working programmers.

The book begins with fundamental questions regarding random numbers and how to use algorithms to generate them. Subsequent chapters demonstrate efficient computation of single-precision and double-precision arithmetic calculations and modular arithmetic. The text then presents prime factorization (which can be used in cryptography, for instance) and algorithms for calculating fractions. This volume ends with algorithms for polynomial arithmetic and manipulation of power-series topics, which will benefit those with some knowledge of calculus.

Throughout this beautifully presented edition, Knuth incorporates hundreds of useful exercises for trying out the algorithms. These range from simple problems to larger research project topics. (The book provides answers, where appropriate, at the end of the book.) The result is a text that's suitable for college or graduate-level computer science courses or individual study by programmers. Volume 2 is an indispensable part of any working programmer's library.

From the Back Cover

The bible of all fundamental algorithms and the work that taught many of today's software developers most of what they know about computer programming.

Byte, September 1995

I can't begin to tell you how many pleasurable hours of study and recreation they have afforded me! I have pored over them in cars, restaurants, at work, at home... and even at a Little League game when my son wasn't in the line-up.

—Charles Long

If you think you're a really good programmer... read [Knuth's] Art of Computer Programming... You should definitely send me a resume if you can read the whole thing.

—Bill Gates

It's always a pleasure when a problem is hard enough that you have to get the Knuths off the shelf. I find that merely opening one has a very useful terrorizing effect on computers.

—Jonathan Laventhol

The second volume offers a complete introduction to the field of seminumerical algorithms, with separate chapters on random numbers and arithmetic. The book summarizes the major paradigms and basic theory of such algorithms, thereby providing a comprehensive interface between computer programming and numerical analysis. Particularly noteworthy in this third edition is Knuth's new treatment of random number generators, and his discussion of calculations with formal power series.



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Product Details

  • Hardcover: 784 pages
  • Publisher: Addison-Wesley Professional; 3 edition (November 14, 1997)
  • Language: English
  • ISBN-10: 0201896842
  • ISBN-13: 978-0201896848
  • Product Dimensions: 6.4 x 1.8 x 9.3 inches
  • Shipping Weight: 2.8 pounds (View shipping rates and policies)
  • Average Customer Review: 4.8 out of 5 stars  See all reviews (14 customer reviews)
  • Amazon Best Sellers Rank: #75,201 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

Format: Hardcover
To an ordinary computer scienist, an algorithm is polynomial-time. To Knuth, it takes 3*n^2 + 17*x + 5 steps on MIX, not counting the time required to display the output, but there might be a way to reduce the number of steps to 3*n^2 + 17*x + 4. For precision and rigor, the Art of Computer Programming books are hard to beat. But, at least for an undergraduate CS student like me, they are slow going. Their greatest value seems to be as a reference for mathematical ideas needed in analysis of algorithms: recurrence relations, combinatorial identities, etc. Like the Bible, the TAOCP books are good to have around even if you don't plan to read them.
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Format: Hardcover
Volume 2 of "The Art of Computer Programming" is about random numbers and also about relearning one of the three Rs from grade school, viz. arithmetic. Each topic gets one chapter.

When you generate random numbers in Excel, or VBA, or Perl, or C using functions packaged with the software, you are really using a deterministic algorithm that is not random at all; the results do however look random and so we call them "pseudorandom".

Chapter 3 contains four main sections. First a section devoted to the linear congruence method (Xn+1=(aXn + c) mod m) of generating a pseudorandom sequence; with subsections on how to choose good values for a, c, and m. Second we get a section about how to test sequences to find if they are acceptably random or not. Third we find a section on other methods, expanding on linear congruence. Finally in a particularly fascinating section, DK provides a rigorous definition of randomness.

I haven't looked much at chapter 4 yet, on arithmetic. In it Knuth covers positional arithmetic, floating point arithmetic, multiplication and division at the machine level, prime numbers and efficient ways of investigating the primeness of very large numbers.

Again, DK is thorough and methodical. Again this is not a for dummies book. Again it is about theorems, algorithms, mechanical processes, and timeless truths. Again the exercises are a fascinating blend of the practical (investigate the random generating functions on the computers in your office) to the mathematical (he asks readers to formally prove many of the theorems he cites). And yes, again Knuth uses MIX, that wonderfully archaic fictional 60s machine language. But that should not stop readers; I use Perl.

Vincent Poirier, Tokyo
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Format: Hardcover
This book offers a stringent treatment of random number generators and algorithms not found anywhere else. It is particularly valuable for those that deal with encryption and the analysis of cyphers. The exercises add admirably to the text. References to other books in the field are extensive. The book is written in a non-wordy, but still very readable style, making it accessible to serious computer scientists at all levels. A mathematical background is necessary.
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By aj on November 11, 2013
Format: Hardcover Verified Purchase
It is simply excellent. Also, the paper and print quality are excellent. Commenting on the paper may sound trivial, but I just received an expensive textbook that looks like a fourth-generation photocopy.
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By A Customer on March 5, 1998
Format: Hardcover
Of course this is a classic programming text, but the book is fascinating from a mathematical point as well. The discussion of random number generation is worth the price alone. Also neat is the discussion of why numbers with lower initial digits are 'more common' in practice than those with higher initial digits, a topic I've never seen treated elsewhere.
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By A Customer on March 25, 1998
Format: Hardcover
These volumes are considered first-class references on the subject of computing and algorithms. And they are... but these aren't really books to read. Nobody has time for that. However, for those computer scientists that really are hard up for something to read one of those rainy nights, Knuth has a personal flair and humor that spills into his algorithm summaries and exercises that is unsurpassed, at least in the field of CS handbooks. An excellent source for solutions to commonly asked questions and problems.
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Format: Hardcover
Knuth's presentation is obscure and difficult, but he's awfully comprehensive. If you want to learn algorithms, or even if you're looking for a reference, there are many better choices (especially Introduction to Algorithms, the CLR book). That said, I can't point to a more thorough book. Among other things, The Art of Computer Programming series is a great source of problems if you're teaching, learning, or just looking for fun. It might be worth the price just for that.
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