- Hardcover: 784 pages
- Publisher: Addison-Wesley Professional; 3 edition (November 14, 1997)
- Language: English
- ISBN-10: 0201896842
- ISBN-13: 978-0201896848
- Product Dimensions: 6.9 x 1.9 x 9.4 inches
- Shipping Weight: 2.8 pounds (View shipping rates and policies)
- Average Customer Review: 16 customer reviews
- Amazon Best Sellers Rank: #592,279 in Books (See Top 100 in Books)
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Art of Computer Programming, Volume 2: Seminumerical Algorithms (3rd Edition) 3rd Edition
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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.
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.
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.
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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I attempted every single exercise in volume 1 and went into this one with the same intent. I got pretty close to at least trying each exercise; the last three sections, which covered exponents, polynomial evaluation and power series, went so deep that I ended up glossing over about half of the exercises in each section (the section on polynomial evaluation has over 70 exercises on its own). The exercises in this book were almost all more difficult, and more mathematically sophisticated, than volume 1 - I wouldn't have believed that was possible, but every time you think you've gone as deep as you can possibly go, Knuth shows you that you're just at the tip of the iceberg. I can't say I solved exercise, but I did at least try almost all of them - don't judge me until you try it yourself!
I did love this book, and enjoyed reading it, but I do think that this is one that a practicing programmer outside of very specific domains can probably safely skip - as fascinating as the topics are, and even after taking into consideration that this is not only the authoritative reference but in many cases the only printed material on some subjects - random number generation and lightning-fast (arbitrary precision) arithmetic aren't topics that most programmers have to deal with too often. Still, if you have the time, it is a really fun book to work through.
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
not very pretty, but they have plenty of use Very happy with this product! the next will continue to buy so pleased I bought another
Most recent customer reviews
It contains algorithms on pseudo-random sequences, algotithms on aritmetic operations on number, matrices ect.Read more