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

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4.8 out of 5 stars See all reviews (5 customer reviews)

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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.

Product Description

The second book in a three volume set, this book provides a complete introduction to this topic. It presents a readable and coherent summary of the major paradigms and basic theory of semi numerical algorithms, providing a comprehensive interface between computer programming and numerical analysis.

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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: 9.4 x 6.7 x 1.6 inches
Shipping Weight: 2.9 pounds (View shipping rates and policies)

Average Customer Review: 4.8 out of 5 stars See all reviews (5 customer reviews)

Amazon.com Sales Rank: #370,709 in Books (See Bestsellers in Books)

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	55% buy the item featured on this page: Art of Computer Programming, Volume 2: Seminumerical Algorithms (3rd Edition) 4.8 out of 5 stars (5) $60.61
	19% buy Art of Computer Programming, Volume 1: Fundamental Algorithms (3rd Edition) 4.2 out of 5 stars (49) $44.42
	16% buy Art of Computer Programming, The, Volumes 1-3 Boxed Set (2nd Edition) (Vol 1-3) 4.5 out of 5 stars (50) $159.99
	6% buy Art of Computer Programming, Volume 3: Sorting and Searching (2nd Edition) 4.8 out of 5 stars (8) $44.42

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Customer Reviews

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4.8 out of 5 stars (5 customer reviews)

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9 of 10 people found the following review helpful:

5.0 out of 5 stars State of the art reference for computer scientists, October 7, 1997

By	Henrik Sandin (Liding�, Sweden) - See all my reviews (REAL NAME)

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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3 of 3 people found the following review helpful:

5.0 out of 5 stars Fascinating, March 5, 1998

By A Customer

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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2 of 2 people found the following review helpful:

5.0 out of 5 stars Numbers: random generations and arithmetic, August 9, 2006

By	Vincent Poirier "CISSP, http://vfp15.wordpres... (Tokyo, Japan) - See all my reviews (TOP 1000 REVIEWER) (REAL NAME)

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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Most Recent Customer Reviews

5.0 out of 5 stars This book is a classic!
I recently modified a program I wrote so that it would do operations on polynomials with multi-precision coefficients. For this, I turned to Knuth. Read more

Published on October 24, 2004 by S. Harris

4.0 out of 5 stars Legendary book
This book is the bible of coputer programming

It contains algorithms on pseudo-random sequences, algotithms on aritmetic operations on number, matrices ect. Read more

Published on December 22, 1999 by Alen Lovrencic

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