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The Art of Computer Programming: Volume 2: Seminumerical Algorithms: Seminumerical Algorithms v. 2 [Hardcover]

Donald E. Knuth
5.0 out of 5 stars  See all reviews (2 customer reviews)
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Book Description

4 Nov 1997 0201896842 978-0201896848 3

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; 3 edition (4 Nov 1997)
  • Language: English
  • ISBN-10: 0201896842
  • ISBN-13: 978-0201896848
  • Product Dimensions: 24.1 x 16.8 x 4.2 cm
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Bestsellers Rank: 781,452 in Books (See Top 100 in Books)
  • See Complete Table of Contents

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Product Description

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.



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
3 of 3 people found the following review helpful
5.0 out of 5 stars Fascinating 5 Mar 1998
By A Customer
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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2 of 2 people found the following review helpful
By A Customer
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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Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com: 4.7 out of 5 stars  11 reviews
18 of 20 people found the following review helpful
5.0 out of 5 stars Can we shave a constant off this running time? 3 April 1998
By A Customer - Published on Amazon.com
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.
12 of 14 people found the following review helpful
5.0 out of 5 stars State of the art reference for computer scientists 7 Oct 1997
By Henrik Sandin - Published on Amazon.com
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.
6 of 6 people found the following review helpful
5.0 out of 5 stars Numbers: random generations and arithmetic 10 Aug 2006
By Vincent Poirier - Published on Amazon.com
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
4 of 4 people found the following review helpful
5.0 out of 5 stars Fascinating 5 Mar 1998
By A Customer - Published on Amazon.com
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.
10 of 13 people found the following review helpful
4.0 out of 5 stars Difficult book, great source for exercises. 1 April 1998
By A Customer - Published on Amazon.com
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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