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

4.6 4.6 out of 5 stars 68 ratings

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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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From the Publisher

TAOCP box set 1-4B

Updated Box Set Now Available!

This new box set now includes Volume 4B - Combinatorial Algorithms, Part 2

"I've had loads of fun writing other parts of these volumes, but without doubt Section 7.2.2.1 [of Combinatorial Algorithms, Part 2] has been the funnest. And I know that my delight in good puzzles is shared by a significant number of leading computer scientists and mathematicians, who have told me that they chose their careers after having been inspired by such intellectual challenges."

— Donald Knuth

The Art of Computer Programming Volumes 1-4B

ISBN-10: 0137935102

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.



Product details

  • Publisher ‏ : ‎ Addison-Wesley Professional; 3rd edition (November 4, 1997)
  • Language ‏ : ‎ English
  • Hardcover ‏ : ‎ 784 pages
  • ISBN-10 ‏ : ‎ 0201896842
  • ISBN-13 ‏ : ‎ 978-0201896848
  • Item Weight ‏ : ‎ 2.8 pounds
  • Dimensions ‏ : ‎ 9.5 x 6.6 x 1.64 inches
  • Customer Reviews:
    4.6 4.6 out of 5 stars 68 ratings

About the author

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Donald E. Knuth
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Donald E. Knuth was born on January 10, 1938 in Milwaukee, Wisconsin. He studied mathematics as an undergraduate at Case Institute of Technology, where he also wrote software at the Computing Center. The Case faculty took the unprecedented step of awarding him a Master's degree together with the B.S. he received in 1960. After graduate studies at California Institute of Technology, he received a Ph.D. in Mathematics in 1963 and then remained on the mathematics faculty. Throughout this period he continued to be involved with software development, serving as consultant to Burroughs Corporation from 1960-1968 and as editor of Programming Languages for ACM publications from 1964-1967.

He joined Stanford University as Professor of Computer Science in 1968, and was appointed to Stanford's first endowed chair in computer science nine years later. As a university professor he introduced a variety of new courses into the curriculum, notably Data Structures and Concrete Mathematics. In 1993 he became Professor Emeritus of The Art of Computer Programming. He has supervised the dissertations of 28 students.

Knuth began in 1962 to prepare textbooks about programming techniques, and this work evolved into a projected seven-volume series entitled The Art of Computer Programming. Volumes 1-3 first appeared in 1968, 1969, and 1973. Having revised these three in 1997, he is now working full time on the remaining volumes. Volume 4A appeared at the beginning of 2011. More than one million copies have already been printed, including translations into ten languages.

He took ten years off from that project to work on digital typography, developing the TeX system for document preparation and the METAFONT system for alphabet design. Noteworthy by-products of those activities were the WEB and CWEB languages for structured documentation, and the accompanying methodology of Literate Programming. TeX is now used to produce most of the world's scientific literature in physics and mathematics.

His research papers have been instrumental in establishing several subareas of computer science and software engineering: LR(k) parsing; attribute grammars; the Knuth-Bendix algorithm for axiomatic reasoning; empirical studies of user programs and profiles; analysis of algorithms. In general, his works have been directed towards the search for a proper balance between theory and practice.

Professor Knuth received the ACM Turing Award in 1974 and became a Fellow of the British Computer Society in 1980, an Honorary Member of the IEEE in 1982. He is a member of the American Academy of Arts and Sciences, the National Academy of Sciences, and the National Academy of Engineering; he is also a foreign associate of l'Academie des Sciences (Paris), Det Norske Videnskaps-Akademi (Oslo), Bayerische Akademie der Wissenschaften (Munich), the Royal Society (London), and Rossiiskaya Akademia Nauk (Moscow). He holds five patents and has published approximately 160 papers in addition to his 28 books. He received the Medal of Science from President Carter in 1979, the American Mathematical Society's Steele Prize for expository writing in 1986, the New York Academy of Sciences Award in 1987, the J.D. Warnier Prize for software methodology in 1989, the Adelskøld Medal from the Swedish Academy of Sciences in 1994, the Harvey Prize from the Technion in 1995, and the Kyoto Prize for advanced technology in 1996. He was a charter recipient of the IEEE Computer Pioneer Award in 1982, after having received the IEEE Computer Society's W. Wallace McDowell Award in 1980; he received the IEEE's John von Neumann Medal in 1995. He holds honorary doctorates from Oxford University, the University of Paris, St. Petersburg University, and more than a dozen colleges and universities in America.

Professor Knuth lives on the Stanford campus with his wife, Jill. They have two children, John and Jennifer. Music is his main avocation.

Customer reviews

4.6 out of 5 stars
68 global ratings

Top reviews from the United States

Reviewed in the United States on February 18, 2014
this was a gift and the recipient loved it. It came in with excellent condition and arrived in time. BTW the recipient has a job related to the content of the book and hopefully this book had some positive effects.
Reviewed in the United States on September 18, 2016
A leader in his field. Written so concepts are easy to understand. Good reference tool.
Reviewed in the United States on August 25, 2014
A classic it remains. Worth the price and the time.
Reviewed in the United States on February 22, 2023
great college memories
Reviewed in the United States on July 6, 2017
I started reading this book immediately after I finished reading volume 1. I loved volume 1, and I feel the same way about this one, although this was actually a very different sort of book. For one thing, this book was way more mathematical than the first. The first half of volume 1 was all math and the last half was all programming. This book, instead, is almost all math and practically no programming. The author starts by covering random number generators - both implementing and testing them (bet you didn't know that you can actually test the randomness of a random number generator, did you? Knuth can spend a hundred pages showing you a dozen different ways!) This takes up about half the book (chapter 3), and then he moves on to discussing the implementation of arithmetic in computers. Again, you might think that this is worth maybe a dozen pages, but not for Knuth - he spends over two hundred pages discussing more tips and tricks for speeding up arithmetic than I would have guessed existed.

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.
5 people found this helpful
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Reviewed in the United States on January 11, 2021
A decent continuation of Knuth’s classic work, this goes into a sufficient level of depth that suits master and apprentice equally well.
Reviewed in the United States on August 10, 2006
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
9 people found this helpful
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Reviewed in the United States on October 24, 2004
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. This 3-volume set is a great starting point for learning how to implement mathematical calculations on a machine.

Don't listen to the "Reader" from CA. This person obviously has a bone to pick with Knuth. Maybe (s)he failed one of his classes. Maybe (s)he should write his/her own book on the subject.
3 people found this helpful
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Top reviews from other countries

sunflower
5.0 out of 5 stars Christmas present
Reviewed in the United Kingdom on January 9, 2021
Bought as Christmas gift.
Dr K
3.0 out of 5 stars The Wikipedia of Algorithms - a start point for careful investigation..
Reviewed in the United Kingdom on August 3, 2022
Mis-titled: all about algorithms and nothing on programming - any sensible programmer could do better than volume 1 page 2.

Sloppy pedantry. Long-windedness.