Art of Computer Programming Volume 2: Seminumerical Algorithms View Larger Image | Donald Ervin Knuth
Addison-Wesley, Hardcover, 3rd edition, Published November 1997, 762 pages, ISBN 0201896842 | List Price: $69.99
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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.
"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 Magazine, September 1995
"...a staple on every programmer's bookshelf"
-Dr. Dobb's Journal, April 1996 A word from Don Knuth:
For the past 20 years I've been making copious notes in my personal copies
of The Art of Computer Programming, whenever I've noticed how those books could
be made better. Finally the time is ripe to typeset those books from scratch,
using the tools of digital typography that I worked on during the 1980s. The
new editions incorporate literally thousands of improvements, including hundreds
of instructive new exercises and answers to exercises. I think most readers
will enjoy these new things as much as I did when I first learned them. I've
been especially careful to include any new historical details that have come
to my attention, and to provide up-to-date information about all the research
problems stated in previous editions. Computer Science has been changing and
growing at a fantastic rate, yet I believe nearly everything in The Art of Computer
Programming is crucial information that will never become obsolete.
Table of Contents
3. Random Numbers.
Introduction.
Generating Uniform Random Numbers.
The Linear Congruential Method.
Other Methods.
Statistical Tests.
General Test Procedures for Studying Random Data.
Empirical Tests.
Theoretical Tests.
The Spectral Test.
Other Types of Random Quantities.
Numerical Distributions.
Random Sampling and Shuffling.
What Is a Random Sequence?
Summary.
4. Arithmetic.
Positional Number Systems.
Floating Point Arithmetic.
Single-Precision Calculations.
Accuracy of Floating Point Arithmetic.
Double-Precision Calculations.
Distribution of Floating Point Numbers.
Multiple Precision Arithmetic.
The Classical Algorithms.
Modular Arithmetic.
How Fast Can We Multiply?
Radix Conversion.
Rational Arithmetic.
Fractions.
The Greatest Common Divisor.
Analysis of Euclid's Algorithm.
Factoring into Primes.
Polynomial Arithmetic.
Division of Polynomials.
Factorization of Polynomials.
Evaluation of Powers.
Evaluation of Polynomials.
Manipulation of Power Series.
Answers to Exercises.
Appendix A. Tables of Numerical Quantities.
Fundamental Constants (decimal).
Fundamental Constants (octal).
Harmonic Numbers, Bernoulli Numbers, Fibonacci Numbers.
Appendix B. Index to Notations.
Index and Glossary.
About the Author
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. Approximately
one million copies have already been printed, including translations into six
languages. He took ten years off from this 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, the National Academy of Engineering, and a foreign associate of
l'Academie des Sciences (Paris) and Det Norske Videnskaps-Akademi (Oslo). He
holds five patents and has published approximately 160 papers in addition to
his 19 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 Adelsköld 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.
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