Customer Reviews

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

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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.

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

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.

This book is the bible of coputer programming

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

The only drawback of this book is that all algprothms are writeen in MIX - some kind of assembler, that make them hard to read.

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.