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Reviewer: Barbara Boucher Owens

The long-awaited third edition of Knuth's volume 1 has arrived. <__?__Pub Fmt italic>Fundamental algorithms<__?__Pub Fmt /italic> has been one of the “must own” books for computer scientists since the first edition came out in 1968. Nearly 25 years have elapsed since that edition was followed closely by the second edition in 1973. According to its dust cover, Volume 1 begins “with basic programming concepts and techniques, then focuses more particularly on information structures.” For those of you who have a previous edition on the shelf, pulled down as a reference from time to time, rest assured that the new edition has changed little from the previous ones, and yes, Knuth still uses his own MIX assembly language to illustrate the algorithms. The table of contents is essentially identical to that of the previous edition. So, what has changed__?__ This edition has been typeset using Knuth's own <__?__Pub Fmt texinput>\TeX<__?__Pub Fmt /texinput> and METAFONT systems, which should make subsequent editions easier to update. Many of the citations of previous work have been updated (the preface ends with a quotation from Bill Gates), and Knuth has updated his writing style by eliminating much of the passive voice. He has added dozens of new exercises. Knuth offers monetary incentives for finding errors in his books. The $2.00 per error reward of the second edition yielded 80 Postscript pages of errata, which have been corrected in this edition, and the $2.56 reward per error found in this edition, as posted on Knuth'<__?__Pub Caret>s Web site, has already had a few takers. The dust jacket also boasts the addition of “dozens of simple and important algorithms and techniques” and the revision of the mathematical preliminaries to “match present trends in research.” A very nice addition is the index to notations found at the end of the book. The book begins with a clear presentation of mathematical preliminaries, which remains both understandable and rigorous. The exercises (with answers) are stimulating and plentiful. I have two major concerns about the new edition. I found few substantive additions to the world of algorithms, with many minor revisions tied to outdated technologies. For example, the MIX program illustrating a table of primes is illustrated with a punched card and labeled “The first lines of Program P punched onto cards, or typed on a terminal” (p. 152). The change from the previous edition is the addition of the words “or typed on a terminal.” Knuth has labeled several sections in the book as “under construction,” apologizes for the fact that they are not “up-to-date,” and promises a new edition in about 15 more years. A more deeply rooted concern is Knuth's insistence on MIX as his programming language. My comprehension of the algorithms would be improved if, in addition to their mathematical representation, I could see an embodiment of them in a functional programming language. All in all, the content and organization of this new edition vary only slightly from its previous renditions. For computer scientists blown away by the rapid changes of the past 30 years, this is both amazing and comforting. Yes, Virginia, there still are fundamental algorithms, and Knuth still is an important and relevant guide to many of the basics.