Books of collected or selected papers are
treasures to be greatly valued, particularly when they collect the work of
people who have had a significant impact on their field. We have just
received several of these. The first, Donald E. Knuth's
Selected Papers on Discrete Mathematics, is part of a
series collecting Knuth's work. This volume, which focuses on
discrete mathematics, is a real gem. Knuth writes well, and his papers are
always interesting. Knuth's introduction notes that some of the papers were written purely as expositions of the work of other people, and that the rest contain material that was new at the time. But even in the latter case his goal was always to be understood: "I tried to make every paper self-contained, so that readers with a general mathematical background would be able to understand the details." In other words, non-specialists will enjoy this book. Most of the papers include addenda on further developments, so that in fact the book is not just a historical artifact but also a useful source of up-to-date information.
As one might expect, the book is very well produced. Knuth says that these volumes present his work "in the form that I most wish people to remember it." He clearly means this not only in mathematical terms, but also in terms of book design and typography. This one you want to have.
We also received two other books of selected papers, both dealing with subjects related to linear programming and optimization. The Basic George B. Dantzig collects the most important papers by the founder of linear programming. Once again, this is significant both as a historical document and as a mathematics book. Dantzig's work is one of the most important parts of 20th century mathematics, so it is really good to have this book.
Alan Hoffman is probably not as well known as
either Knuth or Dantzig, but Selected Papers of Alan
Hoffman with Commentary is still worth noting. Hoffman's work deals,
among other things, with linear programming, combinatorial optimization,
and graph spectra. The papers are not re-set, but rather copied directly
from the original publication, which makes this book physically less
attractive than the previous two, but specialists in the area will want to
have this one too.
Finally, there is Essays on Early Medieval Mathematics: the Latin Tradition, by Menso Folkerts. This is part of the Variorum Collected Studies series, which reproduces papers directly from their original (sometimes quite obscure) sources, preserving even the original pagination. (This is intended to make it easier to trace references to the papers, but it does mean that we get a book that isn't as pleasant to the eye.) Folkerts' work is technical, but this book is worth having in your library because all too many histories short-change the period in question, suggesting that nothing interesting happened in the early medieval period in Europe. The very first essay in the book, called "The Importance of the Latin Middle Ages for the Development of Mathematics", deals with this issue directly. It would make a great reading assignment for a history of mathematics course. The rest of the book is more technical; among other things, it includes editions and translations (not always into English) of important historical sources. Given the price, few people will want to buy themselves a copy, but libraries that aim to have a good collection in the history of mathematics should have this one. [Fernando Q. Gouvêa]
Second editions often pose a problem: are they new
enough, different enough, to be worth getting even if one already owns the
original edition? The answer, of course, is "it depends." Winning Ways, as we have noted in this column before (in fact, twice before), was a ground-breaking book when it came out in 1982. It created a whole new approach to the mathematics of combinatorial games that has led to much progress since then (see, for example, our reviews of Games of No Chance and of More Games of No Chance). But Winning Ways is still valuable, and it is just as much fun today as it was 21 years ago. The new edition has been split into four volumes instead of the original two, so there's still one more to come. Volume 3 (dealing with "Games in Clubs", which means that the games have been grouped together according to how you play them) is considerably fatter, it seems to me, than the first half of the old volume 2. Several of the chapters have been revised, which makes the new edition definitely worth having.
Plus, the games are fun. Every math
teacher should teach students how to play "Sprouts" on the blackboard (just
perfect for those classes just before a holiday when only half the students
are there). And how can one resist things such as "Fox-Flocks-Fox" and
"Chessgo, Kinggo, and Dukego"?
Jenny Olive's Maths: a Student's Survival Guide, is of course, a completely different kind of book. We reviewed the original edition several years ago. The new edition is about 70 pages longer (but a change in the paper makes it seem much bigger than the original). The main change is the addition of a chapter about "working with vectors".
Olive's book is a useful review of elementary mathematics, where elementary includes some topics that are typically covered (in the US) in first-year calculus courses. There are lots of friendly summaries, sample problems with full solutions, and helpful comments. It strikes me as a superior alternative to something like the Schaum Outlines, good to have around to lend to students who are struggling.
If you have the original, should you get the new edition? Probably not. But your library might want to. And, of course, you might want to recommend it to students, in which case it's good to know that basic vector geometry is now included. [Fernando Q. Gouvêa]
Selected Papers on Discrete Mathematics, by Donald E. Knuth. CSLI Lecture Notes, number 106. CSLI Publications, 2003. Paperback, 812 pp., $32.50. ISBN 1-57586-248-4.
The Basic George B. Dantzig, ed. by Richard W. Cottle. Stanford University Press, 2003. Hardcover, 378 pp., $49.95. ISBN 0-8047-4834-9.
Selected Papers of Alan Hoffman with Commentary, edited by Charles A. Micchelli. World Scientific, 2003. Hardcover, 446 pp., $88.00. ISBN 981-02-4198-4.
Essays on Early Medieval Mathematics, by Menso Folkerts. Variorum Collected Studies Series. Ashgate, 2003. Hardcover, $111.95. ISBN 0-86078-895-4.
Winning Ways for Your Mathematical Plays, volume 3, by Elwyn W. Berlekamp, John H. Conway, and Richard K. Guy. A K Peters, 2003. Paperback, 276pp., $49.00. ISBN 1-56881-143-8.
Maths: a Student's Survival Guide, by Jenny Olive. 2nd edition, Cambridge University Press, 2003. Paperback, 634 pp., $40.00. ISBN 0-521-01707-6.
Fernando Q. Gouvêa is Professor of Mathematics at Colby College in Waterville, ME. He is fanatic about number theory, the history of mathematics, Christian theology, poetry, science fiction, comic books, politics, classics, and football (the real thing, not the American version).
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Read This! is the MAA Online book review column. Contributions are welcome; contact the editor if you'd like to be one of our reviewers. Books for review should be sent to the editor: Fernando Gouv&ecric;a, Dept. of Math&CS, Colby College, Waterville, ME 04901. Publishers, please check our reviews information page.
MAA Online is edited by Fernando Q. Gouvêa (fqgouvea@colby.edu). Last modified: Wed Oct 29 15:07:54 EST 2003