Those of us who teach (or would like to teach)
Euclid's Elements will welcome this book enthusiastically. Thomas
L. Heath's three-volume edition of Euclid, originally published in 1908
with a second edition in 1926, is still in print (from Dover) and is
relatively inexpensive, but for classroom use it is less than ideal. For
one thing, it is in three volumes. More seriously, Heath's edition contains
extensive commentary, and it is almost inevitable that students will end up
spending more time reading Heath than reading Euclid. And while Heath's
translation has held up well, not all of his interpretations
have.This book solves those problems by presenting the full text of Heath's Euclid in one handsome volume. The production values of this edition are very high: the margins are wide, the paper is of good quality, diagrams are always on the same page as the text that refers to them (if necessary, diagrams are repeated to achieve this). The editor has done some (very light) revising of Heath's text, mainly to deal with material that Heath presented in brackets for various reasons. These decisions are explained in the introduction.
A very nice short biography of Heath and a glossary of important Euclidean words add to the value of the book. If you want your students to really grapple with Euclid, this is the edition to choose. [Fernando Q. Gouvêa]
About halfway through my first calculus course, I
discovered a copy of Michael Spivak's Calculus in a local
bookstore. This delightful book helped intensify my love for mathematics
and helped me understand calculus better. It also stoked my well-known
mania for books, because it included an annotated bibliography of
mathematics books, several of which I ended up buying and/or reading.
When it came to differential equations, Spivak said "Innumerable books on differential equations have been written, but none of the elementary ones seems to generate much enthusiasm. There is a somewhat more advanced book, however, which is universally admired." The book in question was Hurewicz's Lectures on Ordinary Differential Equations, and it is very nice indeed, short but full of interesting things. Dover has just brought it back, in hardcover, as one of their Phoenix Editions, and that's very good news.
As Spivak says, this isn't an elementary book. (The situation with
elementary books is much improved since the 1970s, of course!) It's
probably not a book you'd want to choose for that intro course. But it's
certainly a book to have on your desk when you're teaching that intro
course. [Fernando Q. Gouvêa]
Titu Andreescu and Zuming Feng have provided a
new installment in the USA and International Mathematical Olympiads
series, this time covering 2001. The book contains three sets of problems:
the USAMO (USA Mathematical Olympiad) problems, the problems from the test
used to select the US team for the International Olympiad, and the IMO
(International Mathematical Olympiad) problems. For each set of problems,
the authors provide first hints, then formal solutions.
These problems are elementary but not easy. Consider the very first one:
Each of eight boxes contains six balls. Each ball has been colored with one of n colors, such that no two balls in the same box are the same color, and no two colors occur together in more than one box. Determine, with justification, the smallest integer n for which this is possible.
The hint for this problem just says "the answer is not 24". Can you
solve it? [Fernando Q. Gouvêa]
Euclid's
Elements, translated by Thomas L. Heath,
edited by Dana Densmore. Green Lion Press, 2002. Hardcover, 499pp., $38.00.
ISBN 1-888009-18-7.
Also available in Softcover, $24.95, ISBN 1-888009-19-5.
Lectures on Ordinary Differential Equations, by Witold Hurewicz. Dover Publications, 2002. (Unabridged and unaltered republication of the first M.I.T. Press paperback edition (1964) of a book first published in 1958.) Hardcover, 122pp., $27.50. ISBN 0-486-49510-8.
USA and International Mathematical Olympiads 2001, ed. by Titu Andreescu and Zuming Feng. Mathematical Association of America, 2002. Paperback, 120 pp., $16.50 ($13.50 to MAA members). ISBN 0-88385-809-6.
Fernando Q. Gouvêa (fqgouvea@colby.edu) is the editor of FOCUS and MAA Online.
|
Go to...
|
Find out...
|
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: Sat Sep 28 16:45:04 -0500 2002