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Thus metaphysics and mathematics are, among all the sciences that belong to reason, those in which imagination has the greatest role. I beg pardon of those delicate spirits who are detractors of mathematics for saying this .... The imagination in a mathematician who creates makes no less difference than in a poet who invents .... Of all the great men of antiquity, Archimedes may be the one who most deserves to be placed beside Homer.
Discours Preliminaire de L'Encyclopedie, Tome 1, 1967, pp. 47-48.
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From Calculus to Computers
From Calculus to Computers: Using the Last 200 Years of Mathematics History in the Classroom, Amy Shell-Gellasch and Dick Jardine (eds), 2005, 200 pp., illustrations, $48.95 (MAA member price $39.50) paperbound. ISBN: 0-88385-178-4. MAA notes, Catalog Code NTE-68, MAA Service Center, P.O. Box 91112, Washington, DC 20090-1112, 1-800-331-1MAA, www.maa.org.
This collection of articles assembled by editors Amy Shell-Gellasch and Dick Jardine grew from a series of proposed talks for MAA Math Fest during the summers of 2001 and 2002. The motivation of this volume was to address a “noticeable lack of information for educators on just how to incorporate” the mathematical history of the last 200 years in the classroom. Twenty-two articles are divided into four sections: Algebra and Calculus, Geometry, Discrete Mathematics and Computer Science, and Pedagogy. Many of these contributions are quite excellent. For example, Shai Simonson gives a very clear explanation of how Euclid’s algorithm and Fermat’s little theorem are used in modern day cryptography. A few of the articles, such as Robert Rogers on the differential, have exceeded the 200 year limit and yet are still worthwhile reading. Fewer of the articles include original source material. David J. Pengelly continues his mission of bringing this material to a greater audience with Cayley’s first paper on group theory and suggestions for its classroom use.
As the reader moves through each section he or she finds that the articles are quite varied in both focus and style as one would expect from such an assemblage. It is not difficult to question the placement of several articles into the stated sections. Perhaps, the collection could have been better organized into articles on subject matter, methods, and issues. The most interesting articles deal with material which can be easily assimilated into particular mathematics courses. The topics considered include abstract algebra, basic calculus, elliptical curves, differential equations, modern geometry, number theory, logic and computer science. Another group of articles deal in particular with the management of including history of mathematics in particular mathematics courses. Finally, there are three or four articles that deal with clarification of historical issues particular to specific branches of mathematics. These may be of limited interest for the more general reader. While the editors readily admit that this is merely a first attempt, they have created a worthwhile collection for anyone who teaches history of mathematics or is interested in bringing an historical component into their mathematics classes.
James F. Kiernan, Adjunct Professor, Brooklyn College, CUNY