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The Calculus: A Genetic Approachby Otto Toeplitz
Synopses & Reviews
When first published posthumously in 1963, this book presented a radically different approach to the teaching of calculus. In sharp contrast to the methods of his time, Otto Toeplitz did not teach calculus as a static system of techniques and facts to be memorized. Instead, he drew on his knowledge of the history of mathematics and presented calculus as an organic evolution of ideas beginning with the discoveries of Greek scholars, such as Archimedes, Pythagoras, and Euclid, and developing through the centuries in the work of Kepler, Galileo, Fermat, Newton, and Leibniz. Through this unique approach, Toeplitz summarized and elucidated the major mathematical advances that contributed to modern calculus.
Reissued for the first time since 1981 and updated with a new foreword, this classic text in the field of mathematics is experiencing a resurgence of interest among students and educators of calculus today.
Book News Annotation:
Published by the U. of Chicago Press in association with the Mathematical Association of America, this is a reprint of Toeplitz' 1963 classic work (that is, the translation from the German edition into English, published by Springer Verlag); it includes a new foreword by David Bressoud. The original is listed as "highly recommended" in Library Recommendations for Undergraduate Mathematics. Following the main currents of calculus, the approach is historical, but this is not a history (no blind alleys). It is appropriate for students who have completed basic or high school calculus but have not yet stepped up to the rigors of advanced calculus. Here those students will find motivation for understanding techniques in response to the original problems that gave rise to them. For example, the study of limits can seem arbitrary, but Toeplitz' discussion offers background on why the Greeks thought they were interesting and what problems they address. ("Genetic" in the subtitle refers to genesis, rather than anything to do with biology.) Annotation ©2008 Book News, Inc., Portland, OR (booknews.com)
About the Author
Otto Toeplitz (1881-1940) was a leading scholar in linear algebra and functional analysis. He was the author of many scholarly articles and coauthor of The Enjoyment of Mathematics.
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