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\iteman{ZMATH 2011b.00046}
\itemau{Grabiner, Judith V.}
\itemti{A historian looks back. The calculus as algebra and selected writings.}
\itemso{MAA Spectrum. Washington, DC: The Mathematical Association of America (MAA) (ISBN 978-0-88385-572-0/hbk). xv, 287~p. (2010).}
\itemab
Editorial remark: Accidentally, this book has been issued twice for reviewing. Therefore, we display both reviews, by adding the second one to the originally published review: The author (born 1938) is a well-known historian of mathematics with particular interests in the use of history in teaching and in the historical development of rigor and method, exemplified by the development of the calculus. She has published two books: The origins of Cauchy's rigorous calculus. Cambridge, Massachusetts - London: MIT Press (1981; Zbl 0517.01002)/2005, and The calculus as algebra. J.-L. Lagrange, 1736-1813. New York etc.: Garland Publishing, Inc. (1990; Zbl 0719.01009). The present book, appearing in the prominent Spectrum series of the Mathematical Association of America (MAA), republishes the latter of the two books and adds 10 articles, several of which have won prizes from the MAA. Referring often to works on the psychology of mathematics (Hadamard, Polya) the author addresses the results of her investigations not principally to other historians, but to mathematicians and teachers of mathematics. Reviewer: Reinhard Siegmund-Schultze (Kristiansand) The author has been recognized as an authority on the history of the calculus even before the publication of her ``Origins of Cauchy's rigorous calculus" [Cambridge, Massachusetts - London: MIT Press. X, 252 p. (1981; (1981; Zbl 0517.01002)] and this anthology of writings contains the key publications that elaborate further on this theme. Over one-third of the book consists of the author's 1966 dissertation, first published in 1990, ``The calculus as algebra. J.-L. Lagrange, 1736-1813" [New York etc.: Garland Publishing, Inc. (1990; Zbl 0719.01009)], here with an updated bibliography. The other ten papers, described as ``reprints,'' are new typesettings, with no indication of original paginations, and most are from journals published by the Mathematical Association of America. They contain significant explorations not only of the main names such as Newton and Leibniz, but also of Euler, d'Alembert and---a topic in which the author has also specialized---Colin Maclaurin, In addition to aspects of the history of calculus, these papers are successful examples of making mathematics and its history accessible to a wide audience; for example, a teacher of any subject may find useful insights in ``The centrality of mathematics in the history of Western thought." [Proc. Int. Congr. Math., Berkeley/Calif. 1986, Vol. 2, 1668--1681 (1987; Zbl 0714.01032)].
\itemrv{Reinhard Siegmund-Schultze (Kristiansand) / Albert C. Lewis (Austin)}
\itemcc{A30 I10 E10 C30}
\itemut{calculus; A.-L. Cauchy; I. Newton; G. W. Leibniz; history of calculus; Maclaurin; Lagrange; Cauchy; rigor and psychology in mathematics; teaching of mathematics}
\itemli{}
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