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Excursions in the history of mathematics. (English) Zbl 1230.01003

Basel: Birkhäuser (ISBN 978-0-8176-8267-5/hbk; 978-0-8176-8268-2/ebook). xxi, 347 p. (2012).
The book under review was written with two main goals in mind: (1) to arouse mathematics teachers’ interest in the history of mathematics, and (2) to encourage mathematics teachers with at least some knowledge of the history of mathematics to offer courses with a strong historical component.
The book consists of five parts. The first three parts contain ten historical essays on important topics, namely: number theory, calculus/analysis and proof, resp. Each of the three parts begins with a survey of the respective subject and is followed in more depth by specialized themes. In particular the number theory part deals with Fermat as a founder of modern number theory and with his last theorem (until Wiles). In the calculus/analysis part various aspects of the history of the concept of a function are described. In the part devoted to proofs the author discusses paradoxes, the principle of continuity as well as a perspective on a debate about proof initiated by the paper by Jaffe and Quinn.
The fourth part of the book deals with four historically oriented courses and the last part provides biographies of five mathematicians who played an important role in the historical events related to the previous parts: Dedekind, Euler, Gauss, Hilbert and Weierstrass.
The book contains (in each chapter) many references – they are mainly to secondary sources which are easier to comprehend and more readily accessible.
The book can serve teachers of mathematics as well as mathematicians who want to get to know historical background of their subjects. It can also be useful to those teaching or studying the history of mathematics. The author’s background is rather mathematics than history of mathematics. His interest in the history of mathematics stems largely from his attempts to improve his teaching of mathematics. The book under review is based on his experiences in this activity.

MSC:

01A05 General histories, source books
01-02 Research exposition (monographs, survey articles) pertaining to history and biography
97A30 History in mathematics education
00A35 Methodology of mathematics
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