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The history of mathematics. A brief course. 2nd ed. (English) Zbl 1073.01005

Hoboken, NJ: Wiley-Interscience (ISBN 0-471-44459-6/hbk). xviii, 607 p. (2005).
This “brief course” of the history of mathematics, which comprises nevertheless 607 pages, is an extensive rewriting of the original in [Wiley-Interscience Publication. New York, NY: Wiley. (1997; Zbl 0997.01501)]. Basically, the order of presentation was changed from an orientation towards periods/cultures into a classification as to subject matter. After a general survey of mathematics and mathematical practice the division of the book is into numbers, geometry, algebra, analysis, and “mathematical inference” (the latter including probability, statistics, logic and set theory). The reason for changing the order of the first edition is, according to the author, twofold: (mathematical) students remember the facts better by focussing on single areas of mathematics, and an over-emphasis on the cultural lines had forced the author to omit valuable material, particularly of biographical character. Each chapter is concluded by stimulating “Questions and problems”; Cooke refers to possible contacts with the publisher who keeps a list of the solutions. On his website [www.cem.uvm.edu/\(sim\)cooke/history/seconded.html] Cooke gives first corrections. In most cases (with some exceptions, for instance H. Bos on Descartes’ geometry) the author has used the most recent secondary literature in the history of mathematics. In spite of the change in orientation, the book is still rather comprehensive in its attention to the contributions of the various European and Asian cultures to the history of mathematics until about 1900. Later events and topics such as Lie theory, functional analysis, topology as well as names such as Brouwer, Banach are mentioned but passingly. Names of more modern mathematicians are for the most part missing (Minkowski, Grothendieck, Serre, H. Hopf). The connection between A. Wiles and Fermat’s last theorem can only be found by chance because the subject index has some insufficiencies. In the case of probability theory not mentioning Kolmogorov seems problematic. But not referring – by mere name-dropping (Arnold, Mandelbrot) – to spectacular applications such as catastrophe theory and fractals only testifies to the solidity of the book, which is a valuable and richly documented introduction into the history of mathematics.

MSC:

01A05 General histories, source books
01-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to history and biography

Citations:

Zbl 0997.01501
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