Search MAA Reviews:
Calculus and its Origins
Publisher: Mathematical Association of America (2012)
Details: 165 pages, Hardcover
Topics: Calculus, History of Mathematics
MAA Review[Reviewed by Luis Henrique de Figueiredo, on 11/24/2012]
The goal of this book is to “teach calculus as the culmination of an intellectual pursuit and place the discovery of calculus at the end.” The author succeeds admirably in describing this pursuit and its culmination in such a short book. It is less clear whether it is possible to teach calculus from this book. (I expect that the author’s own calculus course is wonderful for those who are interested, but I’m less sure that anyone else will be able to teach a calculus course directly from the book).
Nevertheless, this review is about the book, not about the course, and the book is a very good and original addition to the calculus literature. The prose is very agreeable. It looks very nice too: all figures are wonderful hand-drawn pictures. One wonders whether they could be brought to life in the classroom with some computer animation. On the other hand, at least in the first half or so of the book, the pictures embody complicated geometric arguments that mirror historical discoveries but are probably hard to follow for the untrained student (and possibly for the instructor as well!).
The book concentrates on the mathematics, leaving the history in the background, except that the main actors are mentioned. This is not a treatise on the discovery or invention of calculus. For that, the reader is referred to The History of the Calculus and its Conceptual Development, by C. Boyer, and The Historical Development of the Calculus, by C. H. Edwards, Jr. What the book does provide is good side reading for both students and instructors. If the instructor can deliver in the classroom what the book contains, it’ll be a success for its freshness and intrinsic interest. In any case, reading the book is a pleasure, and the exercises are unusual and can be challenging. I’ve enjoyed reading it and I’m certain you will too.
Luiz Henrique de Figueiredo is a researcher at IMPA in Rio de Janeiro, Brazil. His main interests are numerical methods in computer graphics, but he remains an algebraist at heart. He is also one of the designers of the Lua language.