Search Loci: Convergence:
I would in the future make a machine, which would simultaneously print ... on paper any arbitrary arithmetical progression .... After setting the first figure, all one has to do is to turn a handle.
In The Difference Engine, by Doron Swade, Viking, 2000
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Calculus Gems: Brief Lives and Memorable Moments
Professor Simmons’s text truly delivers on the two “gems” identified in the subtitle, Brief Lives and Memorable Moments. I was most pleasantly surprised with the content of the Brief Lives section, which comprises over 60% of the book. When I first glanced through the section I thought that I would find much of the same biographical, historical, and mathematical information that is presented in a dozen similar sources. However, with each “brief life” reading, I found myself experiencing either new information or new insight based on previously-known information. For example, when discussing Descartes, Simmons observes the following about his move to Holland in 1628 “in order to find the peaceful leisure necessary for thinking and writing” (p. 87):
The “brief lives” feature of Simmons’s text is an invaluable resource to secondary and post-secondary teachers who are searching for solidly and for the most part, concisely written historical accounts of mathematicians contributing to the development of calculus. Since the Brief Lives section includes many mathematicians contributing to the development of conceptual ideas used to study calculus, teachers of non-calculus mathematics courses will find the text equally significant.
The Memorable Moments section of the book begins with pre-calculus content accessible to students taking a variety of mathematics courses. The majority of the 26 Memorable Moments, however, appear to be more appropriate for students taking calculus or a topics course with second-semester calculus as the prerequisite. That said, the Memorable Moments certainly deliver a variety of “topics from number theory, geometry, science, etc., …[that are] interesting and eye-opening” (Simmons, p. xiv). My favorite “nugget” is “B.16: The Sequence of Primes” – which I am still working on!
Kathleen M. Clark, Assistant Professor, The Florida State University