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Calculus Gems: Brief Lives and Memorable Mathematics
This text is a spin-off of Appendices A ("A Variety of Additional Topics") and B ("Biographical Notes") of Simmons' successful CALCULUS WITH ANALYTIC GEOMETRY. The text is suitable as a supplement for a calculus course and/or history of mathematics course. The text may also be appropriate for a liberal arts mathematics course for students with minimal mathematics background.
355 pages, Paperback
Published January 1, 1992
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About the author
George F. Simmons
20 books19 followersGeorge Simmons was an American mathematician who worked in topology and classical analysis. He was known as the author of widely used textbooks on university mathematics.
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Displaying 1 - 3 of 3 reviews
May 1, 2025
George F. Simmons wrote a superb book giving brief overviews of the lives and accomplishments of some of the biggest names in the history of calculus. He was at times weirdly opinionated, which is why I knocked off one star. I recommend this book to anyone who loves mathematics who has taken at least one semester of calculus. The first part of the book consists of biographies of mathematicians and the second contains some interesting mathematics developed by said mathematicians.
May 7, 2020
George Simmons is one of those rare teachers who not only has a passion, but has a powerful way of communicating that passion.
Back in the day when he was writing text books, he has always tried to provide a historical perspective into the context in which the mathematics being described can be placed. In the course of such works, potted histories of various mathematicians are given, as chapter appendices and footnotes, which leavens the business of learning how to use the techniques described.
Lots of sources cite his 1985 Calculus book, but this is not his sole source of historical notes. His 1972 work on differential equations (itself stormingly exciting) contains such histories which are also plundered, in some cases practically word for word.
This book, from a later period in his career, gathers many of these potted histories and presents them, from a personal perspective, in one place. But in contrast to many such history works, he also does a comprehensive job of presenting not only the mathematicians, but also the actual mathematics as well. The level of some of this goes up into undergraduate level and beyond. None of it is trivial, all of it is beautiful.
In summary then: highly recommended to anyone studying mathematics seriously, and whose interest and energy may be flagging. You'll fall in love with this stuff all over again. As for people whose mathematical interest and aptitude haven't developed past high school, you may find it challenging - but you might enjoy it, so give it a go anyway.
Back in the day when he was writing text books, he has always tried to provide a historical perspective into the context in which the mathematics being described can be placed. In the course of such works, potted histories of various mathematicians are given, as chapter appendices and footnotes, which leavens the business of learning how to use the techniques described.
Lots of sources cite his 1985 Calculus book, but this is not his sole source of historical notes. His 1972 work on differential equations (itself stormingly exciting) contains such histories which are also plundered, in some cases practically word for word.
This book, from a later period in his career, gathers many of these potted histories and presents them, from a personal perspective, in one place. But in contrast to many such history works, he also does a comprehensive job of presenting not only the mathematicians, but also the actual mathematics as well. The level of some of this goes up into undergraduate level and beyond. None of it is trivial, all of it is beautiful.
In summary then: highly recommended to anyone studying mathematics seriously, and whose interest and energy may be flagging. You'll fall in love with this stuff all over again. As for people whose mathematical interest and aptitude haven't developed past high school, you may find it challenging - but you might enjoy it, so give it a go anyway.
May 31, 2020
El libro tiene dos partes. En la primera, se enlazan las vidas de los matemáticos más destacados con la historia de las matemáticas, poniendo de relieve la contribución de cada cual en su contexto histórico. Aparecen muchos nombres que cualquier estudiante conocerá por sus obras (p.ej., Pitágoras, Newton) junto con otros que solo algunos han podido "disfrutar" (p.ej., Euler o Gauss). Esta primera parte es accesible a todos los lectores.
En la segunda parte del libro, se ofrecen demostraciones de algunos resultados de estos autores. Los hay de todos los colores, pero la mayoría están directamente fuera del alcance de los que nunca derivaron. Otros requerirán esfuerzo de los que hicieron su última derivada hace más de 5 años y otros solo son aptos para los profesionales de la cosa.
En la segunda parte del libro, se ofrecen demostraciones de algunos resultados de estos autores. Los hay de todos los colores, pero la mayoría están directamente fuera del alcance de los que nunca derivaron. Otros requerirán esfuerzo de los que hicieron su última derivada hace más de 5 años y otros solo son aptos para los profesionales de la cosa.
Displaying 1 - 3 of 3 reviews