Talk:Calculus Made Easy

[Untitled]

I am in some doubt whether the article demonstrates the notability of this particular book, and I'd like a more formal reference in a conventional Reliable source than the one provided for this. DGG (talk) 02:40, 19 July 2008 (UTC)

The present version of this article is mainly a criticism of the 1998 update by Gardner on grounds (such as "cultural imperialism") that are largely irrelevant to whether either the original text or the upgrade is a better introduction to calculus. As the editor of the previous version, I will leave it to others as to whether the article should be reverted to an earlier version or if the criticism should be added to an earlier version. Alan R. Fisher (talk) 06:59, 7 October 2008 (UTC)

My chief criticism of the update is that Gardner lets Thompson "discard" higher order differential terms like (dx)² as being "quite inconsiderable" to other terms without explaining that this is just the equivalent of "rounding off" to the nearest real multiple of dx, the"nearest real multiple" being the semantic equivalent to Robinson's "standard part" of that multiple. (This could be done in a single footnote at that point in the updated text.)

A brief but rigorous justification of infinitesimals could be based on the set of real rational functions as a non-Archimedean field. Perhaps I should send these suggestions to Gardner.Alan R. Fisher (talk) 07:44, 7 October 2008 (UTC)

There being no responses to my comments since 7 October, I have updated the article, correcting a misquotation ("first form pupil" to "fifth form boys"), and toned down the exaggerated claims of how much "superfluous material" was added. Three pages in a preliminary chapter is hardly "many pages."

Palpher, the contributor of the criticism I am disputing, claims John Baez (the mathematical physicist at UC, Riverside?) and unnamed others say the Gardner update converts "a succinct, focussed introduction into another lengthy calculus text stuffed with superfluous material." I will attempt to verify whether Dr. Baez indeed holds this opinion (and how strong that opinion is). Palpher should cite the unnamed others who hold that opinion, where it can be found, and justify the relevance of cultural imperialism in this context. Alan R. Fisher (talk) 11:10, 25 November 2008 (UTC)

Here is Dr. Baez's recommedation from his page at math.ucr.edu/home/baez/books.html#calculus

Silvanus P. Thompson, Calculus Made Easy, St. Martin's Press, 1998. (Most college calculus texts weigh a ton; this one from 1910 does not - it just gets to the point. This is how I learned calculus: my uncle gave me a copy. Alas, the new edition has been puffed up to 336 pages by Martin Gardener. People must want calculus to seem hard.)

I think a link to this to this list belongs in the main article. This would preserve Palpher's reservation without suggesting Dr. Baez is also concerned about the cultural imperialism issue.Alan R. Fisher (talk) 08:55, 28 November 2008 (UTC)

In response to the issues Palpher raised, and to my own interest in Thompson's classic, I have started work on my own annotated and updated edition, adhering more closely to the original text with its references to farthings, sovereigns, and motor-cars, but replacing first form boys with the more generalized students. Where Gardner substitutes trillion for Thompson's billion (10¹², I will substitute million million, a compromise between the long and short scales. While I will justify Thompson's infinitesimal approach by siting Robinson, I will do so in a way (I hope) that does not impede the student who just wants to learn the basics of calculus.

I should be able to publish by sometime in the next next year. Alan R. Fisher (talk) 06:34, 7 December 2008 (UTC)