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I'm sure Thompson's books were a fine series back in his time, but are they still worth recommending for, say, interested high-school students or prospective college students that want to brush up their math skills?

How much has notation changed in +70 years? How much basic math education has made any progress? Is the scope of topics still up-to-date?

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    $\begingroup$ Why these specific books? I vaguely know of them from public libraries when I was growing up (early to mid 1970s; before then I wasn't advanced enough to notice them, and after then I was too advanced to bother looking at them), and at that time (especially if you were in a rural area) your choices of math books (and even awareness of the existence of various math books) was extremely limited, so I can imagine someone using them at that time to study by, especially if, say, Calculus for the Practical Man was the only calculus book in the local library. But the situation is different now. $\endgroup$ – Dave L Renfro Sep 4 at 18:28
  • $\begingroup$ I don't know those, but I still love W.W. Sawyer's books, which are quite old. $\endgroup$ – Sue VanHattum Sep 5 at 18:04
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The topic hasn't changed (that) much. And for a neophyte, they are fine, even accessible. They won't replace deeper study, but are fine for a bright kid who wants to play with things a little before AP Calculus. They're not the only option though. Could just get Granville (reasonably readable prose, modern enough not to be annoying, and pleasantly consice (not in an abstract way but in not being too text filled, like many doorstops). Also a Schaum's Outline is fine. For that matter you can get regular texts for cheap through Amazon. Used books are very cheap and any from the 50s on will be relatively modern in terms of treating limits and the like. Whatever you do though, stay away from the hardest books usually recommended by people on MSE (Spivak, etc.) Those are better for those who know the topic already and/or are unlikely to be turned off. Really, for the dabbler something like Caculus Made Easy might be fun.

https://en.wikipedia.org/wiki/Calculus_Made_Easy

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There are tons of good,accessible, calculus texts available online, like the introductory lecture notes by William Chen, and there is the Open Textbook Initiative to look at...

It is very hard to give blanket recommendations, the book I find engaging somebody else might find incomprehensible or plain boring. And the recommendation would depend very much on the background and interests of the prospective reader.

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