Thomas' calculus

What Hacker News says

1. pawelwentpawelOct 2022
   For calculus, I found Thomas' Calculus (https://www.amazon.com/Thomas-Calculus-Early-Transcendentals...) the most helpful. It's a textbook but has a lot of exercises.
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2. insightcheckSep 2022
   It's time-consuming, but there are great resources to learn high school math to a very high level (likely much more effectively in many cases, than actually taking a high school math course, due to thoughtful exercises and more control over the pace of learning).

   I learned a lot from the Art of Problem Solving book series because they're highly focused on the reader solving problems to learn, versus giving explanations. Even if you don't finish all of it, you can strengthen any problem areas.

   For a less-comprehensive but still great introduction to precalculus (with a great section on trigonometry in particular from memory), Simmons' Precalculus in a Nutshell has a great introduction to this. Then you can read a book like Thomas Calculus, which has a great introduction to trigonometry in the first review chapter.

   I would even say that you would be better off working through the books above than if you had the high school classes; the best math students probably took the same approach too (working through books instead of focusing just on the class material). The main obstacle is time, because it's hard to find time when you have work and children to take care of.

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3. insightcheckSep 2022
   > "I’m under the impression that trigonometry is not extensively taught in middle schools and high schools in the USA. While I’m slightly envious you might not have to suffer developing powers of cosine and sine but that would explain the lack of familiarity with radian I see here. Am I wrong?"

   It varies by school, but overall I think this prediction is incorrect. Trigonometry was an important subject in high school — for all of the math, physics, and possibly chemistry courses — and then if you take calculus in university, it's very, very important to learn trigonometry well (or you'll really struggle as a student).

   So, even on the off-chance that trigonometry is not taught in high school (which I predict is rare), a first-year student taking calculus in university must learn it on their own time. Good calculus textbooks (e.g. Thomas Calculus) even account for this, having fairly comprehensive textbook sections on what you need to know about trigonometry to succeed in the calculus course.

   Most students who therefore took math to pre-calculus or calculus (or physics and possibly chemistry), should therefore have a good exposure to the definition of the radian.

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4. hackermailmanMay 2019
   I have Thomas' Calculus from the 1960s, the same book that Knuth promotes in interviews as being responsible for him choosing a math degree. Very high signal to noise ratio without being as terse as Apostol https://www.amazon.com/Calculus-Analytic-Geometry-Supplement...

   However I really enjoy algebraic calculus and wish somebody had taught me this in highschool https://www.youtube.com/playlist?list=PLIljB45xT85CSlgGh3681...

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5. bigtimberNov 2018
   Previous posts have nicely covered almost all of the textbooks and papers I would have mentioned myself, including K&R's _C Programming_, Brooks' _Mythical Man-Month_, Feynman's Lectures, etc. The only glaring omission was any mention of the classic (1965) FFT paper by Cooley and Tukey: "An algorithm for the machine calculation of complex Fourier series." _Mathematics of Computation_, 19(90), 297–297. doi:10.1090/s0025-5718-1965-0178586-1 (https://www.eit.lth.se/fileadmin/eit/courses/eit085f/Cooley_...) I might also have added the _CRC Handbook of Chemistry and Physics_ that seems to have been on every working scientists's and engineer's bookshelf (including mine) during the mid-to-late 20th century. Still in print, nearing the 100th edition. Also, some of my old favorite textbooks that I used at University were not mentioned, including Thomas' _Calculus and Analytical Geometry_. I still have my red cloth covered Addison-Wesley 3rd edition, no longer in print, but a much later edition might still be in print.
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6. agjacobsonApr 2017
   Quick Calculus by Daniel Kleppner

   Also, if you can find an ancient copy of Thomas Calculus when it was two volumes. Buy the first volume. Solve all the odd problems, the solutions are in the back. That's how I learned!

   A later edition of Thomas was a single volume big thick yellowish book. It was very good. We used it as freshmen at MIT. You could learn from it. I don't remember if that version had answers in it. But solving problems and having answers to check against is key.

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