As a high school student who wishes to become a number theorist, which multivariable calculus text should I follow? I have a pretty good understanding of single-variable calculus (From MIT OCW and few other online courses) and elementary number theory (from David.M.Burton's Elementary Number Theory).
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1I think that understanding the intuition behind multivariable calculus is much easier than understanding how to develop the subject rigorously. Some good intuition can be found in Griffiths's Electrodynamics textbook and in the book Div, Grad, Curl and All That. For a more rigorous treatment, I like Folland's vector calculus book, as well as Hubbard and Hubbard, and the first half of Calculus on Manifolds by Spivak. – littleO Jan 22 '19 at 07:30
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I am actually someone in the same position, and I would like to say that I myself found MIT OCW inadequate while talking about single variable calculus. I would recommend you the following books for brushing up on them:
1) Calculus, by Michael Spivak: Quite hard, but will be really helpful. I believe that this is the standard Calulus text.
2) Thomas' Calculus: Try the old editions if possible. The new editions are a little too friendly.
For multivariable calculus, I found Multivariable Calculus with Vectors by Hartley Rogers Jr quite useful, though I have to say that it gets fairly advanced quickly.
I guess you would also be interested in proof writing, so you can check up books on that as well. You can try How to Prove it, by Velleman. I haven't used it myself, but a friend told me that it was a great book.
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