Context: I'm a Grade 11 IBDP student and very fond of math. Assuming that I get the spare time to self-study material alongside the syllabus, I wish to spend it constructively (the only step I've taken thus far in learning mathematics is to complete HS math courses on Khan Academy up to and including Integral Calculus). I want to tackle a heavy-duty calculus book like Spivak or Apostol before entering college (if you feel aspiring mathematicians in HS would be better served by other objectives, please share them in your answer).

I decided against compiling a list of textbooks from various sources and followed the advice given in this answer on Physics Forums (an arbitrary choice; I just thought it was a well-written answer), which mentioned the SMSG textbooks. I am, however, concerned about their obsolescence.

Are these textbooks still relevant? Would I be better off learning different topics from a variety of publishers (like the books recommended on this webpage or in this question?

  • $\begingroup$ The list at ocf.berkeley.edu/~abhishek/chicmath.htm is formidable and has some good insight. Still it misses a lot of recent great books in the Springer line etc. For the Physics forum answer, I would encourage you to not focus merely on those recommendations. There are other excellent cheap choices... sorry to be vague, time is tight today. $\endgroup$ – James S. Cook Aug 7 '20 at 11:30
  • $\begingroup$ possible duplicate of matheducators.stackexchange.com/questions/18551/… $\endgroup$ – Ben Crowell Aug 7 '20 at 14:26
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    $\begingroup$ What makes you think that you're not prepared for Spivak and Apostol? Dive in and try. $\endgroup$ – Ben Crowell Aug 7 '20 at 14:28
  • $\begingroup$ I recommend the SMSG books a lot in my Stack Exchange comments and answers (mainly comments I suspect), but in my opinion they're better for gaining a broader insight into mathematics over a longer period of time than you have available (unless you pick a specific one for a specific topic, like Introduction to Matrix Algebra or Analytic Geometry). Better for your pre-Spivak/Apostol reading are the Gelfand books. $\endgroup$ – Dave L Renfro Aug 7 '20 at 14:29
  • $\begingroup$ As @Ben Crowell suggests, it's probably best to dive right in with Spivak or Apostol, unless you feel that your background is especially weak in some topic you'd like to brush up on first (trig. identities and the many applications of De Moivre's formula, for example). The Gelfand books don't require a huge investment of time if you've seen much of the material before, and provide a lot of the insights that often get omitted in school texts and school classes designed for audiences with goals and abilities different from yours. (continued) $\endgroup$ – Dave L Renfro Aug 7 '20 at 14:36

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