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I am currently self-studying Spivak’s Calculus. Unfortunately I did not have the chance to take math courses in college so I haven’t been formally taught proof based mathematics-I’m trying to learn now from Spivak+a copy of the answer manual. I typically read a chapter twice, then jump into the problem set. I can only do a few of the early problems easily and all the way accurately, but I can make some progress on some of the later problems. Then I look at the answer for the first problem I can’t solve, copy it down, and try to understand why it works. Once I can prove it from memory, that proof technique is generally enough to let me prove the next several problems. When I get stuck in a section I once again look at one solution and often this lets me make great progress on the others. I repeat until I can do most of the non-starred problems and move on to the next chapter, or if I’m really stuck I take a break for a couple of weeks and when I come back it’s easier.

However, since I have no standard of comparison, I’m not sure how to tell if I’m any good at this. Obviously there’s merit in doing math at any pace, but I’d still like to know if I’m struggling way too much (and should move to something easier), if I’m on pace, or if I’m doing really well.

At about what pace and with what level of accuracy should a competent math student be moving through the problems of Spivak’s Calculus? How many hours/days/weeks should a chapter take me? Am I wasting my time, or is math just slow?

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    $\begingroup$ Math is slow. And it takes a variable amount of time to get through. Math is the occupation of the patient. You are not working at an unusual pace. $\endgroup$ – Don Thousand Oct 20 '19 at 17:27
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    $\begingroup$ It would be easier if you have someone to work with, or better still, guide you. Different people have different aptitudes. $\endgroup$ – copper.hat Oct 20 '19 at 17:35
  • $\begingroup$ @copper.hat Yup, and that aptitude isn't universal across all of math. Heck, aptitude for learning concepts varies even within texts. $\endgroup$ – Don Thousand Oct 20 '19 at 17:38
  • $\begingroup$ For me, what could take me a week to work through on my own could be 5 mins. with a (suitable) friend. I find this true not just in mathematics. $\endgroup$ – copper.hat Oct 20 '19 at 17:39
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    $\begingroup$ @copper.hat Reminds me of some terrible nights learning Q Mech all by myself in my school library :( $\endgroup$ – Don Thousand Oct 20 '19 at 18:01