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Understanding real analysis but not calculus?

  1. Dec 24, 2008 #1
    im in a very strange situation. i have recently started self-learning real analysis, using rudin and pugh simulatenously, and i am enjoying it a lot. the problems are difficult but i find i can answer most of them (well more than half anyway)

    yet, when trying to re-learn calculus via spivak and apostol, i am stuck at the problem sets. they are extremely difficult and i find i cannot solve most of them (solve ~30%?). the proofs i also find more convoluted in these elementary texts.

    now... is it okay to continue the way that i am? and does it make sense to continue with analysis even though i dont get those calc books? i was told analysis is way harder. and while it is, the problems are more straight forawrd.
  2. jcsd
  3. Dec 24, 2008 #2
    I don't see anything wrong with it, as long as you're sticking to pure mathematics. Rudin eventually goes through differentiation and integration (Riemann-Stieltjes, and eventually, Lebesgue) anyway, so as long as you continue this path, you should just learn calculus in the process, except in a more rigorous fashion. If I recall correctly, Spivak and Apostol have a lot of exercises emphasizing technique, opposed to concept. Most of these techniques are, for the most part, absolutely useless to pure mathematicians.
  4. Dec 25, 2008 #3
    That is pretty crazy, how far are you in the books? imo calculus is so much simpler than analysis, just look at more examples. You can try Stewart, which focuses way more on the techniques and computations.

    Can you do the problems in rudin?
  5. Dec 25, 2008 #4
    i agree calculus is much simpler. i already learned calculus out of a book similar to stewart, so i know how to do integrals and all that. i was using spivak and apostol for a more theoretical re-introduction. i find i cant do most of spivaks problems. the reading is fine, but his problems are impossible. with rudin and pugh, i'm in the middle of differentiation. while the problems are hard, there are no crazy inequality chains like in spivak and i cant prove the insane integral equalities spivak has in his problems. with analysis i atleast know what tools i use to make the proof in some questions, with spivak i have to guess a trick. only chapter 2 of rudin was impossible, the rest i atleast know how to start.
  6. Dec 25, 2008 #5
    LOL sorry when you said Spivak and Chains, I thought you meant something entirely
  7. Dec 25, 2008 #6


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    I find it odd that you separate 'real analysis' from 'inequality chain': I consider the art of approximation to be the fundamental technique of real analysis! (maybe I misunderstand what you mean by 'inequality chain'?)
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