Currently, I have read and re-read the Stephen Abbott Understanding Analysis for about $3$ or $4$ times up to and including the chapter $6$. However, I can't say that now I am feeling more confident about understanding and completing problems in analysis, than when I hadn't read it. It is so frustrating to read the text, when you think that you get almost everything in the explanation parts, because it is so well written and clear, but after that struggling to complete even the easiest exercise in the problems section of the chapter, even when redoing it the $3$-rd time. Therefore, I am willing to ask, can you suggest a way to start really understanding the analysis? How should I approach to solving the problems? Will it make a sense to switch to another book (I was thinking about Apostol/Pugh/Kolmogorov)?

$P.S.$ I am a self-learner. It is my second book in analysis, after Fichtengoltz's first volume, which was too theoretical for my test as there were no problem sets. My problem is not just in exercises. While reading the proof I understand it, however if I try to do the proof on my own, for example, after $3$ hours from reading I can not manage to recall how it was done.


closed as primarily opinion-based by Sargis Iskandaryan, Cesareo, KReiser, max_zorn, user10354138 Nov 23 '18 at 8:00

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    $\begingroup$ It's good that you attempt to reproduce the proofs yourself and attempt to solve the problems yourself. How long do you spend struggling with a particular problem before giving up? When you are sufficiently stuck, it can help to get just a hint instead of reading the full solution. For example if you are trying to reproduce a proof from the book and you get stuck (and you have struggled but you are still stuck), then you can read just enough of the proof to get unstuck, then try to finish the proof yourself without reading the full solution. $\endgroup$ – littleO Nov 22 '18 at 15:40
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    $\begingroup$ Some proofs aren't meant to be reproduced. Some are just too technical. $\endgroup$ – user370967 Nov 22 '18 at 18:09
  • $\begingroup$ I think this question is specific enough for Mathematics Educators (it's about specific books and about the learning process), so I hope you'll ask it there. I'm interested in the answer. $\endgroup$ – timtfj Dec 16 '18 at 23:40