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I am an undergraduate studying analysis for the first time on my own. I am currently using Understanding Analysis by Stephen Abbott as a guide. I tried using Rudins text but found it difficult to understand the motivation or purpose behind a lot of the theorems. I usually take a few hours to read a section carefully and work through the proofs in the text and examples but find it difficult to do the proofs in the exercises (or end up taking hours to do a single one) and end up feeling lost.

Is this normal or should I expect to be able to do the exercises without looking them up? In my mind if you understand the section then the exercises for said section should feel engaging and the right amount of challenging. Is this still the case in higher math?? When I did take the first couple of weeks of a course in this subject (which I had to drop due to health reasons) the exercises tended to be overly simple and often numerical calculations. Is that the standard by which an entire analysis course is taught? More importantly, what standards and expectations should I set for myself in self studying the material so as to best prepare for my future in the subject?

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  • $\begingroup$ Yes it is still the case for higher math provided the textbook author believes in the same philosophy. I don't think Rudin believes that. $\endgroup$ – Paramanand Singh Feb 8 '18 at 3:58
  • $\begingroup$ May I ask: Why are you studying analysis on your own while you're an undergraduate? $\endgroup$ – zhw. Feb 8 '18 at 23:54
  • $\begingroup$ @zhw. To further my math education in general and be able to move on to topics like topology and number theory... $\endgroup$ – Red Feb 9 '18 at 1:35

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