I'm an undergraduate self-studying mathematics. I was wondering about which was the most efficient way to study with textbooks. For example, I'm using a textbook (about measure theory and lebuesgue integral) with a classical format: a lot of theory (lemmas/ proporties/theorems then demonstrations, followed by some Exercices with hints at the end of the chapter). I would usually read the theorems, reflect for like 5 minutes, then spend a lot of time trying to understand the demonstrations, then going to the next one etc., but I feel that I'm not able to remember firmly, or have a good grasp on the material, and it makes it hard to get some kind of intuition.

What would be some general advices that could apply to other people studying math with textbooks? How do you balance theory and problems? Thanks in advance!


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    $\begingroup$ Hi Zippo, what subject are you interested in? $\endgroup$ – Will M. Jan 21 at 21:04
  • $\begingroup$ Whomever voted down the question, provide a reason as to why. $\endgroup$ – Will M. Jan 21 at 21:06
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    $\begingroup$ One thing I would like to mention is to never base your knowledge on only one source. Use different sources. Then you will be given different explanations of the same concepts. This will probably give you a broader and better understanding of different concepts. Also, do MANY problems. That is the only way to gain true mastery and great underatanding of a subject. $\endgroup$ – Markus Jan 21 at 21:07
  • $\begingroup$ These answers have some potentially useful tips (they have helped me a lot): math.stackexchange.com/questions/3782/…, math.stackexchange.com/questions/222338/…. There are many questions on this site (and some on MO) on this topic. Have a browse! :-) $\endgroup$ – user445909 Jan 21 at 21:13
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    $\begingroup$ Don’t worry about not remembering. Nobody can remember everything. The mist important thing is to understand the intuition underneath the proof, the reasoning and the useful “tools”. Also, do many exercises, otherwise you won’t really grasp concepts you thought you had. What field are you interested to? What’s your “general level”? (For instance, if you want to study Analysis you need some linear algebra and topology) $\endgroup$ – tommy1996q Jan 21 at 21:16