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Do you have any advices, tips and tricks on it? I have a feeling that there is never enough time to read every math book I find interesting, to learn about a new area etc. etc.

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I hope this doesn't sound jerky, but Euclid said that there is no royal road to geometry, and I think he was right. –  MJD Apr 9 '13 at 4:50
    
I don't find it jerky, but I'm not asking for a magic solution, but several tips and tricks on how to get better. Some people are quicker learners than other people, and I try to find out why. –  ante.ceperic Apr 9 '13 at 8:49

1 Answer 1

up vote 2 down vote accepted

I suggest the following points:

  1. Try to find the general (universal) pattern common in several concepts. For example, a homomorphism between two groups preserves the group multiplication and group multiplications are the only composition rule in groups. Then it is easy to learn a homomorphism should be in between two algebras, rings, vector spaces, etc. Maybe the names change but the underlying concepts are similar.
  2. Take notes during reading new concepts, theorems, etc.
  3. Try to generalize the statements.
  4. Find the relationship between different concepts, definitions, statements, etc.
  5. Try to solve some exercises, especially those which make you to review the content of the course (book, lecture, paper, etc).
  6. Give a presentation or teach a course.
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