How to digest new math more quickly?

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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