Should the theory be studied thoroughly before solving exercises?

Question

Most of the books claim in the preface that the important part of the book is in the exercises, which makes sense considering that solving problems improves in great depth the understanding of the theorem and the proofs involved, but no book I've read answered the question I'm posting here: How much attention should I paid to the theorems, proofs and examples before attempting to solve the exercises?.

I usually skim throught the chapter or sometimes I don't even read it and flip the pages back and forth looking for what I need to solve an exercise, but is this truly effective, or my learning would be faster and better taking a deep care of the theory before attempting problem solving?.

Answer 1

Try reading the chapter thoroughly first, rather than skimming, before you attempt the exercises. Try to make note of any major points that the textbook authors emphasize, e.g. important theorems/corollaries/lemmas/etc.

Then attempt an exercise. If you are stuck, re-read the chapter again, or at least the relevant theorem(s)/corollaries/etc. that the exercise calls for.

If you tried all this but you are still stuck, try asking your teacher/professor about your problem. Or you can always ask here at Math.SE if your teacher/professor is not currently available at the moment.

Answer 2

You'll need to be at least somewhat familiar with the subject matter before atempting the exercises. But on the other hand, trying to solve the exercises shows how the results are used, and allow you to review the material. So you have a catch 22 situation here. Only way out is to (a) read the chapter (or section, whatever carries exercises) carefully, (b) try to solve the exercises, more or less sequentially. If you have doubts or get stuck, go to (a). If all clear, go to the next chapter/section.