We all know that when learning math, one has to do more than just simply read - one must try to solve problems and work actively with the material.
Many books try to force the reader to participate in the learning experience by actually consisting of no proofs (or close to none), with some guidance to the big ideas. This is clearly a valuable approach, but it can sometimes come at the price of:
- Making (quick) reviews somewhat hard, since you have to rework out all the details, and it is easy to think that one has reviewed something in full detail, when one really hasn't.
- One might progress a bit slower than usual, which is obviously not ideal. One might argue that the slower pace is compensated by actually learning the material deeper the first time, but how does this compare to reviewing the material several times (which for me, can be done more easily by a "traditional" book)?
My main question(s) are the following:
What should one think about when trying to learn a subject through a problem based book? Should one try to supplement it with something not containing only problems, so that one maybe get a deeper exposition from someone who has already digested the material?