I agree that it's necessary to do exercises in order to understand the subject, but I disagree that you need to have them checked by someone else -- in many cases, you should be check it for yourself, honestly.

Beyond the junior undergraduate level, computation-style problems go away, and you're just left with exercises that ask you to prove a certain something. It takes a long time to build up a sufficient degree of rigor, but it happens eventually -- I did go get some of my proofs checked by serious Mathematicians at some point, and it turned out that my intuition wasn't far behind.