This is why I did terribly in quantum mechanics; I was never able to generate a whiff of insight about anything that was going on. The thing is, I'm not sure the top students really did either.
Like everything there is a balance. I think that if I could go back in time and give myself one piece of advice it would be: Don't try to gain insight into everything. There isn't time. Its fine to do this for fundamental things like calculus but for laplace transforms, fourier series etc it can take too long given the time that a college student has. If it is your profession then that is a different story. Also for things that are sufficiently alien to our everyday experience (like relativity) I think maybe you just have to accept it and,work with it for a while and then possibly try and look for insight after because initially we have no other intuition to relate it to.
I wholly disagree. I don't buy the OP's argument for tactically how to learn one bit, but knowing concepts for everything you "learned" is the only way to do it. After first year, I almost never had to work hard, I could just derive anything I needed, and yeah, this included using fourier series and laplace transforms.
To me the key is to observe that concepts are important then observe that the easiest way to learn concepts is to learn them at the optimal time of day (ie, not 8 am during the class when you are tired, that is a waste of time), from the optimal person (ie, not your prof that just wants to get back to research), during the optimal time of the term (ie, not in the first week of class, more like the week before the midterm and the 10 days before the final). To achieve all of this just requires two skills: 1. Knowing how to learn from a text book 2. Knowing when a textbook is crap and getting a better one from internet review sites.
Learning from a text book is easy. Cover the page with a piece of paper and read each line. When they come up with a problem that you don't have a function for derive it and bam, you've invented the formula for lateral-torsional buckling of non-uniform crossectional beams you will never have trouble with the concept again. If you get stuck (stuck to the point of it hurting your ego, not "I'm sure I would get it if I had the time" stuck then look at the formula (not the proof if you can avoid it). Try to prove it again! If you still can't prove it, find the proof somewhere (hopefully the text, but if not email your prof or the book author for the proof). I corrected the same (otherwise super awesome) text book 3 times over the course of two years. The author loved me because out of the 5 corrections he did 1 was from himself, 1 was an email that said "I think this is wrong" and the other 3 were from me proving that he was wrong.
Anyways got kind of long there, but don't waste time learning from other people, just learn how to learn and damn well get the concepts otherwise what's the point?
