<p>I tend to find that the best approach for me is for there to be homework that is not more or less challenging than the material at hand warrants. One needs to grapple at close range many times to really get something out of it, and weekly or biweekly problems tend to be a nice way to learn the stuff efficiently, so as to be able to research it later. A very famous professor at my school even said that hard homework tends to defeat the point – usually one is trying to learn the material so that one can use it later in research. Why not be doing research instead?? An occasional very hard problem can be a good exercise to get things together, though. I personally dislike exams, just because I concentrate much better when I decide when I want to do it.</p>
<p>As for flexibility, I anticipate many schools offer plenty of it – Caltech, MIT, Stanford, etc. I’m not explicitly 100% certain, but have a strong feeling. I can see some preferring the close advising system, but I definitely prefer having total freedom.</p>