At this point in my life (40 years old) I really wish I could go back and take a few courses over again. Calc and DiffEq would be on the list. As an engineering undergrad I had to take 3 semesters of calc and one of diff eq. I had the misfortune of having a really nice old, grandfatherly (Gandalf-like, in fact), prof for the first semester (intro to derivatives, etc.). Class was at 8am four days a week. Ugh. Anyway, the prof was way past his prime and I later learned that his wife was ill (I believe she died sometime the next year). Classes were not productive and I was immediately behind in understanding calc.

Second semester (integral calc) I had this energetic little middle-aged woman prof who was big on memorization. It sucked. Third semester was multi-variate calc and I had a really great post doc for lecture. He was very energetic, entertaining, and descriptive in his teaching. I made up a lot of lost ground there. I'll always remember the way he explained the equation for a cycloid. He grabbed the trashcan and emptied it on the floor in the corner, put its open face flat against the chalkboard with the rim resting on the chalk tray, then he held a piece of chalk firmly against the seam of the can (touching the board) while rolling the can down the chalk tray. Not only was this fun to watch, it actually clarified the whole thing in my head nearly instantly. He was also into jazz and fusion. When Shadowfax played on campus that semester he was on the front row and clearly having a blast despite his leg cast (rock climbing accident a few weeks earlier).

Diff eq was taught by an ex-Navy lecturer. Very rigid, very dry, like something out of the 40s or 50s...which he was. His one quirk was throwing in a little numerical solutions stuff. You had to have one of those $$ old cruddy first gen BASIC calculators to take the exams because he always had one numerical problem on them.

So, what's my point? The teacher and the method of teaching makes at least as much difference (sorry...) as the student with respect to information transfer.

A P

p.s. Wavebourn--in grad school I took a graph theory class that was taught in the "prove everything from first principles" style. It really worked for me--that was, by far, my favorite math class of all time. Got to meet Paul Erdos hat semester--he was gone five years later.

p.p.s. I've forgotten how to do special chars--umlauts and such...