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Even if you understand
every word in lecture and in the textbook, the only way to really learn
mathematics is by *doing* mathematics. Sometimes this means doing
even more than the assigned problems. (See ``time committment'' above.) This is how to avoid the common pitfall of ``understanding everything in class but blanking out on the exams.''

I realize this isn't welcome advice, and I admit that I haven't always followed it myself. But in years of teaching (and 20+ years of learning) mathematics I haven't found any shortcut.

Jonathan Rogness
2003-01-19