FWIW (and I know you're not making this claim) I don't believe Math 55 is a good example of how mathematics should be taught at large, nor do I think calling it an intro class accurately conveys what it is. It's effectively the compression of an entire undergraduate degree into a single freshman course. I say "effectively" because the material covered depends heavily on who's teaching it, but certainly anyone coming out of Math 55 can pick up any undergraduate math content trivially. For example, undergraduates who have taken it are generally explicitly prohibited in course descriptions from taking further undergraduate mathematics classes (because it would be free credit for retreading the same ground) and can only take graduate courses from then on out.
It's strongly self-selecting and as a result can afford to cover a truly insane amount of ground. The overwhelming majority of people who take it drop out (the usual dropout rate from people who take it in the first week is probably > 90%), but the people who stay almost all get As. And you will need to be almost entirely self-motivated because a lot (maybe most) of your waking hours will be thinking about math.
There's a very small minority of students for whom this is an optimal way of learning. For most students this is the quickest way to make them run screaming away from mathematics even faster than they already do.
