[Cowen]

> It's not just a dramatic change; for most, it's a cliff thrown in the middle of the learning curve.

When I transferred to a new university I was placed in their first year calculus program over my own protests. I had already done AP Calculus in high school, and completed the first year calculus course at my previous college, which was admittedly of much lower quality than the university I was transferring to. I thought this new one would be a complete waste of my time.

The first thing we covered in this new course were limits. I rolled my eyes; everyone knows how to find a limit. Was this really the kind of thing we were going to cover in this class? Then the professor said these words I had never heard in relation to limits before, "epsilon" and "delta." And here my troubles began.

That turned out to be one of the hardest courses I've ever taken, I had to relearn almost everything I thought I knew about math.

[jackmaney]

[nod] Yep, sadly, there are too many "calculus" courses that don't mention epsilon and delta at all (I'm looking at you, Business Calc). Without thinking about epsilon and delta, it's prettymuch impossible to have anything but a vague, fuzzy notion of what a limit is.

In Calc I, I kept my eyes out for two groups of students: those who did really poorly on the first exam, and those who did really well. The first I watched for obvious reasons, but some of the folks in the latter group--especially those who took some calculus in high school--would start to think "Oh, I know all of this now! Cool. Easy A." and then coast. And they'd be mincemeat somewhere in between implicit differentiation and related rates.