[golwengaud]

(Single) integrals are freshman calculus, which is nominally taught in the first year of university. In reality, my experience is that many students (and, I would guess most science/engineering/math majors) take AP calculus during their last year of high school (17-18 years old), and proceed to differential equations, multivariable calculus, or whatever is next in their major's sequence during the first year of university.

[GFischer]

Thanks for the answers. For all the flak US education receives, the option of taking AP classes sounds good (and it gives college credits, which is even better!).

From your post I could find http://en.wikipedia.org/wiki/Advanced_Placement_Calculus which shows that AP Calculus does indeed include integrals.

[jgg]

Thanks for the answers. For all the flak US education receives, the option of taking AP classes sounds good (and it gives college credits, which is even better!).

This is utterly derailing the main topic of conversation, but...

I know that a lot of mathematicians dislike AP Calculus. The original thinking was that Calculus couldn't be taught to highschoolers, so you waited until University to take it. Aspiring mathematicians would take a rigorous, proof-based Caclulus course, which would prepare them to tackle harder subjects in the future. Everyone else (engineers, chemists, physicists, etc.) would take a more general/applied course. Now, all but a handful of universities offer such courses, under the assumption that anyone who wants to be a mathematician has surely taken AP Caclulus. So the idea of proof-based Calc. for future mathematicians has been lost in transition, and the end result is that you have kids hitting Multivariate Calculus and Differential Equations who haven't seen a proof in their lives.

The current AP Calculus courses are 99% computation. I was challenged while working through Spviak's book with no teacher guidance in highschool, but I scored a perfect 5 on the AP test with little effort.

[mturmon]

In short, the lack of a proof-based class renders students Calc-clueless. (groan)

This happened to me. I went straight from high school calc into college differential equations because the AP score allowed me. It took a Rudin-based analysis course, much later, for me to appreciate proofs of convergence or epsilon-delta arguments, because my H.S. calc did not have them, and the college diff-eq assumed you knew them already. The shock was painful.

Eventually though, you learn what you need to know.

[jgg]

It took a Rudin-based analysis course, much later, for me to appreciate proofs of convergence or epsilon-delta arguments, because my H.S. calc did not have them, and the college diff-eq assumed you knew them already. The shock was painful.

I have yet to take a course that uses the so-called "terse little blue book from hell". (:

Eventually though, you learn what you need to know.

Indeed, although I wonder about people becoming discouraged about being mathematicians simply because they've been misled for so long about what's on the "other side" of college math.

[biotech]

you have kids hitting Multivariate Calculus and Differential Equations who haven't seen a proof in their lives.

Really? My AP Calc class was not very proof-focus (probably because the AP Calc test was not), but 10th grade (~15-16 y.o.) Geometry was mostly just proofs. As was Trigonometry. This was 10 years ago, but those same teachers are still at my old school. Presumably they teach the same material. I guess this is atypical? That's too bad, because those trig proofs were actually kinda fun.