I don't buy it. AoPS is a great organization, but the focus is on pure, theoretical mathematics. Understanding calculus is key to understanding many beautiful

I don't buy it. AoPS is a great organization, but the focus is on pure, theoretical mathematics. Understanding calculus is key to understanding many beautiful areas of applied mathematics: image processing, signal processing, control systems, electronics, etc. I consider them more elegant than theoretical mathematics. Now, for that, you don't need all the messy manipulation (integration-by-parts and similar), but you do need the basics of area-under-the-curve, of derivative-as-slope, and similar, as well as some of the theory. But that's not too hard to learn. My own opinion is that the basics of calculus should be taught alongside the basics of algebra in elementary school. Plenty of people have had success doing both.