[crpatino]

How could you possibly write a program that "approximates nearly any integral" without having learned calculus in the first place. I by that I don't mean to "spend half a year memorizing" any tricks. (If that's what they taught you, I am sorry to say you had a pretty awful teacher and you should seek to educate yourself elsewhere).

Oh yes, I forgot about the 3 minute part. You didn't write anything from scratch. You just at best googled for a math library and hooked it up to your hello world program... if not downloaded the whole damned thing from easy-Aplus.com!!!

Nevermind, rest assured that grownups never had to learn anything in order to build the infrastructure you happen to enjoy today.

[alexvr]

First, these are all exaggerated cases, inspired by experience. I appreciate the infrastructure a great deal, but I'm saying that there's a tremendous amount you can do if you focus on learning concepts and have a computer. School doesn't even care if you understand concepts; memorization is usually sufficient. And anyone who understands basic conceptual 1-var calculus and programming can indeed easily write functions in plain C that perform numerical integration and derivation because the hard part about calculus is putting up with the countless algebra tricks that are not obvious to mortals. Don't know how to manipulate that monstrous algebraic expression to take the limit? Good thing your computer can use some tiny floats. People who are not going to be math/physics professors or NASA physicists who need to plan a Mars voyage to the nearest nanometer would really benefit from focusing on the concepts instead of algebra. And my calculus teachers were pretty superb, by the way.