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.