This has been stated in a few topics in some places in physicsforums; that people did not really understand Calculus until they studied analysis or advanced calculus in graduate school. So what did such people really accomplish when they studied their first-year Calculus and their semester of Intermediate/Multivariable Calculus? How is it that students did not really understand it in their undergrad situations but did understand it as graduate students? What made the difference, specifically? As a possible comparison, one may say, "I really understood Algebra much better once I finished my three semesters of Calculus"; but what are the details which makes the undergrad Calculus to graduate level Calculus work?