Should I even consider retaking Calc A?

<p>So far, I've had both AP Calculus AB and BC at my school, and I've gotten A's on both courses and I did fine on the on the BC test (feeling a easy 5 coming along). I also took the placement test for next year's placement (into A or B) and finished that test in about 30 minutes. Still, I don't feel like I know calculus in and out. I know how to do the problems, but I don't know the intricacies and proofs of it all. I can do derivatives, integrals, and just about everything problem wise for both courses quite easily, but I still don't feel like I truly know the subject at a level that is true mastery. For that reason, I have been considering taking Calculus A at my university in the honors program honors course. Apparently the course is some sort of super math course that teaches just incredible depth into calculus. Afterwards I figured I might go into the honors course for Calculus B for the same thing. Anyways, I'm wondering if this is a good go of things, or if I should just place out of both and go straight to Calculus C rather than retake Calc A and B. I'm majoring in Biomedical Engineering and the normal program requirement indicated Calculus A as the first calculus course for incoming freshman (I'm assuming for people who can't or choose not to place out of the course). So, should I retake the honors college course even though I already took the AP course?</p>

<p>Thanks for the help!</p>

<p>See if you can find the final exams for the regular and honors calculus A and B courses for your college. Try them to see how you stand relative to what is taught in each course.</p>

<p>Here is another alternative, assuming you know the material in the regular courses well based on reviewing the college final exams: start in the more advanced math course to clear the math prerequisites and requirements for your major quickly, then consider taking real analysis and other advanced math courses to learn math from a rigorous theoretical proof-oriented approach.</p>