Hello, I am currently a senior in High School (America). I am enrolled in AP Calculus BC, AP Physics B and C: Mechanics. I have taken 6 previous AP exams, (most importantly AP Chemistry with a score of 5). I am enthralled with the study of mathematics and physics and maintained a grade of 100 in both my physics and Calculus class (The average grade is a D to a C). Due to my success in these courses and my adoration for the subjects, I desire to continue my exploration in these topics. I self studied Calculus I and II in my junior year (thus leading to my success in AP Calculus). Despite my academic success in these areas, I fear that the academic courses in universities will be overwhelmingly more difficult than my AP courses. Therefore, I decided to begin self studying Multivariable calculus, Differential Equations, and Linear Algebra. I attend Differential Equations lectures at a local community college and have been watching the DE and Linear Algebra lectures at MIT via the OCW. My question is primarily this: What can I do to better prepare myself for a double major in mathematics and physics? Am I well enough prepared now? How well versed in mathematics and physics should I be before entering college? My physics course covers calculus based mechanics, noncalculus based electricity and magnetism, thermodynamics, optics, and waves, plus other areas. My Calculus BC course covers the typical areas of Calculus I and II (save for hyperbolic functions, a topic that I will be self studying.) What should I do to further prepare myself? I've heard stories of students with 5's on AP Calculus and AP Physics doing miserably in college. Any specific courses I should take? I ultimately plan to go for a Ph.D. in mathematics or physics (depening on how well I do in my undergraduate studies.) Lastly, are there any textbooks in particular I should have and study from? I have been studying Calculus out of Larson's Calculus I-III and physics out of Serway and Faughn. My physics teacher has a copy of Apostol's Calculus and Walker and Resnick's Physics; I'm sure I could borrow those for study if they are superior study aides. Thank you for your time and any advice.