So, I think I have done a thread here with some questions related to academic guidance before... when I was a tad younger. (https://www.physicsforums.com/showthread.php?t=561141) Well, I'm a Brazilian student, I'm in my senior year in high school. It is very likely that I will study Physics in college - in the beginning of next year I'll start the course here at University of São Paulo. However, I will also apply to some US schools - those that there is a considerable chance I get rejected - MIT, Caltech, Harvard, Princeton... One of the things that attracts me most in these institutions is the structure of the courses and the larger flexibility you have to design your own major. I have a slight preference for physics, but I do also enjoy math! While I don't think I could fit some Analysis and Algebra in my graduation here in Brazil, that seems possible in those US schools... Caltech's Math 1 Analytical is pretty much an Analysis (+ Linear Algebra) course, Harvard's Math 23 is also very enticing, for example. And as a young, foolish dreamer, I have analyzed the possibility of a double major. While I saw that it was somewhat manageable in Harvard or MIT, it was clearly impossible at Caltech. I wonder - is it common for young prospective physics students with strong math interest such as myself to dream about this double major but end up choosing one side or another? I mean, I sometimes think - oh, I should put a lot of effort into these applications, so I can study both math and physics, which won't happen here in Brazil... Is that plainly stupid? If not so... do you guys have any other recommendation of a school with a top notch math/physics program? A bit about my background - I have self studied computational single variable Calculus and Linear Algebra during some of my free time in high school. I also have a taste of what proof-based rigorous math is like, but I didn't go too deeply, since I know I would probably burnout, but I do find it enticing. If I enter an US school, I will already have the first semester of USP's Physics course, which includes Calc I (I think they use Spivak), a first course in Classical Mechanics, a course called "Vectors and Geometry", which covers Analytic Geometry in R3, Experimental Physics and probably introductory courses in Chemistry and CS. So, what do you guys think? Is the preparation good? Are my plans feasible? Thank you.