Hey Elena,
So sorry your Freshman year was rough, mine was a little bit too. I think that it’s cool that you reached for Stanford and Yale because it shows how serious you are about academics. But Lindagaf hit the nail in the head, everybody dreams of going to Stanford and Yale and all these fun schools. But literally, they are so hard to get into that you don’t only need brains, but a lot of luck too because they’re almost impossible to get into. Plus, there is also an enormous number of great colleges that you can go to. I’ve heard that some colleges like UC Berkeley, UCLA, MIT, and NYU have some of the best Math programs in the world, while at the same time, they’re in lively cities (LA, Boston, NYC.) These colleges are also still very hard to get into, but not as hard as Stanford and Yale.
Hope this helps and best of luck Sophomore Year!