I am currently a high school freshman and have finished most of the math my school offers. I understand Calculus I/II(BC/Single Variable) and have a relatively good understanding of Calculus III(Multivariate) up to surface integrals. I have some understanding of differential equations, linear algebra, and some real analysis(though very little). What should I study to keep going in math? I am very interested in math and want to keep learning. The few things I have to consider though is that I have to do most of the learning on my own since I know no one who is anywhere near my level at math(well at least no students teacher is probably close) irl. I also am applying to a program called TAMS that basically has you live at college for two years to finish high school. One of the things they want you to do though is take a test at the beginning that is supposed to tell them where you are in math. From what I've heard it goes through linear algebra and differential equations. I would love to do really good at that test and at the least get out of most of the classes so I can do math I haven't already taught myself. thanks for any help.
EDIT: Basically what I'm trying to ask is what should I study next in math? It seems there are a lot of choices and I want to study something interesting, but I also want it to help me later on in college and high school.
