Where do you live? In most Europe public university is free and you can attend courses. I don’t know about US or other parts of the world. If you just “show up

Where do you live? In most Europe public university is free and you can attend courses. I don’t know about US or other parts of the world. If you just “show up one day”, you’ll be seen as pretty weird, but hey, it’s math, there will certainly be people more weird than you. My recommendation would be to introduce yourself to the teachers and be very careful/polite/diligent in attending the course. Some teachers can be very opinionated, just go with the flow. Given your initial level, I’d recommend to focus on breadth instead of depth. It’s likely the case that you don’t know enough yet to make an informed decision. For example, in my case I love algebraic geometry, number theory, and cryptography. And I hate calculus with a passion, including analytical number theory. None of this was clear to me until the 2nd-3rd year of university, foundamentally because what you learn in high school (liceo, in Italy) is kind ok fixed and biased towards calculus.