I understand that usually the next step after $3$ semesters of calculus and $1$ semester of ordinary differential equations (plus one semester of linear algebra, for some) is something like an introduction or analysis, algebra, or maybe topology. I'm also aware that it is possible to branch off and do number theory, or something like that.
But speaking strictly as someone with a hobby interest in math: are there any topics (not necessarily the size of a whole course) that do not usually appear in a standard undergraduate math curriculum and that someone with my background can learn about for fun?
If possible, resources to study the suggested topics are always welcome.