I've taken differential,integral,multivariate calculus, DEQs, Introductory Linear Algebra, and am currently taking complex analysis and vector calculus (an extension of vector calc from multivariate). As a math student, how do you decide what to study after that? Is it time to specialize? I don't have a broad road map of mathematics but I do know that I like to think about space, mappings, surfaces. How do mathematicians go about finding what they like to research/learn (either as a hobby or for their research)?