<p>To the OP - I very much agree with the above; it’s a good idea to actually enroll in the courses and try them out; if you don’t find yourself appreciating them and/or if they become a problem, drop them. Definitely you should get through some basic linear algebra if you want to consider doing more. </p>
<p>To give you an idea, since you mentioned not knowing – the key thing about college math, which people tirelessly mention, is that you need to read and write proofs. You shouldn’t be intimidated by this, though – writing a proof is just communicating your reasoning in an appropriate way, which you’ll get used to only by practice. </p>
<p>A slight overview of subjects: linear and abstract algebra both deal with the structure of certain objects with familiar binary operations. Linear algebra deals with vector spaces, which you can view as a generalization of vectors as you learned about them in precalculus. The thing is, when you generalize, you end up finding that quite a few things you see (e.g. polynomials) in math have a structure that involves taking finite linear combinations of some basic elements. Abstract algebra just deals with many structures of this nature. And you see a lot of problems in mathematics as special cases of the theory of these structures. The idea is to pinpoint why familiar objects have the properties they do. </p>
<p>Real analysis deals with questions that have a calculus-like flavor – how continuous functions behave on different subsets of the reals, how they behave on convergent sequences, and eventually you generalize what continuity means. You also develop abstract versions of integration, where you integrate over things other than your favorite Euclidean space. Doing calculus on different objects is imaginably a powerful thing.</p>