Fair warning: I was a math major in college, so I probably look at math from an extremely different angle, given that the intersection of math that you find in the major and math that you're taught in middle and high school is almost zero.

Mathematics, as it stands, is derived from a few fundamental assumptions (I'll call these postulates from now on). Everything else is completely derived from these postulates. These postulates consist of things like the A = A and other low level assumptions that seem extraordinarily basic. From these postulates, pretty much everything else is derived. These derived things include things as simple and basic as the natural numbers or real numbers and go as complex as vector-valued multi-variable calculus. (It's really beautiful and amazing when you look at it deeply enough).

Which brings me back to the actual question at hand: would aliens understand our mathematics? Without a doubt, they would have different notation and numbers and methods of writing things. They may also have adopted different postulates (a famous one which there is debate about whether we should include is known as the Axiom of Choice: Axiom of choice - Wikipedia, the free encyclopedia). If they had different postulates, well, the conclusions you get can be radically different (consider, for instance, the differences between Euclidean and non-Euclidean Geometry), and our mathematics would probably be completely different from theirs.

However, if they start with the same (or very similar) postulates/axioms, you'd probably find that their mathematical system, at its core (if not its language) would be very very similar to ours.