What is the order of math topics that people learn math in?

Question

You know how they say to learn algebra first, then learn geometry, then trig, then calculus...etc? So after that, is there an order of what to learn next? If so, I'd like to know what comes after basic calc, and what comes after that.
For example: Can I just learn something like abstract algebra without knowing linear algebra or learn real-analysis with only basic calc? Thanks.

Answer 1

You can learn some real analysis with only basic calc, but it'll only be a little while before you start hitting calculus again. The beauty of math is, in part, that it all fits together.

Usually, after single-variable calculus, you take an introduction to analysis (in which you'll be exposed to sets, functions, equivalence classes, $\mathbb{Z},\mathbb{Q}$, you'll learn how to construct $\mathbb{R}$) do some linear algebra, maybe try on multivariate calculus, and then you can take on algebra and real analysis, and thereafter, abstract algebra, topology, complex/numerical analysis, etc. At this point you'll probably have figured out what the courses you want to take next are.

Learning abstract algebra without knowing linear algebra seems unlikely to me.