It's fun because its incredibly rewarding! The elation of the "a-ha!" moment in math is second to none.

> 4) Calculus and Linear Algebra ...

Though I wouldn't get too caught up in the rigor of analysis or vector spaces right away. If you are self-studying, just spend enough time to feel confident computing and manipulating integrals, differentiation, and matrix math.

Then find a good intro to discrete math textbook covering a wide range of topics: number theory, graph theory, logic, set theory, etc, and learn how to write a "good" proof. This will open up a number of mathematical doors.