Ironically, I'm on a mathematics-based forum using the terms "variables" and "differentiate" in entirely non-mathematical ways, but what I mean by this question is as follows:
I'm self-studying and looking to gain an overarching understanding of math and the various fields and topics it addresses.
What I am looking for are the major elements which make one field different from another.
For example what makes calculus different from topology? Among those differences, what are the major categories that those differences would belong to?
For example:
- The sets of numbers used (real, irrational, natural, etc.)
- The set of operations/operators used (i.e. multiplication, exponents, differentiation)
- The axioms, postulates, or theorems of the field
- The "domain" of the field's focus, (i.e. change, structure, quantity, space)
Basically when it comes down to it, I'm looking to gain a greater holistic understanding, rather than learning a specific principle in a specific field and not knowing where it fits in or how to compare it to anything else.
So ultimately I'd like to know the "variables" of a field of math, and how those "variables" fit in together to make the field what it is.
This way I could make a more rich and interrelated web, by saying "in x field, the axioms are abc, compared to y field where they're def"
I think in this case it is not the worst choice to look into the wikipedia-entries to get an overview:
Areas of mathematics
and Outline of mathematics