IN SUMMARY
How do I best go about becoming an amateur mathematician?
MORE SPECIFICALLY
I've been a computer consultant for a decade now. Math has always intrigued me. My knowledge and understanding is pretty good up through integral calculus. I'm new to differential equations. I'd like very much to become a mathematician. It won't be a career, but I look forward to it becoming one heck of a hobby.
My question is: How do I best go about becoming an amateur mathematician? For example, I have studied courses and text in pretty much the following order:
- Arithemtic
- Algebra
- Geometry
- Trigonometry
- Differential Calculus
- Integral Calculus
- Differential Equations
It may be a good start, but its far from where I need to be. Where do I go from here? What about vector and linear algebras, multi-variable calculus, non-euclidean geometry, number theory, and others? I'm unsure of what path to take, that is, which particular field leads to the next one(s). What habits should I develop to increase my results and success? Are there software programs I should use? And finally, how do I go about doing research?
This is a very broad inquiry and may be difficult to answer completely, but any advice or guidance you may have would be most appreciated.
Thanks in advance.
