This post falls into the question I have about the flow and direction of the math needed. I don't want to re-invent the wheel, I've got a smattering of math thru self study of physics from applied to GR and SR. I understand the concept behind Feynmans many body diagrams and can also follow the books I have acquired over the yrs in the various branch's of physics.
I'm very aware of my lack of a formalized mathematics background and would like to resolve that. I've got about a half dozen comp books I've filled with my own notes and abstracted math I made up to 'test' my ideas and try to put a 'proof' to my thoughts. Recently I decided to actually teach myself the math needed as I was reading Penroses' latest book 'the road to reality' the math intro was great and I realized I need to merge 'own' math with what everyone else is using.
So what comes first?
linear algebra ----> calculus ----> geometry (flavor?) -----> ???
I've got background geometry, trig and algebra. I also have a strong intuitive compass on Cartesian coordinates, polar and linear. I've been working with 3D software for 20yrs, it was a godsend over the borco table of old! finally I could work as I see it in my head. I'm an internally visual thinker, I see pictures and graphs to equations and numbers. the abstract is easy, the rigorous math can draw a blank.
Basically I don't want to study in circles, If I study out of turn then I have to back track. is there a generally accepted direction on the math flow?
I'm at the point where I'm trying to further my knowledge and I see that my lack in this area is holding my progress back. I can formalize a theory but I'm unable to show the math behind it. I'll dig the net and this forum, find that I was right and then be able to see the math and with some backtracking of the equations I can see the picture and it confirms the process I visually went thru to get there.
My apologies for the long post.