I've found this thread, and forum, most interesting.
I'm going to try not to write a wall of text, but I've had a lot of thoughts and ideas with no outlet for the last few months and it seems I've just found one. So apologies if it's long-winded. I'm probably going to ask about 3 semi-related questions so I'll try to section this thing off so it can be read...
1. My background in school/academia is as follows: Dropped out of high school in 9th grade, so middle school education. Found my way into university (don't ask how XD) and have junior status currently. I grew tired of the simplicity of my major (psychology) which is...a joke in difficulty, so I took calc 1 on a whim. I realized quickly that it was "plug and chug" I think they call it...but at least it was harder than social sciences. I am accustomed to solving most things faster/easier than most of my peers, as meaningless as SAT may be, I got a 1450 with 8th grade education, maybe that will give some indicator of natural ability for what it's worth. I give this as some kind of context to measure my first question.
I recently bought spivak's book on calculus since I actually want to learn it, not just do glorified algebra masquerading as calculus. It's certainly rigorous. However, as I'm accustomed to learning things much faster than most (academic things anyway...life is another matter), I'm a little curious about why...the proofs...make my head hurt XD. Should I expect to be able to do these? I'm talking chapter 1 mind you. I looked at a few of the problems...I've solved 3 after an embarassing interval it seems...maybe 4 hours of looking at them. Is this a sign I'm not suited for "real" math? It's not the difficulty, I enjoy that for a change, I know everything isn't easy. But I just kind of sit there and look at it...I try different avenues that don't really help. And some of them, I just can't see a way to even simplify at all. Should I just keep at it or what? Is it normal to struggle like this when it's your first time seeing it? What kind of strategy should I take? I'm confused b/c just sitting looking at these problems when I have no insight doesn't seem to be the best way to learn. I'll do it if that's what you have to do though, I really want to be able to understand this stuff.
Do bear in mind that my uni calc was a joke and really just consisted of plug n chug, we didn't learn *any* proofs or theory whatsoever. Felt easier than algebra really.
2. I'm trying to find tools and a vocabulary for the kind of research I'll eventually want to do. It's nebulous to say the least but...I'm looking at mathematics as a possible way to give me those tools. I want to be able to design simulations of populations of human beings exhibiting behaviors, maybe using computer models, to see what comes out. This would most certainly require designing models of some kind which involves math at least more complex than what I currently am able to do/grasp. I already think about things in this way, but I don't know *what* it is I'm wanting to do. I'm certain it has been thought of/tried before. I don't know what it's called. Game theory? Decision Theory? Nonlinear Dynamics? A branch/area of statistics? At this point in my understanding of maths I'm not really qualified to understand what I could do with those, let alone if I can find some novel applications in social sciences for them. Or if I can apply them in the way I'd like, or if it is even wise/logical to do so. Anyone have any insight into this?
3. Also, what would you suggest for someone with a spotty education to "shore up" their gaps in maths? I tried to go back and review high school curricula, but it's hard to see exactly what I'm missing. I couldn't tell from my calc and stat courses at my uni since they were a joke(we used set notations and whatnot in stat which were never explained...that my reason for taking calc, I wanted to see the nuts and bolts under the math which I knew they glossed over). I don't know if I can understand/complete spivak with my present knowledge base.
