Ok, I know this is vague, but assume I never really had a good working knowledge of math in any area. I want to pursue X related work, which calls for X, Z, E, A, L, C, Q, etc. math. I realize that knowing more of those maths will be necessary to model and solve certain problems in field X. However, how do I go about learning X, Z, E, A, L, C, Q? I need the uttermost basics of some areas, because, say, to learn Z, I'd need more of a grasp of X. But I may want to jump into E, A, or Q even, yet, I fall short because of X.
I may want to skip X altogether, but some of it keeps popping out in L, C, Z, E, etc. I am trying to get the grasp of the required math for X, but everything can't be perfectly linear, e.g. learn X 100%, then Z 100%, etc. Math does not work linearly like that. I mean, sure, there's basics like everything, 1 + 1 = 2, etc. But this is beyond that.
I may have to learn 1 + 1 = 2 before tackling 2(x) = y sufficiently, but in my area of interest it's not so linear, can vary, it depends on what I might be doing, working on, etc. I just don't have the math.
But how should I learn the different maths if I'm pretty much zeroed out from even some mere basics of some areas, like X? What should I do? I need help from the math skilled on here.
Do I try and work more with X, then continue on as necessary with Z or maybe E, etc.?
Or should I learn as much from every separate aspect, and try to link them all together(will taken longer and will be harder)?
PS: X and several others may have many different areas, like Pre-X, Linear-X.
The way I have done this (and I have been doing this for at least 4 years) is that I find resources in a subject and all its prerequisites, usually in the form of a book, but often via Wikipedia or other websites (wolfram math world, for example). Then, I start going the main subject (subject X) and once I get to a place through which I can't advance without some prerequisite, I start at the beginning of that prerequisite and go as far as I can. Although this seems slow, it is actually much faster, because I really end up knowing a good amount of the subject and all its prerequisites. Additionally, although this is how I have approached math a different levels, I could probably give more specific advice if you told me more about what level you are specifically asking about. I started with pre-calculus/trigonometry, and I am now working through graduate Analysis books/Algebraic topology, so I may be able to help you out with more specifics.
A more concrete example of what I have done is how I worked through a typical undergraduate analysis book. I began by going through the book, but much of the second half of the book really relied upon a lot of point-set topology, so I then studied that as much as I could. This eventually led to algebraic topology, and algebra, but I was able to continue working through the analysis book after getting a little bit of background in topology. However, the key component to this is that you don't end up viewing prerequisites as "work." You need to be as interested in the prerequisites as you are in the main topic, which typically happens in you view the topics in the context of the original subject and enjoy math.
I don't know how much this helps you, but I thought I'd explain my methodology at least. There's my 2 pennies of the day.