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Yeah, so I ultimately want to understand Eigenvalves, but before that I need to understand linear transformations but before that vector spaces but before that ring theory but before that field theory but before that group theory (I might not need this background, I don´t really know, but I´d like to understand them nonetheless). I read the wikibook on group theory, thought I got it, tried the first problem set, and noticed I did not get it. Is there a prereq to group theory? I have a high school mathematics background up to integrals (Calc II) (I also learned modulo systems from somewhere, but it wasn´t in the high school curriculum).
I´m guessing set theory might be a good idea, but are there pre-reqs for that too?
Reply to Above
You don't really need to know field/group/ring theory to understand eigenvalues. Generally, math curriculums teach linear algebra before those topics, and that usually includes eigenvalues and eigenvectors. If you know a little bit about matrices already, it's not a huge leap to linear transformations and then to eigenvalues. Group/Field/Ring theory is generally reserved for those majoring in mathematics and are not used or learned by most people in scientific and technical fields.
I have never tried this before, but here goes. I am a member of the over the hill gang (60 yrs), but a long time ago in a universe far far away I studied math for awhile (never finished tho) Actually, my background is somewhat non-standard as I was involved in an experimental program that spent a good deal of time constructing the real numbers instead of doing "real" real analysis. Now I am starting to read Tom Apostol's Volume I and am having a fairly good time doing it. I plan to read both Volumes I and II. I have no idea if I will continue in this reading, but I may very well do it. How much maths I may learn probably depends on how long my brain continues to function. At my stage in life, I am really not interested in getting formal credit for anything but I thought it would be nice to talk with some person about what I am doing from time to time. If you are interested in beginning a conversation, let me know by adding to this page.
Don't know when you wrote the above, but I'm in your situation. Over 60, interested in math, took calculus, statistics, a bit of this and that in college in the last millennium. I do some reading in math, am trying to learn a little tensor algebra, and took some MOOCs. I heard about Very Large Numbers, and am fascinated by that topic. Am willing to engage and see if we are on the same page.