I try and be a very self-taught person, but I've lately found myself sorely lacking in a few areas of mathematics. I'm very good at algebra, geometry/trig and calculus, but I've just never been exposed to these other fields until lately. My school offers courses on these, but I would much rather teach myself, if only I could find some good resources to learn from. I have found plenty of material, but it's hard to find resources that are both high-quality, and easier for a more casual learner to understand (for instance, I find wikipedia articles are written in a very formal language, using terms you'd only know if you were already very familiar with theoretical mathematics). These are the specific things I want to learn more about:
- The kind of statistics used in cryptography. The papers and books I'm reading throw around probabilities with very little explanation behind them, and I'd like to know how those numbers are derived. I'm taking a course in statistics "for scientists and engineers" but it deals with deviations, etc... and seems to touch very little on this branch of statistics.
- General linear algebra. Anything and everything.
- Number theory, especially Galois fields, generators, etc...
If you have any recommendations, I'd love to hear them. Online sources are ideal, but I'm certainly not opposed to books.
To give you an example of what I'm looking for I've found that onlinemathlearning.com has good explanations for the absolute beginner, my only concern is that since it doesn't have a very formal feel, I might be missing the proper terminology that one would find when reading academic papers. At the same time, I've found that mathworld.wolfram.com has some excellent articles, but some of them (like the article on Galois fields) already assume a very strong understanding of some concepts I've never heard of before. mathworld.wolfram is probably closest to what I'm looking for so far, but I'm just worried I might be missing some more effective resources you guys may have come across.