Resources for learning statistics, linear algebra, number theory

Hello all,

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.

edit:

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.

I also need to learn linear algebra if I'm ever going to start contributing to Octave...hope someone has a good resource for that.

The way I did was with a very good book. I found the book:
Linear algebra and its applications by David C. Lay.
to very good and easy to understand. I'd start reading that, doing the exercises and find a good math board for posting questions you don't understand.

See if your local university has class tapes you can borrow buy. That's what I'm using to supplement my books. They are nice; you get to pound away at your own pace in the books and things, but if you find you don't understand something you can watch a few of the relevant episodes.

I don't know about the quality, but several universities have released similar tapes to "Youtube" or other sites.

Soma

Ah, I forgot about that. Of course. If there are video lectures on something, then usually watching those is a good idea.
One good resource for video lectures is: Free Online Course Materials | Courses | MIT OpenCourseWare
The video quality may not be great and I never did like the teacher for the linear algebra, but you may differ.

Wow, Elysia - that is exactly what I want! I've looked at a few samples, and it seems like the perfect combination I was looking for - written for new learners, but from a reliable, reputable source! Thank you so much.

And thanks for the tip phantomotap - I'll definitely look into that.

I'd say Elysia already did that for you. ^_^

Soma

Another thought:
While the book is good, it does lack some things. Particularly planes and lines. To complement that, I actually used a different book:
Elementary linear algebra : applications version by Howard Anton, Chris Rorres (chapter 3)
I also used it as a reference for diagnoalization of matrices.