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I go to a school known only for its golf program...so I need SOMETHING to strengthen my application. I'd like to have some graduate courses, but it would have to be online because there are none near me. Does anyone know of any university that offers graduate courses in algebra, analysis, topology, or something?

I would not know how a graduate course in mathematics online would be like. Usually a graduate course in math is very rigorous that requires a lot of explanation that can only be done efficiently in person. Online requires too much work.

But you can easily create your own online course.
Go to a university with the course you want to take.
Email the professor that will be teaching the graduate course that semester/quarter.
Find out what book he is using. Ask for a course syllabus. If there is weekly homework then ask him to post it on his website or email it to you weekly.
Then you do it turn it in and he grade it for you. You can either write it up by pen and scan it on your computer. THen send it to him. OR you can type it up using LaTEX.
I recommend learning LaTEX. It is a software that let you write mathematic symbols and equations.
Mathematicians use LaTEX to write papers.

Of course this would only work if the professor is nice enough to agree to it.
Usually professors are busy enough as it is to grade the official students in the class. Making him grade your work and sending you weekly homework is something he might not be willing to do. Just explain to him your passion for mathematics and your situation.
And even if he agree to it, you will probably have a harder time understanding the material. Unless you are really good.

Good luck.

I found a few online classes at Texas A&M...I have no idea what they would be like, either. Unfortunately, they are all very applied. I was thinking more about an algebra or topology course.

Yeah, I can't imagine what they are like, either. I would have to get the book and learn it on my own, which is fine, but I'm not sure how testing would be...

I have used LaTEX before, and I like it! I really think what you're suggesting would be too much for most professors...I could try, but I'm not sure how that would work as far as actually being enrolled in the course. I suppose I could try, though! Thanks for the suggestion.

Can you arrange a supervised independent study course with a professor at your home university?

There are schools that offer online courses with residential components. Open University in the UK is a good example. I've always thought the argument that pure math is too hard to teach online as rather fallacious. Schools do it. It used to be that all mathematicians were autodidacts.

I believe there is not enough demand for pure mathematics or theoretical science to justify an online degree. There is certainly a learning barrier, but anyone attracted to those fields would likely be more apt to deal with the added rigour. Why is it that MIT OCW, Berkeley, and other has lots of advanced course work in everything but pure math and theoretical physics. You can't find a blowhard physicist to tape their rambling on QM? You'd think they'd be lining up to be the next Feynman.

FWIW, UIS has a decent undergraduate math degree program online:
http://www.uis.edu/math/

They offer courses in abstract algebra and topology (on the undergraduate level).

University of Houston Math Department website states they offer grad courses online.
http://www.math.uh.edu/Matweb/grad_mam.htm
Admittedly, they seem like glorified senior level courses, but you might find a course or two.

Additionally, the following schools offer applied math and statistics courses online:
http://www.amathonline.washington.edu/amo/
http://www.cvn.columbia.edu/
http://scpd.stanford.edu/publicViewHome.do?method=load

There are actually quite a few online applied math (and Statistics) programs. Graduate level applied math isn't exactly a cake walk. I really think there is little industrial demand for theoretical work. Numerous engineering programs (at prestigious schools) exist online as well. I imagine there aren't many companies that would pay for an online MS degree in string theory or algebraic topology. Remember there has to be enough demand to justify designing and staffing a whole online degree program.

Hi Frnds,
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Thanks everyone, I ended up arranging an independent study in matrix theory at my university, which includes an independent research paper. I think it should be sufficient. I'll just learn as much as I can outside class.