I’m interested in studying mathematics, but in my current situation, taking courses isn’t an option (I’m trying to finish my philosophy degree). So, would it be incredibly difficult for me to study on my own (I only got to Cal 1 in High School). Also, what books/web recources would do the best job of facilitating home learning. Thanks in advance.
Well you can sure give it a try, and I wish you the best of luck. I think there were many times in higher math where I needed some hand holding, but that was my experience.
I would try to get a good grasp on Calculus first. You can go to your local library and check out a big heavy Calculus book. I know our Calculus book was covered in 3 semesters, so you might want to concentrate mostly on the first half of the book.
You will want to get a good grasp of analysis too. Infinite sums and series just keep popping up over and over again in advanced math courses.
Then there’s linear algebra. The first course I had was fairly easy, I think you should be able to pick up an elementary linear algebra book at the library. I’m not sure if you want to mess with advanced linear algebra, but I will leave that up to you.
There’s also abstract algebra. I would think you could learn the fundamentals of abstract algebra on your own with a decent textbook. Again, advanced abstract algebra, I will leave that up to you.
I didn’t learn much about differential equations, but you might want to get a grasp on the basics. Along with Dif-E-Q, a basic understanding of complex analysis is probably a good idea.
You will want to understand elementary probability and statistics. There are many good texts out there for these subjects. Then maybe dabble into a bit of advanced probability, linear statistical models, and experimental designs.
Beyond the things listed, you have topology (can you do this by yourself?, I don’t think I could), number theory, and all the advanced courses of algebra, calculus, analysis and statistics. I’m sure I missed a few things, like non-euclidian geometry, but a quick glance at any math graduate school curriculum should give you a good idea of what else is available.
There are online courses, for a fee. I’m not aware of any free online math classes.
I think my approach would be to check out math texts from your college library, and talk to students and professors if you get stuck.
Good luck.
An excellent math resource on the web is Drexel’s Math Forum. They cover a broad range of all math subjects. The ‘Ask Dr. Math’ is a good place to go if you have a tough conceptual question, and they list links to other resources as well. I’ve been studying real analysis on my own during my commute, and I’ve had a lot of help from them (as well as some good help from the SDMB here when I was stuck).