I kinda ran into a little problem the other day. I thought I knew enough about math to get myself through a simple Quantum Physics for Dummies book but apparently I don't. Right now my education goes up to Algebra II. but where do I go from here? I have no idea whether I need to learn trig before calculus or vice-versa and what kinda math I need to learn about from there. It's not just for the QPFD book though. I'd kinda like learn it just for the hell of it.

Assuming high school knowledge the order of courses I did before doing my first QM course was :

Differential equations, algebra & geometry, vector calculus, mechanics, linear algebra and then quantum mechanics.

'Algebra and geometry' is a bit vague in title, it was basic linear algebra, matrices, linear operators, vectors and a slew of group theory.

You need both trigonometry and calculus, and ideally an introduction to complex analysis.

Central to much of easrly quantum physics development are complex exponentials, e^{a+bi} = e^a \left( \cos b + i \sin b \right), complex conjugation, \left(a + bi \right)^{*} = a - b i, z^{*} z = z z^{*} = |z|^2, and integration, <A> = \frac{\int \psi^{*} A \psi dx}{\int \psi^{*} \psi dx} , and differentiation.

Later the math gets much more serious.

//Edit -- Oh yes -- Linear algebra is very important also, and vital if you are going to understand eigenstates and their related eigenvectors or eigenfunctions.

Thanks guys. Is there anyway to learn this stuff without actually taking college classes on it? Right now the only thing I really have access to is a public library, which I'm hoping should have books on this stuff right?

Many college universities have introductory textbooks in their stacks, but access for even in-library use is often limited to students, staff and faculty. In the US, I have not been too impressed with science materials in branch and smaller city libraries. Big cities do often have these materials in their central libraries, but it is not so easy to grab this material from books alone.

MIT's math dept has put many of these courses online.

http://ocw.mit.edu/courses/#mathematics

http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2005/video-lectures/

Many college universities have introductory textbooks in their stacks, but access for even in-library use is often limited to students, staff and faculty. In the US, I have not been too impressed with science materials in branch and smaller city libraries. Big cities do often have these materials in their central libraries, but it is not so easy to grab this material from books alone.

MIT's math dept has put many of these courses online.




Wow. I think you just blew my mind with the number of different types of math there are. I'm sure I will be able to make sense out of it all soon...hopefully :)

Those MIT courses look pretty sweet. Thanks alot! I usually do my forum posting from work so unfortunately I won't be able to check it out for a little while, but just from the looks of it I have a feeling that will come in handy. I have a hard time learning just by reading anyway. but if someone explains it to me I can catch on in an instant.

btw, I didn't mean to edit your post but until my post count gets over 20 I had to take the URL's out.

Just remember to have some patience in learning this stuff, make sure you spend tons of time doing practice problems and exercises, rather than just going through examples and assuming you understand them. If you haven't done calculus yet, I'd say you need at least 2 years of intensive training to be ready for QM, if not 3-4 years. This is based on the pace at which full-time students taking 10 intensive courses per year would be expected to learn it, and they've got access to constant guidance and assistance whenever they get stuck or have trouble with a concept. High school really is just about learning how to learn, then the pace of said learning shoots up 10X as soon as you hit college.

Some very good lecture notes on math and physics are here:

http://www.phys.uu.nl/~thooft/theorist.html

Some of the best are almost stand alone textbooks. They start at a low enough level that the op shouldn't have to much trouble. Iirc, there are some good ones on complex math and analytical classical mechanics.

Some very good lecture notes on math and physics are here:



Some of the best are almost stand alone textbooks. They start at a low enough level that the op shouldn't have to much trouble. Iirc, there are some good ones on complex math and analytical classical mechanics.

Wow! These sites look like they are more than enough to get me started on this. I really appreciate the help guys. I went and got enrolled for my Fall 2010 classes and one of them I have to take is college algebra which should help in refreshing my memory a bit, or at least in picking up some slack.

Have a look at KhanAcademy.org if you haven't heard of it. Tons of introductory math videos on up through calculus and linear algebra. Helped me out a lot.