Reddit mentions of Mathematical Methods for Physicists, 6th Edition

What are you trying to be? Have one book just slightly deeper than Greene's book, or actually learn theoretical physics to say become a theoretical physicist or at least understand it?

If the former, it will be difficult as there's a lot of things that might be tacitly assumed that you know about more basic physics. However, a very good intro to Quantum Mechanics is Shankar. I'd also look into Foster and Nightingale's relativity book for a brief introduction to special (read Appendix A first) and general relativity. Maybe after both try A. Zee intro to QFT if you want to learn more about QFT. If you want to learn about phenomenological particle physics, say look at Perkins. Also it may help to have a book on mathematical physics, such as Boas or Arfken. (Arfken is the more advanced book, but has less examples). Also it may help to get a basic modern physics book that has very little math, though I can't think of any good ones.

If the latter than you will have to learn a lot. Here's advice from Nobel Laureate theoretical physicist Gerardus t'Hooft.

I used alonso and finn:

http://www.amazon.com/Physics-Marcelo-Alonso/dp/0201565188

It's big, it's fat, but it has a lot. It's not the best book around, but you'll find everything you need from basic mechanics to statistical physics, thermodynamics and basic quantummechanics. It builds up to the equations of Maxwell quite nicely, however in general the structure is quite flawed. I wouldn't recommend it if you like them fancy books with shiney pages and purple boxes with "Interesting note!". It's black and white, bit outdated, very dry, and hard to follow. This book was rarely used in the US, but it was a huge hit in Europe. The first edition was written in the sixties, this is the 1992 (sixth? seventh?) edition.

On a sidenote though, if you DO like fancy pictures and easy math, AND want to learn astronomy, I can recommend the following book:

http://www.amazon.com/Cosmic-Perspective-5th-Jeffrey-Bennett/dp/0321505670/ref=sr_1_1?ie=UTF8&s=books&qid=1239527234&sr=1-1

It is very airy, intended for non-physicist use actually. It's quite embarassing sometimes to read it as a second bachelor in physics, but it is a breeze to read none the less. It goes over everything from basic earth rotation and it's consequences, up to black holes and quasars. It's not very mathmatical, it's just the storytelling behind the theory, with sometimes a bit of math in a small box, which is still sometimes even at highschool level.

If you are looking to become a specialist in quantum mechanics, I used to following book:

http://www.amazon.com/Quantum-Mechanics-2nd-B-H-Bransden/dp/0582356911/ref=sr_1_1?ie=UTF8&s=books&qid=1239527384&sr=1-1

It's quite interesting, and it explains everything. It starts off with black body radiation, then starts with wave mechanics, and then you end up at matrix mechanics. It does require a lot of mathematical insight though, even though some basic principles such as dirac distrubtion, and fourier transformations are explain in the appendix.

If you want a bible to carry around with all the math help you need:

http://www.amazon.com/Mathematical-Methods-Physicists-George-Arfken/dp/0120598760/ref=sr_1_1?ie=UTF8&s=books&qid=1239527524&sr=1-1

This is the book I own. It's a bible, I can guarantee you that. It's not meant to start by page 1 and read it through till the end. It's something you use to regularly look stuff up in. It has everything you need for an undergraduate course in physics. It also requires some first year calculus knowledge though. It starts off by assuming you know everything about integrals and derivatives. I think the rest is explained though. You even get a small introduction to physics-applied group theory. If you ever need a polynome, it has everything from Bessel, to Chebyshev.

Damnit, I gotta lay off reddit just after taking my concentration pills...

Here's how I was taught, but I was taught in physics not math.
Fourier transforms are more intuitive, so think about how you take a derivative of a FT. You carry the derivative operator into the integral and you just get a factor of 2(pi)ix under the integrand. Logically, if you want a second derivative, just take the FT of the functions transform times x^2 etc. If you want a 1.3^th derivative (yes fractional derivatives exist) then FT the function times x^1.3 etc. This means taking a n^th derivative in real space is the same as multiplying by x^n in transform space. Sounds alot like what logarithms did for multiplication back in the day doesn't it? So now you can turn a differential equation into a polynomial equation if you just take the Fourier transform of it. However, if the diff eq is more complex than just n^th order with constant coefficients, maybe the FT isn't the best transform available for simplifying it? Then use a transform that's tailored for the particular function you have.

If I remember correctly this book has a nice description. I consider this book to be the "readable" version of this one