Physics: where to start?

Hi /sci/,

I'm a math nerd but of late have become exasperated with how little my field seems to apply to reality.  Plus what I've seen and heard about theoretical physics (NOVA specials lol) is interesting as fuck.

My background is limited: 2 semesters of shitty "general physics" (collegiate plug and chug) and I've read Einstein's "Relativity: The Special & General Theory". 

So my question is, where do I start?  Are there any good, comprehensive sources for actually learning physics?  Any books suitable for self-study (if this is even possible) but still hard science?  I want to learn more about a lot of this stuff - QM, E&M, astrophysics, classical mechanics - but I don't want a Stephen Hawking-esque "Oh lol I understand physics" feeling, I want to understand the motivation for the theory and how and why the experimental data supports it.  I feel like an emphasis on the math would be helpful for me, too.

So yeah, if anyone can help a brother out, I'd appreciate it.  Thanks in advance.

If you want basic calculus-based stuff, I hear the book by Gasiorowicz is quite good.  For modern physics, I'm not sure which is the best but I used the book by Tipler.  These books will have a lot simpler math (though still at least calculus) than upper-division texts like Griffiths, but they will introduce concepts from a more experimental point of view, which you seem to want.

If you want to learn real physics, though, the books are generally written by theorists and don't contain much about experiments.  I would recommend Taylor's Classical Mechanics, Griffiths for E&M, and Shankar for Quantum.  The other fundamental subject you need is Statistical Mechanics, but I haven't taken that yet so I don't know what book to use (though, if you don't mind looking at a grad-level text, check out Pathria).

If you're into particle physics, Perkins wrote a book that talks a lot about experiment (since he's an experimentalist). You need the quantum background, though, especially Fermi's Golden Rule.  There's also a (supposedly better) particle book by Griffiths which has more theory.

If you have a little exposure to quantum mechanics and want to learn what it's really about (i.e., past all the phenomenology and approximations), there's a book on foundations of quantum mechanics by Asher Peres called "Quantum Theory: Concepts and Methods".  I was thinking of going into quantum information theory so this book was highly recommended to me.  I went ahead and bought it, and while I haven't really read it yet, I plan to read it and work through the problems over the coming summer.  The math isn't too intensive (linear algebra) but the physics is extremely profound.

Finally, about the math...You've probably had vector calculus, but just want to make sure since it's essential for E&M.  PDEs are equally important to understand before you get into the Schroedinger Equation (they don't come up as much in classical physics, except maybe the wave equation).  Complex analysis is also useful and comes up in random places.  That's really all you need at the undergrad level (that you don't already have, as far as I can tell).  Lie groups become important at the grad level, and you definitely need differential geometry for general relativity, but this is all generally taught in the relevant physics classes.  Of course, the higher you go (at least in fields like string theory), the more advanced math you'll run into.