Self-studying Physics with a math background

[BuriedAlive]

Hi everyone,

I've been interested in self-studying physics for a while now but I really have no idea what's the best to tackle first in terms of subject matter (mechanics, e&m, etc.) or what textbooks are conducive to self study. I'm currently a grad student in a math program, and I've taken lots of the basic "abstract math" classes (semester of abstract algebra, semester of topology, semester of diff. geometry, etc.), but my physics background is woefully inadequate. I've taken the year long intro freshman physics sequence for engineers (so I know all about boxes on inclined planes! haha) but that's it. I would like to (eventually) get to the point that I can understand the applications of topology and and manifold theory in physics, but I'm perfectly fine meandering through other branches of physics along the way to take in the sights. Hopefully someone can point me in the right direction!

Thanks.

 

[NumericalFEA]

You'd be better off to start from a book that would be a "bridge" between maths and physics.
I would suggest to begin with the following classical book:
"Computer Methods for Mathematical Calculations" by Forsythe, Malcolm and Moler