Book for Independent Study in Modern, Thermal, or Mathematical Physics?

[quasarpulse]

I'm looking to do a guided independent study course at my college next term; the college doesn't offer physics beyond the introductory calculus-based sequence, which I've completed, and I'm not yet ready to transfer. The physics major sequence at the school to which I intend to transfer continues with thermal physics, modern physics, and a mathematical methods sequence. I'm hoping to get a little bit ahead in one of those areas (not terribly picky about which).

I have a solid math background including multivariable calculus and linear algebra and will be taking differential equations concurrently. I will have access to two wonderful instructors who will be happy to help explain any sticky parts, so I can probably handle a book geared to upper-level undergraduates. However, I don't want to get too far over my head - I don't think I can handle books written at the graduate level. I'd prefer a book in more-or-less "textbook" format with problem sets rather than a reference-style book, since I don't want to have to ask my professors to write problems just for me.

So, can anyone recommend a text in one of those three areas that they consider an ideal follow-up to the first-year introductory sequence?

 

[George Jones]

There are lots of books in each of the areas that you've listed. Here are example for each area.

Thermal Physics: An Introduction to Thermal Physics by Daniel Scroeder.

Modern Physics: Modern Physics by Tipler and Llewellyn.

Mathematical Methods: Mathematical Methods in the Physical Science by Mary Boas.

 

[Troponin]

Mathematical Methods:
I agree with George Jones on Boas' book.
I've also found R. Shankar's book "Basic Training in Mathematics" to be of some help. It leaves off at linear vector spaces, so it really is relatively basic, but Shankar shows some interesting tips and notes on things you might not normally notice in self study.

Modern Physics:
I believe you can find Tipler's Modern Physics for $1.99 online. At that price, it's at least worth a look.