What should I study over summer?

[radiator0505]

I'm almost done with my first year of maths and physics at university and I'm thinking of doing a bit of studying in my free time.
What are some good books or subjects to look into (either maths or physics)?

So far I've covered:
Maths:
Intro to proofs (short sections on sets, functions, numbers and small amounts on groups and number theory)
Vector calc (up to stokes theorem, personally I think I'm going to go over this a bit. I'm shaky on line integrals and spherical polars)
Linear algebra (up to eigenspaces, the prof hardly did any proofs)
ODE's(1st ans 2nd order, inhomogeneous, non linear and perturbation solutions)
Physics:
Dynamics (rotation, work energy, gravitation and so on)
Intro to quantum and relativity (lorentz transformations and upto deriving the 1D Schrödinger equation)
Vibrations and waves (many coupled systems, 2D wave equation)
Electricity and magnetism (up to deriving maxwells euqations)

I'm completely open to suggestions on subjects or books , apparently group theory is something I could start on now?

 

[00Donut]

Study Analysis! If you want a gentle and friendly intro I highly highly recommend Stephen Abbott's Understanding Analysis book.

 

[jedishrfu]

Another would be boundary value problems and partial differential equations.

Differential geometry, differential forms and/or tensor analysis.

My favorite computational physics (see compadre.org/osp).