What should I study over summer?

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The discussion centers on recommendations for additional study materials in mathematics and physics after completing a first year at university. Key areas of study already covered include introductory proofs, vector calculus, linear algebra, ordinary differential equations (ODEs), dynamics, introductory quantum mechanics and relativity, vibrations and waves, and electricity and magnetism. Suggestions for further exploration include group theory, analysis with a recommendation for Stephen Abbott's "Understanding Analysis," boundary value problems, partial differential equations, differential geometry, differential forms, tensor analysis, and computational physics resources. The emphasis is on broadening knowledge in both theoretical and applied aspects of these fields.
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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 schrodinger 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?
 
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Study Analysis! If you want a gentle and friendly intro I highly highly recommend Stephen Abbott's Understanding Analysis book.
 
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).
 
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