I'm taking a dual Math,Physics undergraduate course.I want to study GR and a few parts of relativistic Quantum Mechanics.I've a decent amount of knowledge in linear algebra. Though we have tensor products in a rigorous manner in math, I don't see how I can relate it easily to what is in the physics books.
Is there any book from which I can learn the math used in physics?
Synge and Schild's "Tensor Calculus" has the old, component-heavy, "physics-style" discussion of tensors, and it has bits devoted especially to GR.
I would recommend you supplement it with a more modern text like Bishop and Goldberg's "Calculus on Manifolds" or "Geometry, Topology and Physics" by M. Nakahara because thinking of tensors exclusively in terms of their components can be quite limiting.