You could try http://www.its.caltech.edu/~sean/book.html by Sean Mauch of Caltech. It's HUGE and contains over 2000 pages of mathematical physics with exercises
and solutions, though I don't think it contains
anything on Algebraic Structures. Are you saying it's a math physics course with a focus on abstract algebra?
In that case, I would maybe recommend
The Theory of Groups and Its Application to Physical Problems , an older book by Bhagavantam and Venkatarayudu, which you can find
here.
You could also try:
Rowlatt - Group Theory and Elementary Particles
And if you're just looking for good abstract algebra books...
Artin - Abstract Algebra
Dummit and Foote - Abstract Algebra
Lang - Algebra or Undergraduate Algebra
Or
these awesome lecture notes covering a ton of different aspects of abstract algebra by J. S. Milne, a mathematician from New Zealand.
Or graduate abstract algebra lecture notes by PhysicsForums's own mathwonk
here.