I'm not duplicating how to study abstract algebra. I recently downloaded Herstein's Abstract algebra and there are many contents in the book and I actually want to know if I need to read through all of the chapters if I learn it just for relativity. And what are the connections between physics and abstract algebra apart from relativity? If the purpose is to have a better understanding of physics, to which degree should one dig into this?
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There are tight connections between (operator) algebra and quantum dynamics as well. The entire comcept of $C^*$-algebras originated from a desire to better understand the mathematical properties of observable quantities. – Arthur Apr 07 '14 at 13:14