[lumost]

Curious why you find it so fundamental. In my experience abstract algebras primary benefit was drilling rigorous proofs for group theory etc.

Between physics and comp sci I'd rate abstract algebras contribution to understanding as one of the least important contributors ( although AA does provide a rigorous framework underpinning these fields in one way or another)

[jcranberry]

When I was in school, I felt it was very important because it taught me how to think of things in terms of mappings and structure-preserving mappings. After learning algebra found learning everything else became much easier.