Don't recall learning Group Theory, Ring Theory, Field Theory, Galois Theory, or Module Theory in my undergrad math classes. Did cover linear algebra though.
All of those are typically in a single undergraduate course on abstract algebra. Depending on the specific course you might only touch on Galois theory and modules, but you'll definitely get exposure to both. Most undergraduate textbooks will have a chapter/section devoted to each of those topics.
Is this going by the quarter system or a semester system? I can't imagine doing groups, rings, and fields in a single quarter with significant rigor. That would suck.
I haven't yet seen an algebra class that would start from scratch, define groups and rings for the first time, and do commutative algebra with modules, and fields with Galois theory in a single semester. Usually these take around 2 semesters.
Almost every math major covers an intro to Group Theory, Ring Theory, Field Theory. That's just about all you can do in pure math immediately after Linear Algebra (except number theory and some probability), and the foundation for almost everything you'd try.
If "applied math" was not separated from "pure math" in your school, and you did non-math electives after the minimum core math classes, then you might avoid these topics in favor of a broad curriculum of differential equations, graph theory, probability, and such.
Galois Theory, or Module Theory would be electives or touched on in high-expectations program.
I took all of those except module theory in my undergrad math classes back in the early 90s. However some of them (for example Galois theory) were optional courses.
