Ahh, "problems", not problems :)

I thought this was going to be about the abc conjecture.

https://www.quantamagazine.org/titans-of-mathematics-clash-o...

There is also Problems in Analytic Number Theory, which teaches the field as a series of problems and exercises. It's a great way to learn, and one that I haven't seen implemented well in other areas (even the corresponding book for Algebraic Number Theory isn't as good) https://www.amazon.com/Problems-Analytic-Number-Graduate-Mat...

I would really like to see something like this for probability

try 50 Challenging Problems In Probability by Mosteller. it starts pretty basic and works up slowly to a good foundation for learning probability theory in a rigorous way using very neat problems.

https://www.amazon.com/Challenging-Problems-Probability-Solu...

For some reason, all of the links are opening in new tabs. Is there any way for me to configure my browser to ignore the html and not do this? (A way to revert to system default scrolling would also be nice.)

A link normalizing addon would be cool, add some safe rel tags and a setting to prefer new tab/same tab

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.

Semester system. The first half of the semester would be groups and rings.

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.

Were you a math major?

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.

Those were all standard topics, generally in years 2-3, at my undergrad program circa 2006.

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.