Abstract algebra learning recommendations

Abstract algebra is an important component of undergraduate mathematics that includes group theory, ring theory, field theory, and some advanced aspects of linear algebra (such as the Jordan canonical form and rational canonical form) that rely on some knowledge of ring theory and field theory.

Usefulness

• Abstract algebra is largely useful only for people who intend to major in mathematics and do further work in a mathematics-intensive area (such as physics, some parts of computer science, and some parts of chemistry).
• Abstract algebra provides a deeper conceptual foundation for linear algebra, which is quite useful.
• The modes of thinking introduced in abstract algebra, particularly the ideas of isomorphism and homomorphism, can be useful for understanding logic, philosophy, and various cognitive science-based subjects. However, the specifics of algebraic structures are not relevant.