Step 24 of 37
The study of structure: groups, rings, and fields.
Topics, in order
- Groups, subgroups, and cyclic groups
- Homomorphisms and quotient groups
- Group actions and the Sylow theorems
- Rings and ideals
- Polynomial rings and factorization
- Fields and field extensions
- Galois theory
Learn from
- Pinter, A Book of Abstract Algebra
- Then Artin, Algebra, or Dummit and Foote, Abstract Algebra
Move on when
You can prove the first isomorphism theorem and classify groups of small order.