Abstract Algebra

Group Theory

1. Groups & Subgroupsdefinitions, examples, order, cyclic groups, subgroups6.5–11.5 h
2. Cosets & Lagrange's Theoremindex, consequences for orders, normal subgroups6.5–11.5 h
3. Homomorphisms & Isomorphism Theoremskernel, image, first/second/third isomorphism theorems6.5–11.5 h
4. Group Actionsorbits, stabilizers, class equation, Sylow theorems intro6.5–11.5 h

Rings & Fields

1. Rings & Idealssubrings, ideals, quotient rings, homomorphisms, domains and fields6.5–11.5 h
2. Polynomial Ringsdivision algorithm, irreducibility, Euclidean domains, Gauss's lemma6.5–11.5 h
3. Unique Factorization DomainsUFD/PID/ED hierarchy, examples6.5–11.5 h

Field Theory

1. Field Extensionsalgebraic vs transcendental, splitting fields, algebraic closure6.5–11.5 h
2. Finite Fieldsconstruction, cyclotomic polynomials, applications to coding/crypto6.5–11.5 h
3. Galois Theory Introautomorphism groups, fundamental theorem, solvability by radicals, insolvability of the quintic7–13 h