Algebra II

Algebra II is where the abstract structures from group theory get extended into rings, modules, and fields, culminating in Galois theory and the classical proof that the general quintic has no radical solution — the payoff that ties symmetry, polynomial roots, and field extensions into one coherent story. You'll work through Dummit and Foote chapter by chapter, grinding out homework sets on ideals, UFDs, irreducibility criteria, and Galois correspondences, with a midterm and final that lean heavily on proof-writing rather than computation. This is the natural follow-up to MATH 323, and the language it teaches — extensions, automorphism groups, module decompositions — becomes the baseline for algebraic number theory, algebraic geometry, and most graduate algebra you'll encounter later.