Abstract Algebra II — Galois Theory & Modules

Field extensions, splitting fields, Galois correspondence, modules over rings, and the Sylow theorems. Where algebra reveals deep structural truths about solvability and symmetry.

Course Overview

Textbook

Dummit & Foote, Abstract Algebra (Part III-IV)

Chapters

TBD

Sections

TBD

Prerequisites

Abstract Algebra I

Target

Foundation for Algebraic Topology, Algebraic Geometry, Representation Theory

Status

Planned

Chapters will be scaffolded when this course becomes active.

Why This Course

  • Galois theory — the impossibility of quintic formula, one of mathematics' great achievements

  • Cryptography — finite field extensions are the foundation of elliptic curve crypto

  • Coding theory — BCH and Reed-Solomon codes use Galois fields

  • Algebraic topology — homology and cohomology are modules

  • Foundation — unlocks Algebraic Topology and Algebraic Geometry