Abstract Algebra I

The study of algebraic structures: groups, subgroups, homomorphisms, rings, ideals, and fields. The abstract machinery behind number systems, symmetry, and cryptography.

Course Overview

Textbook

Artin, Algebra (or Dummit & Foote, Abstract Algebra)

Chapters

TBD

Sections

TBD

Prerequisites

Linear Algebra, Discrete Mathematics

Target

Foundation for Number Theory, Abstract Algebra II, Algebraic Topology

Status

Planned

Chapters will be scaffolded when this course becomes active.

Why This Course

  • Cryptography — RSA, Diffie-Hellman, elliptic curves are group/field theory

  • Error correction — coding theory is ring and field theory (Reed-Solomon, BCH)

  • Symmetry — group theory classifies all symmetry in nature and computation

  • Computer science — automata theory, formal languages connect to algebraic structures

  • Foundation — unlocks Number Theory, Galois Theory, and Algebraic Topology