Abstract algebra
Undergraduate · Math
Syllabus focus
Topics typically covered
Click a topic for the full text and related unit practice.
Undergraduate Abstract Algebra — scope drawn from open algebra texts (e.g. Judson Abstract Algebra: Theory and Applications, AIM-approved) and typical US undergraduate algebra syllabi.
Groups
- Binary operations and equivalence relations — Binary operations and equivalence relations
- Modular arithmetic — Modular arithmetic
- Groups: definitions, examples (Z, Z_n, dihedral, symmetric groups) — Groups: definitions, examples (Z, Z_n, dihedral, symmetric groups)
- Subgroups and cyclic groups — Subgroups and cyclic groups; generators and order
- Cosets, Lagrange's theorem, and index — Cosets, Lagrange's theorem, and index
- Normal subgroups and quotient groups — Normal subgroups and quotient groups
- Group homomorphisms — Group homomorphisms
- The first isomorphism theorem — The first isomorphism theorem
- Direct products — Direct products
- Simple groups (introduction) — Simple groups (introduction)
Rings and fields
- Rings: definitions and examples (Z, polynomial rings, matrix rings) — Rings: definitions and examples (Z, polynomial rings, matrix rings)
- Integral domains, fields, and ideals — Integral domains, fields, and ideals
- Quotient rings and ring homomorphisms — Quotient rings and ring homomorphisms
- Polynomial rings — Polynomial rings; irreducibility and factorization over Q and R
- Field extensions — Field extensions
- Constructibility (introduction) — Constructibility (introduction)
Optional capstone
- Sylow theorems (optional capstone in a second semester) — Sylow theorems (optional capstone in a second semester)
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Groups
Binary operations and equivalence relations
Coming soon - Rings and fields
Rings: definitions and examples (Z, polynomial rings, matrix rings)
Coming soon - Optional capstone
Sylow theorems (optional capstone in a second semester)
Coming soon
Notes
Undergraduate Abstract Algebra — scope drawn from open algebra texts (e.g. Judson Abstract Algebra: Theory and Applications, AIM-approved) and typical US undergraduate algebra syllabi. Topic outline: `content/topics/undergraduate/abstract_algebra.json`.