Graduate algebra
Graduate · Math
Syllabus focus
Topics typically covered
Click a topic for the full text and related unit practice.
Graduate Algebra — scope drawn from open graduate algebra notes (e.g. Milne Group Theory / field-algebra OER) and typical first-year graduate algebra syllabi.
Groups and modules
- Review of groups and homomorphisms — Review of groups and homomorphisms
- Quotient groups — Quotient groups
- Sylow theorems and solvable groups — Sylow theorems and solvable groups
- Modules over rings — Modules over rings
- Projective modules — Projective modules
- Structure theorem for modules over PIDs (as covered) — Structure theorem for modules over PIDs (as covered)
Rings and fields
- Rings, ideals, and quotient rings — Rings, ideals, and quotient rings
- Polynomial rings and factorization — Polynomial rings and factorization
- Field extensions and algebraic closures — Field extensions and algebraic closures
- Galois theory — Galois theory
- Applications — Applications
Commutative and homological intro
- Noetherian rings — Noetherian rings
- Primary decomposition (introduction) — Primary decomposition (introduction)
- Tensor products of modules — Tensor products of modules
- Ext and Tor (overview, if in syllabus) — Ext and Tor (overview, if in syllabus)
Problem sets
- Research-level algebra problem sets — Research-level algebra problem sets
- Qualifying-exam style proof practice by topic area — Qualifying-exam style proof practice by topic area
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 and modules
Review of groups and homomorphisms
Coming soon - Rings and fields
Rings, ideals, and quotient rings
Coming soon - Commutative and homological intro
Noetherian rings
Coming soon - Problem sets
Research-level algebra problem sets
Coming soon
Notes
Graduate Algebra — scope drawn from open graduate algebra notes (e.g. Milne Group Theory / field-algebra OER) and typical first-year graduate algebra syllabi. Topic outline: `content/topics/graduate/algebra.json`.