Algebra: finite groups, commutative rings, modules, field extensions, and linear algebra.
- Preliminaries
- Groups and subgroups
- Group actions and counting
- Sylow theory
- Permutation groups
- Series, solvability, and nilpotence
- Presentations, products, and classification
- Rings and ideals
- Factorization and polynomials
- Commutative algebra
- Modules
- The structure theorem over a PID
- Fields and extensions
- Galois theory
- Linear algebra
- Canonical forms
- Semisimplicity and representations