(2011)

**Notes:**

- Modules: basic constructions, free modules
- Modules: finiteness conditions, the determinant trick, presentations, Smith normal form
- Modules: structure theorem for abelian groups. Field extensions: basic concepts
- Field extensions: degree of an extension
- Algebras, integral dependence
- Noether normalization, Nullstellensatz, affine varieties, morphisms (Warning: there are several typos in the proof of Noether normalization)
- Irreducibility, finite morphisms, Noether normalization (geometric form)

**Problem sets:**

- Problem set 1
- Problem set 2
- Problem set 3
- Problem set 4
- Problem set 5
- Problem set 6
- Problem set 7
- Problem set 8

*Last updated: 23 May, 2011*