# Summary

- Groups and rings, including Sylow theorems,
- Classifying small groups,
- Finitely generated abelian groups,
- Jordan-Holder theorem,
- Solvable groups,
- Simplicity of the alternating group,
- Euclidean domains,
- Principal ideal domains,
- Unique factorization domains,
- Noetherian rings,
- Hilbert basis theorem,
- Zorn's lemma, and
- Existence of maximal ideals and vector space bases.

Previous course web pages:

- [Fall 2017, Asilata Bapat](https://asilata.github.io/8000fall17/)