I took Modern Algebra II with Professor Matthias Beck in Spring 2016. These comprehensive notes were compiled using lecture notes and the textbook, David S. Dummit & Richard M. Foote, Abstract Algebra (3rd edition), Wiley 2004. [errata]
Please feel free to download and print these notes for your convenience.
Featured Image: Icosahedron and dodecahedron Duality
Credit: Images from Algebra: Abstract and Concrete by Frederick M. Goodman
Disclaimer: my notes are meant to be a toolbox while doing proofs and studying/practicing the course in general. There may contain typos or mistakes. Please feel free to let me know if you find any errors!
- Review of basic properties of groups and rings and their quotient structures and homomorphisms,
- group actions,
- Sylow’s theorems,
- principal ideal domains,
- unique factorization,
- Euclidean domains,
- polynomial rings,
- field extensions,
- primitive roots,
- finite fields.