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!

Topics Covered:

• 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,
• modules,
• field extensions,
• primitive roots,
• finite fields.