I took Graduate Algebra with Professor Matthias Beck in Spring 2017. 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.

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:

• Polynomial rings,
• irreducibility criteria,
• Gröbner bases & Buchberger’s algorithm,
• field extensions,
• splitting fields,
• Galois groups,
• fundamental theorem of Galois theory,
• applications of Galois extensions,
• introduction to the polynomial method with applications in graph theory and incidence geometry.