Notes: Graduate Algebra

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.