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.

Notes: Modern Algebra II

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.

Notes: Modern Algebra I

I took Modern Algebra I with Professor Matthias Beck in Fall 2015. These comprehensive notes were compiled using lecture notes and the textbooks,

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:

  • Integers & the Euclidean algorithm
  • Complex numbers, roots of unity & Cardano’s formula
  • Modular arithmetic & commutative rings
  • Polynomials, power series & integral domains
  • Permutations & groups

Featured Image: Dodecahedron-Icosahedron Duality
Credit: Images from Algebra: Abstract and Concrete by Frederick M. Goodman