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.

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.

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

• Al Cuoco & Joseph J. Rotman, Learning Modern Algebra, MAA Textbooks, 2013.
• Frederick M. Goodman, Algebra: Abstract and Concrete, edition 2.6.

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