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