Abstract Algebra

Comprehensive notes cover each section of the textbook. Zip files corresponding to each pdf contain the respective lecture audio.

Textbook

"A First Course In Abstract Algebra", John B. Fraleigh, 7th edition

Download it on LBRY at lbry://abstractalgebra

Table of Contents

• Sets and Relations
• Intro to Groups and Examples
• Binary operations
• Isomorphic binary structures
• Groups
• Subgroups
• Cyclic groups
• Permutations, cosets, and Direct Products
• Orbits, Cycles, the Alternating Group
• Cosets
• Theorem of Lagrange
• Direct Product and Finitely Generated Abelian Groups
• Theorems of Direct Products
• Homomorphisms and Factor Groups
• Cosets of the Kernel
• Kernel Isomorphisms
• Factor Groups
• Automorphisms, Factor Group Computations and Simple Groups
• Simple Group
• Rings and Fields
• Ring Homomorphisms