Math 302 - Abstract Algebra
Spring 2025
Emily Proctor




Here are the videos for our course, arranged chronologically by topic.





Preliminaries

• Chapter 0 (properties of integers): Part 1/notes, Part 2/notes, and Part 3/notes.


• Chapter 0 (modular arithmetic): Part 4/notes.


• Chapter 0 (equivalence relations): Part 5/notes and Part 6/notes.


• Chapter 0 (mathematical induction): Part 7/notes.


• Chapter 0 (functions): Part 8/notes and Part 9/notes.

Groups

• Chapter 1 (introduction to groups: dihedral groups): Part 1/notes


• Chapter 2 (definition and examples of groups): Part 1/notes, Part 2/notes, and Part 3/notes.


• Chapter 2 (elementary properties of groups): Part 4/notes and Part 5/notes.


• Chapter 3 (order): Part 1/notes.

Subgroups

• Chapter 3 (definition of subgroup): Part 2/notes.


• Chapter 3 (subgroup tests): Part 3/notes, Part 4/notes, and Part 5/notes.


• Chapter 3 (common subgroups): Part 6/notes.

Cyclic Groups

• Chapter 4 (introduction to cyclic groups): Part 1/notes, Part 2/notes, Part 3/notes, and Part 4/notes.


• Chapter 4 (generators in cyclic groups): Part 5/notes, Part 6/notes, and Part 7/notes.


• Chapter 4 (the fundamental theorem of cyclic groups): Part 8/notes, Part 9/notes, Part 10/notes, and Part 11/notes.

Permutation Groups

• Chapter 5 (introduction to permutation groups): Part 1/notes and Part 2/notes.


• Chapter 5 (cycle notation and order): Part 3/notes, Part 4/notes, and Part 5/notes.


• Chapter 5 (even and odd permutations): Part 6/notes, Part 7/notes, and Part 8/notes.

Isomorphisms

• Chapter 6 (definition and properties of isomorphisms): Part 1/notes, Part 2/notes, and Part 3/notes.


• Chapter 6 (automorphisms): Part 4/notes.


• Chapter 6 (Cayley's theorem): Part 5/notes and Part 6/notes.

Cosets

• Chapter 7 (definition and properties of cosets): Part 1/notes, Part 2/notes, and Part 3/notes.


• Chapter 7 (Lagrange's theorem): Part 4/notes and Part 5/notes.

External Direct Products

• Chapter 8 (introduction and examples): Part 1/notes and Part 2/notes.


• Chapter 8 (order and products of cyclic groups): Part 3/notes and Part 4/notes.

Normal Subgroups and Factor Groups

• Chapter 9 (normal subgroups and the normal subgroup test): Part 1/notes and Part 2/notes.


• Chapter 9 (factor groups): Part 3/notes, Part 4/notes, and Part 5/notes.


• Chapter 9 (examples of factor groups): Part 6/notes and Part 7/notes.

Internal Direct Products

• Chapter 9 (internal direct products): Part 8/notes, Part 9/notes, and Part 10/notes.


• Chapter 9 (examples of internal direct products): Part 11/notes and Part 12/notes.

Homomorphisms

• Chapter 10 (introduction to and properties of homomorphisms): Part 1/notes, Part 2/notes, Part 3/notes, and Part 4/notes.


• Chapter 10 (homomorphisms and subgroups): Part 5/notes and Part 6/notes.


• Chapter 10 (the first isomorphism theorem): Part 7/notes, Part 8/notes, Part 9/notes, and Part 10/notes.

Rings

• Chapter 12 (definition and examples of rings): Part 1/notes, Part 2/notes, and Part 3/notes.


• Chapter 12 (subrings and properties of rings): Part 4/notes, Part 5/notes, and Part 6/notes.

Integral Domains and Fields

• Chapter 13 (definitions, examples, and relationships): Part 1/notes, Part 2/notes, and Part 3/notes.


• Chapter 13 (characteristic of a ring): Part 4/notes and Part 5/notes.

Ideals and Factor Rings

• Chapter 14 (introduction to ideals): Part 1/notes and Part 2/notes.


• Chapter 14 (factor rings): Part 3/notes and Part 4/notes.

Ring Homomorphisms

• Chapter 15 (definition and examples of ring homomorphisms): Part 1/notes and Part 2/notes.


• Chapter 15 (properties of ring homomorphisms): Part 3/notes and Part 4/notes.


• Chapter 15 (the first isomorphism theorem for rings): Part 5/notes, Part 6/notes, Part 7/notes, and Part 8/notes.