These are notes from a first term abstract algebra course, an introduction to groups, rings, and fields. There is an emphasis on specific examples.

I hope to get the notes for additional topics in abstract algebra written soon.

The first link in each item is to a Web page; the second is to a PDF (Adobe Acrobat) file. Use the PDF if you want to print it.

- Groups

[PDF] - Examples of groups

[PDF] - Subgroups

[PDF] - Group homomorphisms and isomorphisms

[PDF] - Matrix groups

[PDF] - Divisibility

[PDF] - Greatest common divisors; the Euclidean and Extended Euclidean algorithms

[PDF] - Prime numbers

[PDF] - Modular arithmetic

[PDF] - Cyclic groups

[PDF] - The group of units in the integers mod n; Fermat's theorem; Wilson's theorem

[PDF] - Permutations

[PDF] - Direct products

[PDF] - The Structure Theorem for Finitely Generated Abelian Groups

[PDF] (Examples only - the theorem is stated, but not proved)

Finitely generated abelian groups - part 1 [video: 30 MB, 24 min] - Cosets and Lagrange's theorem

[PDF] - Normal subgroups and quotient groups

[PDF]

Normal subgroups and quotient groups - introduction - part 1 [video: 17 MB, 14 min]

Normal subgroups and quotient groups - introduction - part 2 [video: 23 MB, 19 min]

Normal subgroups and quotient groups - examples - part 1 [video: 25 MB, 21 min] - The Universal Property of the Quotient

[PDF]

- The First Isomorphism Theorem

[PDF]

First Isomorphism Theorem examples - part 1 [video: 34 MB, 25 min]

First Isomorphism Theorem examples - part 2 [video: 22 MB, 18 min]

First Isomorphism Theorem examples - part 3 (the title in the video says "Part 2") [video: 23 MB, 19 min] - Group maps from Z
_{m}to Z_{n}

[PDF] - Rings

[PDF] - Ring homomorphisms and isomorphisms

[PDF] - Ideals and subrings

[PDF] - Integral domains and fields

[PDF] - Polynomial rings; the Root and Factor Theorems; polynomial gcds

[PDF] - Quotient fields

[PDF] - Quotient rings

[PDF] - Quotient rings of polynomial rings

[PDF]