11:51
General Operations
Professor Heather Pierce
5:25
Properties of Operations
5:42
Examples of Operations
8:39
Definition of a Group
13:45
Examples of Groups
8:34
Elementary Properties of Groups
6:34
Subgroups
5:38
Cyclic Subgroups
9:24
Subgroup Lattice
5:53
Examples of Subgroups
11:22
Group Presentations
8:27
Cayley Diagrams
5:02
Basics of Functions
7:11
Injective and Surjective
7:24
Composition of Functions
5:04
Inverse Functions
8:24
Group of Permutations
7:04
Group of Rotations
5:43
Dihedral Groups
9:32
Permutations and Cycles
8:33
Disjoint Cycles
5:17
Transpositions
8:29
Even and Odd Permutations
Isomorphisms
9:51
Isomorphism Examples
9:55
Cayley's Theorem
9:12
Order of Group Elements
7:05
Properties of Order
6:43
Working with Order
4:50
Cyclic Groups
5:19
Subgroups of Cyclic Groups
5:28
Partitions
7:12
Equivalence Relations
4:42
Equivalence Relations and Partitions
7:57
Cosets
6:15
Properties of Cosets
3:03
Lagrange's Theorem
2:02
Groups of Prime Order
9:11
Homomorphisms
5:37
The Kernel
8:37
Normal Subgroups
10:11
Normal Subgroups and Their Cosets
6:48
Quotient Groups
6:18
Quotient Groups and Modular Arithmetic
5:47
"Factoring Out" with Quotient Groups
8:16
Examples of Quotient Groups
6:55
Fundamental Homomorphism Theorem
7:44
Using the Fundamental Homomorphism Theorem
Rings
4:09
Properties of Rings
4:46
Different Types of Rings
7:18
Fields and Integral Domains
6:32
Subrings
7:03
Ideals
8:51
Ring Homomorphisms
5:05
Cosets in a Ring
9:05
Quotient Rings
6:03
Prime and Maximal Ideal
6:28
Properties of Integral Domains
2:33
Finite Integral Domains
