University of Reddit Course: Introduction to Group Theory
Here are prerequisite videos on proofs, sets, and the integers (completed):
BM4.1. Example of Complete Induction
BM6.1. Two Tough Set Equalities
BM8.2. Mappings: Basic Properties
BM8.3. Mappings: Composition and Inverse Functions
BM9.1. Cardinality 1: Finite Sets
BM9.2. Cardinality 2: Ininite Sets
BM10: Basic Properties of the Integers
BM10.1. The Euclidean Algorithm for the Integers
Here is the file list for Intro to Group Theory (Spring 2012):
Feb. 8, 2012: Video - GT1. Definition of Group
Feb. 8, 2012: Video - GT1.1. Example of Group Inverse
Feb. 15, 2012: Video - GT2. Definition of Subgroup
Feb. 22, 2012: Video - GT3. Cosets and Lagrange's Theorem
Feb. 29, 2012: Video - GT4. Normal Subgroups and Quotient Groups
Mar. 7, 2012: Video - GT5. Index 2 Theorem and Dihedral Groups
Mar. 7, 2012: Video - GT6. Centralizers, Normalizers, and Direct Products
Mar. 7, 2012: Video - GT7. The Commutator Subgroup
Mar. 14, 2012: Video - GT8. Group Homomorphisms
Mar. 14, 2012: Video - GT9. Group Isomorphisms
Mar. 21, 2012: Video - GT10. Examples of Non-Isomorphic Groups
Mar. 21, 2012: Video - GT11. Group Automorphisms
Mar. 28, 2012: Video - GT11.1. Automorphisms of A4
Mar. 28, 2012: Video - GT12. Aut(Z/n) and Fermat's Little Theorem
Mar. 28, 2012: Video - GT12.1. Automorphisms of Dihedral Groups
Apr. 4, 2012: Video - GT13. Groups of Order 8
Apr. 4, 2012: Video - GT14. Semidirect Products
Apr. 11, 2012: Video - GT15. Group Actions
Apr. 11, 2012: Video - GT16. Cayley's Theorem
Apr. 11, 2012: Video - GT16.1. Examples of Cayley's Theorem
Apr. 18, 2012: Video - GT17. Symmetric and Alternating Groups
Apr. 18, 2012: Video - GT17.1. Permutation Matrices
Apr. 18, 2012: Video - GT18. Conjugacy and the Class Equation
Apr. 18, 2012: Video - GT18.1. The Class Equation for Dihedral Groups
Apr. 18, 2012: Video - GT18.2. An is Simple (n>5)
Apr. 25, 2012: Video - GT19. Cauchy's Theorem
Apr. 25, 2012: Video - GT20. Overview of Sylow Theory
Apr. 25, 2012: Video - GT20.1. Sylow Theorems - Proofs
Apr. 25, 2012: Video - GT20.2. Sylow Theory for Simple 60
May. 2, 2012: Video - GT21. Internal Products
May. 2, 2012: Video - GT22. The Fundamental Theorem of Finite Abelian Groups