Plan for the lectures

Part I - Groups
* Monday November 2, sections 1.1-1.3
* Groups - basic axioms and examples
* Dihedral groups
* Symmetric groups

* Monday November 9, sections 1.3-1.7
* Matrix groups
* The quaternion group
* Homomorphisms and isomorphisms
* Group actions

* Monday November 16, sections 2.1-2.4
* Subgroups - definitions and examples
* Centralizers and normalizers, stabilizers and kernels
* Cyclic groups and cyclic subgroups
* Subgroups generated by a subset of a group

* Monday November 23, sections 3.1-3.3
* Quotient groups and homomorphisms - definitions and examples
* More on cosets and Lagrange's Theorem
* The Isomorphism Theorems

* Monday November 30, sections 4.1.4-3
* Group actions and permutation representations
* Groups acting on themselves by left multiplication and Cayley's Theorem
* Groups acting on themselves by conjugation and the Class Equation

* Monday December 7, sections 4.4-4.5
* Automorphisms
* The Sylow Theorems

Part II - Rings
* Monday December 14, sections 5.1-5.2
* Direct products
* The Fundamental Theorem of finitely generated abelian groups

Part II - Rings
* Monday January 25, sections 7.1-7.2
* Rings, fields, integral domain, examples

* Monday February 1, sections 7.3-7.4
* Homomorphisms, kernel, ideal
* Operations on ideals, prime ideal