Grad Algebra I

Textbook: Groups and Representations, by Alperin and Bell.
Course Notes Date Details
Abstract Structure Theory of Groups
Homework 1 Solutions Thurs, Sept 5 Course Notes
Philosophy of 661/662
The Concept of a Lattice
The Lattice of Subgroups
Group Isomorphism Theorems
Homework 2
Tues, Oct 8 Course Notes
Semi-Direct Products
Dihedral Groups
Isometries of R^n
Jordan-Hölder Theorem
Solvable Groups
Homework 3 Solutions Tues, Oct 22 Course Notes
The Hölder Program
Structure of G-Sets
The Sylow Theorems
Groups of Small Order
Matrix Groups and Representations
Homework 4 Solutions Tues, Nov 12 Course Notes
Representations (G-modules)
Vector Spaces (K-modules)
Steinitz and Dimension
Coordinates and Matrices
Rank-Nullity Theorem
No HW5 Yet TBA Course Notes
Change of Coordinates
Jordan Decomposition
Finite Fields
General Linear Group
Bruhat Decomposition
Transvections Generate SL
Proof that PSL is Simple
Homework 5 Solutions Thurs, Dec 5 Course Notes
What is a Group?
Maschke's Theorem
Unitary Representations
Schur's Lemma
Representations of Abelian Groups
U(1) and Fourier Series
Final Exam Solutions Thurs, Dec 12