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 Solutions 
Tues, Oct 8 
Course Notes SemiDirect Products Dihedral Groups Isometries of R^n JordanHölder Theorem Solvable Groups 
Homework 3 Solutions  Tues, Oct 22 
Course Notes The Hölder Program Structure of GSets The Sylow Theorems Groups of Small Order 
Matrix Groups and Representations  
Homework 4 Solutions  Tues, Nov 12 
Course Notes Representations (Gmodules) Vector Spaces (Kmodules) Steinitz and Dimension Coordinates and Matrices RankNullity 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? KGmodules Maschke's Theorem Unitary Representations Schur's Lemma Representations of Abelian Groups U(1) and Fourier Series 
Final Exam Solutions  Thurs, Dec 12 
