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 |
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Homework 2 Solutions |
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? KG-modules Maschke's Theorem Unitary Representations Schur's Lemma Representations of Abelian Groups U(1) and Fourier Series |
| Final Exam Solutions | Thurs, Dec 12 |
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