Here are a number of short notes, written mainly for my benefit or for the benefit of my students. Each file is in pdf format.
- Algebraic Groups, Grassmannians, and Flag Varieties
- The Alternating Group A_{n} is simple for n > 4
- Artin’s Construction of an Algebraic Closure of a Field
- Automorphisms of S_{n} and A_{n}
- Central Simple Algebras
- The Classification of Wallpaper Patterns
- Direct Limits
- Division Algebras over Local Fields
- Dualities in Lattice Theory
- Examples of Localization
- Group Actions
- Group Actions, p-Groups, and the Sylow Theorems
- Group Extensions and H^{3}
- Isometries of R^{n}
- Locally Free Sheaves
- Nonabelian Cohomology
- Normed Spaces and Double Duals
- A Note about Profinite Groups
- Projective Modules and the Sphere S^{2}
- Rings with No Maximal Ideals
- Root Space Decomposition of the Classical Lie Algebras
- Semidirect Products
- On Severi-Brauer Varieties
- Sheaf Cohomology
- The Smith Normal Form of a Matrix
- Transitive Subgroups of S_{5}