What I've learnt

I am back to the position I was in sometime last semester, where I am beginning to doubt my abilities as a mathematician. Given that this is a passing phase (I hope!), I decided to make a list of some of the things I have learnt since I got back from India in June.

C* algebras :
- Semi-projectivity and its relation to Shape theory for C* algebras
- Asymptotic morphisms and Shape equivalence
- Bartle-Graves selection principle and its relation to asymptotic morphisms
- C* bundles and C(X)-algebras
- Dauns-Hoffman theorem about bundles over the primitive spectrum
- Dixmier-Douady's results on local triviality of bundles of compact operators
- Inductive limit representation of bundles of semiprojective algebras
- K-theory sheaf associated to a C* bundle over the unit interval
- UCT and Kunneth theorem and the usefulness of geometric/projective resolutions
- Brown-Douglas-Fillmore theorem
- Generalized homology theories for C* algebras
- Mod-p K-theory and associated invariants
- Construction of Hochschild/Cyclic homology
- Construction of the (non-commutative) Chern character
- Finally understood Stokes' theorem

Unrelated to C* algebras :
- Structure theorem for finitely generated modules
- Presentation of modules and canonical forms of matrices

Hopefully, reading this sometime in the future will help me feel better about myself :)