Mathematics
Functional Analysis
Part of Functional Analysis, level 7. About 39 hours of study across the topics below.
Banach & Hilbert Spaces
- Normed & Banach Spacesconvergence, completeness, examples (sequence and function spaces)6.5–12 h
- Hilbert Spacesinner products, orthonormal bases, projections, Riesz representation6.5–12 h
- Bounded Linear Operatorsoperator norm, dual spaces, adjoints, compact operators6.5–12 h
Theorems & Applications
- Fundamental TheoremsHahn-Banach, open mapping, closed graph, uniform boundedness6.5–12 h
- Spectral Theory Introspectrum of operators, spectral theorem for compact/self-adjoint operators6.5–12 h
- Distributions & Sobolev Spacestest functions, weak derivatives, applications to PDE6.5–12 h