Theoretical / proof-based
Mathematical physics · Graduate · Physics
Topics
Advanced analysis
- Measure theory and Lebesgue integration
- Hilbert spaces and unbounded operators
- Distribution theory for Green's functions
- Spectral theory and resolvents
- Sobolev spaces for PDEs (intro)
Geometry and topology
- Differential forms and Stokes' theorem
- Fiber bundles and connections
- Characteristic classes overview
- Index theorems sketch (Atiyah–Singer)
- Topology in condensed matter contexts
Group theory and representations
- Compact Lie groups and Haar measure
- Representations of SU(2) and SU(3)
- Clebsch–Gordan and Wigner–Eckart in depth
- Young diagrams and tensor products
- Applications to quantum field theory
Pricing
Graduate-level rates are set on consultation. See the pricing page for K–12 and undergraduate rates.