Mathematical physics
Graduate · Physics
Syllabus focus
Topics typically covered
Theoretical / proof-based
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
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Advanced analysis
Measure theory and Lebesgue integration
Coming soon - Geometry and topology
Differential forms and Stokes' theorem
Coming soon - Group theory and representations
Compact Lie groups and Haar measure
Coming soon
Notes
Topics reflect common graduate physics core and elective syllabi at US universities. Sequencing and emphasis vary between one- and two-semester treatments.