MP8 · Group theory & symmetry
A 19-module path through mp8 · group theory & symmetry, in study order from foundations to the frontier.
Modules
- Groups, Subgroups, and Cosets
- Conjugacy Classes and Normal Subgroups
- Group Homomorphisms and Quotient Groups
- Group Representations
- Reducible and Irreducible Representations
- Schur's Lemmas
- Characters and Orthogonality Theorems
- Character Tables and Decomposition of Representations
- Tensor Products and Clebsch–Gordan Decomposition
- Lie Groups
- Lie Algebras and the Exponential Map
- The Rotation Group SO(3)
- SU(2) and the Spin Double Cover
- Irreducible Representations of SU(2) and Angular Momentum
- Casimir Operators and Invariants
- Point Groups and Crystal Symmetry
- Physical Applications of Group Theory
- Wigner–Eckart Theorem
- Root Systems and Cartan Classification