This thesis is about the physics and the mathematical structures associated with the fractional quantum Hall effect, with a focus on the k=3 Read-Rezayi state. We introduce some basic ideas relevant for the quantum Hall effect, including useful wave functions and the notion of quasiholes. We briefly outline how these concepts can be related to conformal field theory (CFT). The CFT description is then shown to naturally lead to the language of matrix product states, which can be used for efficient numerical computations for fractional quantum Hall states. Matrix product states and CFT are the key ideas underlying a numerical technique described in one of the included articles. This technique allows e.g. density profiles and spins of quasiholes in the k=3 Read-Rezayi state to be computed. From these spins, braiding phases of quasiholes can be inferred. We have also used these methods to numerically demonstrate a form of bulk-boundary correspondence in fractional quantum Hall states, where spin fractionalizes between a quasihole in the bulk and the distorted edge.
