MAT3082

Hilbert spaces

(SCI)

Coordinator: Dr Tom Hall

4 points + Two 1-hour lectures and one 1-hour support class per week + Second semester + Clayton + Prerequisites: MAT2020 and MAT2051 + Prohibitions: MAP3082

Synopsis: Inner product spaces, orthogonality. Hilbert spaces. Orthonormal systems, Gram-Schmidt process, Fourier expansions. Bounded linear operators and functionals. Riesz representation theorem. Spectral theory for self-adjoint operators: applications, for example to quantum mechanics and differential equations.

Assessment: Examination (2 hours): 70% + Assignments: 30%