To introduce the theory of infinite-dimensional normed vector spaces, the linear mappings between them.
A. Work effectively with the notions of metric, normed and inner product spaces.
B. State and prove theorems about Banach spaces and Hilbert spaces.
C. State and prove fundamental results about bounded linear operators and self-adjoint operators.
D. Apply the essential concepts and theorems of functional analysis to simple examples.
This module will be delivered using formal lectures.