Learning

Functional Analysis: Banach and Hilbert Spaces

Metric Spaces and Completeness → Spectral Theorem for Compact Self-Adjoint Operators

A systematic graduate-level path through the core structure theory of normed and inner product spaces, bounded linear operators, dual spaces, and the foundations of spectral theory. It builds from real analysis and linear algebra prerequisites to the central theorems of functional analysis, preparing learners for advanced work in analysis, PDEs, and mathematical physics.