Introduction to Functional Analysis
MIT OpenCourseWare's graduate-level introduction covers functional analysis, the study of linear and nonlinear problems on normed spaces that are no longer finite-dimensional. Topics include normed spaces, completeness, functionals, the Hahn-Banach Theorem, duality, and operators, followed by Lebesgue measure, measurable functions, integrability, and the completeness of L^p spaces. The course moves on to Hilbert spaces, compact and self-adjoint operators, and closes with the Spectral Theorem. Materials come from MIT's OpenCourseWare archive and typically include lecture notes, problem sets, and exam materials used in MIT's own classroom, free to access with no enrollment or certificate. The course assumes solid grounding in real analysis and linear algebra and is meant for students moving from finite-dimensional linear algebra into infinite-dimensional spaces where the same tools require new machinery to work.