Introduction to Functional Analysis
MIT OpenCourseWare's undergraduate course covers the core machinery of functional analysis: normed spaces, completeness, linear functionals, the Hahn-Banach theorem, duality, and bounded operators. It moves into measure theory, covering Lebesgue measure, measurable functions, integrability, and the completeness of L-p spaces, before turning to Hilbert space theory, including compact, Hilbert-Schmidt, and trace class operators, ending with the spectral theorem. Materials include lecture notes and assignments consistent with MIT's OCW format, free to access with no certificate attached. The course assumes prior exposure to real analysis and linear algebra and is built for students moving from undergraduate analysis toward the operator-theoretic tools used throughout modern analysis and mathematical physics.