terrytao.wordpress.com
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Terence Tao's personal math blog provides accessible expositions, lecture notes, and problem discussions by a Fields Medalist. It features substantial material on functional analysis and related topics (harmonic analysis, PDE, probability), including course notes and updates on his research.
More resources on Functional Analysis
nLab: Functional Analysis
Comprehensive wiki on functional analysis topics.
Geometric Anatomy of Theoretical Physics (Lectures on Functional Analysis)
Learn functional analysis through a geometric lens with Frederic Schuller's lectures! Explore key concepts in theoretical physics.
mathworld.wolfram.com
MathWorld is an online mathematics encyclopedia by Wolfram that offers comprehensive articles on mathematical topics. For functional analysis, you can find definitions, key concepts, theorems, formulas, and illustrative examples with explanations and references.
Introductory Functional Analysis with Applications
Introductory Functional Analysis with Applications - A book resource
ocw.mit.edu
MIT OpenCourseWare offers free, openly licensed course materials from MIT classes, available to anyone online. You can access lecture notes, problem sets, exams, and video lectures across subjects (including functional analysis) to study at your own pace.
A Course in Functional Analysis
A Course in Functional Analysis - A book resource