ocw.mit.edu
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MIT OpenCourseWare offers free, openly accessible course materials from MIT, including lecture notes, assignments, exams, and video lectures across many subjects. You can find math courses with concepts relevant to spectral theory, such as functional analysis and operator theory, along with reading lists and syllabi.
More resources on Spectral Theory
MathOverflow: Spectral Theory Resources
Curated list from practitioners
nLab: Spectral Theory
Comprehensive overview and references
Spectral Theory Lectures
Learn spectral theory from Nigel Higson's lectures! Explore fundamental concepts and applications in this comprehensive course.
Spectral Theory and Its Applications
Spectral Theory and Its Applications - A book resource
mathworld.wolfram.com
MathWorld is a comprehensive online mathematics encyclopedia by Wolfram that offers concise, well-organized articles on mathematical concepts, terms, and theorems. For spectral theory, it provides entries on topics like the spectral theorem, spectrum, eigenvalues, operators, and Hilbert spaces, including definitions, formulas, and references.
nptel.ac.in
NPTEL is India's national online learning platform offering free and paid courses with video lectures, notes, assignments, and certificates across engineering, science, and mathematics. It hosts mathematics courses and resources that cover spectral theory concepts through lectures, reading materials, and problem sets (e.g., linear algebra, functional analysis, and operator theory).