MAST 662
Functional Analysis I
Winter 2025 · Topics in Pure and Applied Mathematics
Topics
- Hilbert and Banach spaces
- Dual spaces and bounded linear operators
- Adjoints
- Hahn–Banach and Baire category theorems
- Banach–Steinhaus, open mapping and closed graph theorems
- Compact operators and the spectral theorem
- Fredholm alternative
- Weak and weak-star topologies
- Distributions and Sobolev spaces
Readings
- Listed textbook (requirement not stated): Barbara D. MacCluer. Elementary Functional Analysis. Springer, 2009. Chapters 1–4.
- Reference (not explicitly required): H. Brezis. Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer, 2011.
- Reference (not explicitly required): Avner Friedman. Foundations of Modern Analysis. Dover, 2003.
- Reference (not explicitly required): Elias M. Stein and Rami Shakarchi. Functional Analysis: Introduction to Further Topics in Analysis. Princeton, 2011.
Fall 2022 · MATH 494
Readings
- Elementary Functional Analysis by Barbara D. MacCluer, Springer.
- Functional Analysis, Sobolev Spaces and Partial Differential Equations by H. Brezis, Springer, 2011.
- Foundations of Modern Analysis by Avner Friedman, Dover, 2003.
- Functional Analysis: Introduction to Further Topics in Analysis by Elias M. Stein & Rami Shakarchi, Princeton, 2011.
Sources
- Course catalogue ↗2026–2027
- Syllabus or course outline ↗Winter 2025
- Historical course outline ↗Fall 2022
- Winter 2025 outline. Course header explicitly lists MAST 662, MATH 494, MAST 837.
- Historical source. Generic Textbook/References headings remain requirement-unspecified. Bibliographic editions and years are retained as printed; source inconsistencies may remain. Automated extraction with conservative filtering; distinct bibliography strings screened for false positives; entire syllabus not manually reviewed.