Analysis

Books

• P. Halmos: Measure Theory (1950)
• W. Rudin: Real and complex analysis, 3rd ed (1987)
• W. Rudin: Functional Analysis, 2nd ed (1991)
• M. Reed, B. Simon: Methods of Modern Mathematical Physics
  • I: Functional Analysis, 2nd edn. (1980)
  • II: Fourier Analysis, Self-Adjointness (1975).
  • III: Scattering Theory (1979).
  • IV: Analysis of Operators (1978)

Courses

• Advanced Real Analysis with Ole Christensen,youtube,textbook (2015). This is an introductory course for engineers and physicists, and skips some of the theory and proofs, however, the missing material will be in one of Rudin’s books.
• R. Melrose: Differential Analysis, Introduction to Functional Analysis

Links

• Math
  • Abstract Nonsense
  • Algebra
  • Algebraic Geometry
  • Analysis
  • Automated Theorem Proving
  • Engineering Math
  • Linear Algebra
  • Mathematical Physics
  • Representation Theory
  • Topology
• Physics