Theoretical / proof-based
Graduate analysis · Graduate · Math
Topics
Measure and integration
- Sigma-algebras, measurable functions, and measures
- Lebesgue integral and convergence theorems (MCT, Fatou, DCT)
- L^p spaces and Hölder / Minkowski inequalities
- Product measures and Fubini–Tonelli
Banach and Hilbert spaces
- Normed spaces, completeness, and Banach spaces
- Linear operators; boundedness and operator norm
- Hilbert spaces, orthogonality, and Riesz representation
- Hahn–Banach and open mapping theorems (introduction)
Functional analysis topics
- Weak and weak-* topologies (introduction)
- Compact operators and Fredholm theory (overview)
- Spectral theorem for bounded self-adjoint operators (introduction)
Applications and problem sets
- Research-level problem sets aligned to your course syllabus
- Connections to PDE and probability (as covered in your program)
Pricing calculator
Choose materials, tutoring, or both — or book a single session as needed. Customize your plan on the subscribe page.
$1,162 · Graduate analysis · 18 tutoring hrs
Study guides, worksheets, reviews, practice tests, and answer keys for 1 class. 18 tutoring hours (1 hr / week · semester). Bundle discount applied vs buying separately. Pay in full via Zelle or Venmo.