Notes

A collection of typeset notes, exercises, and course materials.

• MATH 507 · PDF Measure Theory & Integration

  Notes transcribed from UBC's MATH 507 (Winter Term 1, 2025/26). Covers σ-algebras, measures and outer measures, Borel measures, the Lebesgue integral, convergence theorems, product measures and the Fubini-Tonelli theorems, signed measures, the Radon-Nikodym theorem, and differentiation.

• MATH 510 · PDF Functional Analysis

  Notes transcribed from UBC's MATH 510 (Winter Term 2, 2025/26). Covers Banach spaces, bounded linear maps and functionals, the Baire category theorem and its consequences, Lp and Hilbert spaces, weak and weak* topologies, the Fourier transform and Schwartz class, Fourier series, and further topics including interpolation theory and distribution theory.

• Series · 4 PDFs Generative Modelling & Diffusion

  Notes on score-based generative models and diffusion.

  1. Intuition for Score-Based Generative Models
  2. Score Matching
  3. Probability Flow ODE
  4. Flow Matching
• STAT 547C · PDF Probability Theory

  Notes drawn from UBC's STAT 547C (Winter Term 1, 2025/26). Covers the measure-theoretic foundations of probability, probability kernels, conditioning and independence, concentration inequalities, integral probability metrics, φ-divergences.

• Solutions · PDF Folland Exercises

  Selected solutions to exercises from Folland's Real Analysis: Modern Techniques and Their Applications.