Resources

• Terence Tao’s Notes
• Keith Conrad’s Notes
• Topics of Interest:
  • Lectures on the Combinatorics of Free Probability
  • Free Probability and Random Matrices
  • A Guided Tour of the Connes Embedding Problem
  • Introduction to Random Matrices
  • Strong Convergence: A Short Survey
  • An Introduction to Hyperlinear and Sofic Groups
  • Free Entropy
• AMS Open Math Notes
• Class notes:
  • Graduate classes:
    • Differential Topology
    • Algebra I
  • Qualifier prep:
    • Real Analysis
    • Complex Analysis
  • Undergraduate classes:
    • Real Analysis II
    • Real Analysis
    • Complex Analysis
    • Partial Differential Equations
    • Ordinary Differential Equations
    • Multivariable Calculus
    • Mathematical Methods of Physics II
    • Mathematical Methods of Physics I
    • Advanced Linear Algebra
    • Algebra II
    • Set Theory and Foundations of Mathematics
    • Graph Theory Notes (i) and (ii)
• Supplementary Personal Notes:
  • Algebra:
    • Conjugation and the Sylow Theorems
    • Algebraic Geometry (partial work-through)
  • Analysis:
    • Measure Theory/Real Analysis:
      • Inequalities and the $L_p$-Spaces
      • Egorov’s Theorem and Lusin’s Theorem
      • Three Convergence Theorems
      • The Lebesgue Measure
      • Signed Measures and the Lebesgue–Radon–Nikodym Theorem
    • Functional Analysis/Operator Algebras:
      • Extreme Points, the Krein–Milman Theorem, and Applications
      • Compact and Fredholm Operators
      • Functional Calculus in Banach and $C^{\ast}$-Algebras
      • Spectral Theory for Normal Operators
      • Positive Elements and Ideals in $C^{\ast}$-Algebras
      • States and Representations
      • Fixed-Point Theorems
      • Generalized Limits
      • Structure of von Neumann Algebras (in progress)
      • Projections in von Neumann Algebras (in progress)
      • Orbit Equivalence (in progress)
    • Miscellaneous Notes/Workthroughs:
      • Functional Analysis Exercises
      • Folland Exercise Workthrough
      • Quantum Theory for Mathematicians
      • Banach Algebras and Operator Theory
  • Topology:
    • Urysohn’s Lemma
    • Compactness in Topological Spaces