MATH

• functional analysis
  • Shapiro - Functional Analysis Lecture Notes
  • Reed & Simon - Methods of Modern Mathematics I: Functional Analysis
  • Rudin - Functional Analysis
  • Aliprantis & Border - Infinite-Dimensional Analysis: A Hitchhiker's Guide
  • Conway - A Course in Functional Analysis
  • Oxtoby - Measure and Category
  • Rordam - An Introduction to K-Theory for C* Algebras
  • Jaksic - Topics in Spectral Theory
  • Szego - Orthogonal Polynomials
• GMT and geometry
  • Heinonen - Nonsmooth Calculus
  • Krantz & Parks - Geometric Integration Theory
  • Robinson - Dimensions, Embeddings, & Attractors
  • Adler & Taylor - Random Fields and Geometry
  • Simon - Introduction to Geometric Measure Theory
  • Evans & Gareipy - Measure Theory and Fine Properties of Functions
  • Vakil - The Rising Sea: Foundations of Algebraic Geometry
  • Camillo - Lecture Notes on Rectifiable Sets, Densities, and Tangent Measures
  • "An introduction to infinite-dimensional differential geometry" - A. Schmeding
• probability theory
  • Van Handel - Probability in High Dimension
  • Klenke - Probability Theory: A Comprehensive Course
  • Kemp - Random Matrix Theory
  • Kallenberg - Foundations of Modern Probability
• convex analysis
  • Bauschke - Convex Analysis
• algebraic things
  • Judson - Abstract Algebra: Theory and Applications
  • Ghrist - Elementary Applied Topology

PHYSICS

• Hall - Quantum Theory for Mathematicians
• Cheung - Phase Transitions and Collective Phenomena
• Tong - Statistical Field Theory

COMPUTER SCIENCE

• Boumal - An introduction to optimization on smooth manifolds
• Hanin, Roberts, Yaida - The Principles of Deep Learning Theory
• Telgarsky - Deep Learning Theory
• Baserville - Random Matrix Theory and the Loss Surfaces of Neural Networks
• Hazan & Singh - Online Nonstochastic Control
• Hazan - Online Convex Optimization