Here, I keep 2 lists for mathematical reading. One for texts I’ve enjoyed/am enjoying, and another for texts I plan to read.

Good Reads

  1. Linear Algebra Done Wrong - Sergei Treil Absolutely fantastic book on linear algebra. Free to read online, 286 pages of clear motivation and explanations. It is an introduction to formal mathematics and rigorous proof writing, which makes it possible to follow along without constantly getting totally lost.
  2. AN INTRODUCTION TO STOCHASTIC DIFFERENTIAL EQUATIONS - Lawrence C. Evans I have been trying so hard to find a good introductory text on stochastic calculus, and this is the best one I’ve found so far. It skips out on a lot of the nitty-gritty details to focus on the main applications. It is a very readable and well-organized book so far, and includes a motivated crash course on probability theory, perfect for a beginner like me.

Plan to Read

  1. Understanding Analysis - Stephen Abbott I’ve read about a fifth of it, it’s easy to follow. I plan on finishing it.

Study plan

Probability and Statistics

  • Probability Theory
  • Bayesian Statistics
  • Measure Theory (for a rigorous foundation)
  • Stochastic Processes (e.g., Markov Chains, Brownian Motion)

Optimization and Information Theory

  • Optimization Theory
  • Convex Analysis
  • Information Theory
  • Information Geometry
  • Numerical Analysis

Additional Topics for Machine Learning

  • Linear Algebra (Advanced Topics)
    • Matrix Analysis and Spectral Theory
    • Advanced Topics in Linear Algebra (e.g., Jordan Canonical Form, Matrix Calculus)
  • Random Matrix Theory (to understand the dynamics of complex models)
  • Tensor Calculus
  • Basic Physics (to understand the principles that inspire machine learning, such as dynamics, forces, and conservation laws)
  • Statistical Mechanics (understanding concepts like entropy, energy landscapes, and Boltzmann distribution)
  • Graph Theory and Combinatorics (for graph-based machine learning)

Analysis

  • Functional Analysis
  • Real Analysis
  • Tensor Analysis
  • Complex Analysis
  • Topology and Differential Geometry

Geometric Algebra and Lie Theory

  • Geometric Algebra (Clifford Algebra)
  • Lie Theory
  • Abstract Algebra (for Lie Groups and Representation Theory)

Additional Complementary Topics

  • Category Theory
  • Differential Equations (rigorous)
    • Ordinary Differential Equations (ODEs)
    • Partial Differential Equations (PDEs)
  • Computational Complexity and Algorithm Design
    • Algorithm Analysis and Efficiency