PHE3ID's Micro Math Wiki

A semi-random collection of possibly useful facts compiled from various sources explored using OpenAI ChatGPT with (very minimal) manual curation. Not to be used for mission-critical tasks.

Optimization

• Newton's method

Automatic differentiation

• Autodiff overview
• Various first and second derivatives
• Derivatives of the reconstruction of a matrix from its eigenvalues and eigenvectors

Decision support

• Expectation over an unknown distribution
• Bilevel optimization

Continuous dynamic processes

• Brownian motion
• Ornstein-Uhlenbeck process

Discrete dynamic processes

• Properties of the transition rate matrix
• Explicit inverse of small matrices
• Generalized Jukes-Cantor model
• Generalized Time-Reversible model

Non-mathematical considerations

• LLM cognition