# notes

Notes and tutorials loosely organized by topic.

#### machine Learning

A brief mathematical introduction to GANâ€™s

The Transformer model in equations

Information theory: an alternative introduction with applications to concentration of measure

Conditional Random Fields as a generalization of logistic regression

Kernels and Mercerâ€™s Theorem

Some notes on Hilbert-Schmidt operators

#### probability

The fast Johnson-Lindenstrauss transform

Probability densities from a measure-theoretic perspective

#### other computer science

Estimating the Shannon capacity of a graph

Thoughts on proof assistants with companion Lean code

#### finance

Three perspectives on the Black-Scholes formula:

- The limit of a discrete time CRR model
- Hedging with a martingale representation
- The solution of the Black-Scholes PDE

Heuristics for manipulating stochastic differential equations

Negative probabilities in the binomial option pricing model