An introduction to path signatures, from rough path foundations to signature kernels and machine-learning applications.

Working solutions to exercises from High-Dimensional Probability, expanded and updated over time.

Evolving notes on graph theory, covering foundational counting arguments, connectivity, colouring, and extremal methods.

A concise proof that every eigenvalue of a real symmetric matrix is real.

A concise guide to diagnosing and enabling the Bluetooth service on Arch Linux.

A compact Lean 4 and Mathlib reference connecting familiar mathematical reasoning with formal proofs.

A proof of the representation of continuous linear functionals on sequence spaces without assuming an inner product.

Derivations of fundamental vector calculus identities using index notation and the Einstein summation convention.

An introduction to the Erdös–Stone theorem and its role in asymptotic extremal graph theory.

A personal guide to improving the macOS command-line experience with iTerm2, Oh My Zsh, plugins, and themes.