Alea: A Modern C++ Library for Algebraic Random Elements

I describe Alea, a C++20 header-only library for probability distributions and Monte Carlo methods. It combines type-erased distribution interfaces, a fluent API for composing distributions, parallel Monte Carlo integration, and batch sampling. The document includes examples from financial modeling, A/B testing, and quality control, with comparisons to existing C++ libraries. The full text and PDF are available below.