Notes on cosmology, dynamical systems, numerical methods and markets.https://kemalakin.github.io/https://kemalakin.github.io/writing/geometric-brownian-motion/https://kemalakin.github.io/writing/geometric-brownian-motion/Geometric Brownian motion, the model behind the Monte Carlo scene on the home page. A price can grow on average and still end below its start more often than not.Sat, 07 Nov 2026 00:00:00 GMTQuantitative financeMonte CarloStochastic calculushttps://kemalakin.github.io/writing/dynamical-system-lcdm/https://kemalakin.github.io/writing/dynamical-system-lcdm/The matter, radiation and dark-energy densities of ΛCDM as a dynamical system, reduced to two dimensions with the constraint equation.Mon, 04 Apr 2022 00:00:00 GMTCosmologyStability analysisPhase spacehttps://kemalakin.github.io/writing/sir-model/https://kemalakin.github.io/writing/sir-model/Three coupled equations explain why an outbreak peaks and then burns out. Below they are derived, integrated and put on sliders.Sun, 03 Apr 2022 00:00:00 GMTComputational epidemiologyNumerical methodsSciPyhttps://kemalakin.github.io/writing/frw-universe/https://kemalakin.github.io/writing/frw-universe/How the scale factor evolves for different matter and energy contents, and why the age of the universe needs a numerical integral.Sun, 04 Apr 2021 00:00:00 GMTCosmologyFriedmann equationsNumerical integration