Posts tagged "mathematics"
13 posts
Decorating Christmas Trees with Group Theory
Applying Burnside's lemma and Polyna's enumeration theorem to quantify the number of patterns I can choose to arrange the baubles on my Christmas tree.
Building a Semantic Blog Post Clustering System
I implemented an automated system to find related blog posts using embeddings and k-means clustering. The system runs at build time, using semantic similarity to group posts by topic and generate intelligent recommendations without any runtime overhead.
Solving Terni Lapilli: A 2000-Year-Old Game
I investigate how it's possible to apply optimisation techniques and group theory to the ancient game of Terni Lapilli. Terni Lapilli is a version of tic-tac-toe, and like tic-tac-toe it's possible to model optimal decision making. I used this analysis to explore various areas of mathematics I hadn't encountered yet, like group theory.
Understanding Ship Deceleration: Interactive Calculator and Mathematical Methods
How long does it take a ship to stop? I built an interactive calculator and worked through the hydrodynamics from first principles. Without friction brakes, we can see that hull form and propulsion type dominate stopping performance.
From Naval Warfare to the Grimdark
I adapted a naval combat model to Warhammer 40k and built interactive calculators using iterative expected values, Markov chains, and Monte Carlo simulation. Monte Carlo wins for accuracy, but Markov chains reveal the probability distributions that expected values hide.
Classifying data with Python
Using scikit-learn and some Python features to set up a machine learning pipeline to quantify the efficiency of different classifers for classifying the movement of a stock price.
Calculating covariance matrices with Python
I wanted to use lower level linear algebra constructs in Python to calculate a covariance matrix.
Learning about data science
Useful resources for learning about data science.
Reconstructing a point set from a Euclidean Distance Matrix
Recovering point locations from vectors.
A review of Matrix Methods in Data Analysis
A review of the MIT 18.065 Spring 2018 opencourseware course, instructed by Gilbert Strang.
Numerical Linear Algebra Cookbook
A review of numerical linear algebra for machine learning.
Linear Algebra for Data Science Cookbook
A review of mathematical concepts helpful for data science.
Uncertainty analysis literature review
A review of the literature on uncertainty and sensitivity analysis when applied to optimisation models.