The following is a solution to TTM book 4, lecture 5, exercise 1: Given the metric $g_{\mu \nu}(X)$, show that the Euler-Lagrange equation, to minimize the action along a trajectory in space-ti...

My mind map for Theoretical Minimum, General Relativity. Lecture 1 - Equivalence Principle and Tensor Analysis Lecture 2 - Tensor Mathematics Check out my Vector Viewer app to see contravar...

This is a second post on electrical circuits and their similarity to mechanical oscillators. The previous post covers the mechanical harmonic oscillator and the LC circuit. This post focuses on the...

A weight on a spring has a mathematical similarity with an electrical circuit consisting of a capacitor and inductor (LC circuit). They are both examples of harmonic oscillators which exhibit a sin...

Here is a summary of how to link code in jekyll websites. Markdown Code Snippet For very fast code blocks that do not need to be synced to an code repo, we can simply wrap code in backticks: Code...

Consider a nonnegative random variable $X$ (i.e. annual income, home value, stock price). Here is the famous Markov Inequality 1: [\begin{flalign} \mathbb E [X] &= \int_{-\infty}^{\infty} x ...

A post on how to combine an LLM with the Monte Carlo Tree Search (MCTS) algorithm. There are numerous versions of MCTS, I follow Planning with Large Language Models for Code Generation’s implementa...

Xiàngqí (Chinese Chess) Xiàngqí yǒu hěn duō jué sè. Tā mén shì: jiàng (hēi sè) huò zhě shuài (hóng sè), shì, xiàng, mǎ, jū, pào, zú (hēi sè) huò zhě bīng (hóng sè). Translation Xiangqi has many r...

Details of an experiment originally explained in Albert Einstein’s 1905 paper on Special Relativity entitled On The Electrodynamics Of Moving Bodies. The experiment consists of an electric charge a...

A follow up from my previous post on time dilation to explain length contraction. Consider a rocket ship traveling between two planets, $A$ and $B$. There is an observer on planet $A$ that observes...