One-step recursion in Markov chains
May 06, 2026How to intuitively solve Markov chain expectation problems, illustrated using a classic coin-flipping puzzle.
“If you're thinking without writing, you only think you're thinking.” - Leslie Lamport
How to intuitively solve Markov chain expectation problems, illustrated using a classic coin-flipping puzzle.
A simple mental model for working with graphs in Python using pointer-like assignments and node references.
We explore the theory of Markov chains using a random walk around a square.
We derive an interesting relationship between the number of additions required to compute the $n$th Fibonnaci number and the golden ratio $\varphi$.
If you have spent time grinding LeetCode, you know that certain patterns emerge. While every problem is unique, the underlying data structures used to solve them often repeat.
We derive the Direct Form I and Direct Form II implementations of a discrete-time infinite impulse response (IIR) filter from first principles.
We prove that every square can be partitioned into $n$ squares for every $n \geq 6$.
We describe what fencepost errors are, how to avoid them, and provide a precise derivation for why they occur.