Math

A monoid is one of the smallest useful abstractions in algebra: a set closed under an associative binary operation, with an identity element. That simplicity is exactly why it shows up everywhere—from summing numbers and concatenating strings to powering divide-and-conquer algorithms and elegant data structures like finger trees. This post walks through what monoids are, why they give you “compute power” for free when you can phrase a problem in terms of them, and how to think about choosing the right monoid and predicate when you do.

I’m reading Linear Algebra Done Right by Axler and found the section on quotient spaces difficult to understand, so I researched and took these notes. Definitions 3.95 notion: $v + U$ Suppose $v \in V$ and $U \subseteq V$. Then $v + U$ is the subset of $V$ defined by…

@miloyip has published a post recently which motioned the Alias Method to generate a discrete random variable in O(1). After some research, I find out that it is a neat and clever algorithm. Following are some notes of my study on it.