## The Harmonic Series and Friends

A lot of times, math can be deceptive and unexpected A few examples are the Monty Hall problem, the Banach-Tarski paradox, and the Weierstrass function. Today we will look at one of the most famous and classic counterexamples, that is that if a sequence converges to zero, it’s series does not necessarily converge. What does … Read more

## The Spooky Function Horror Show

Be prepared, for you are about to see some of the scariest functions this Halloween. The excerpt is like this to not spoil what’s within!

## A Tale of Drunk Worms and Random Walks

Meet Larry the worm. Larry had a wonderful night drinking at a bar with his friends. Alas, Larry got a bit too drunk, so when he and his friends finished drinking, he went to walk (err, crawl) home, drunk. Larry and his friends live on a one dimensional road. As Larry is drunk, he walks … Read more

## Necklaces and Groups. The Burnside Lemma

Here is a fun riddle: suppose you have beads in n different colors, and you want to make a necklace with say, 5 beads. How many different ways are there to do this? Well, you can first look at the possible colors for the beads: Each position can have n different colors, and there are … Read more

## Stable pairings and how to find them (Gale-Shapley algorithm and also puppies)

From dating apps to matchmaking in video games, and matching computers to the best servers, matching problems have a notable presence in computer science and game theory nowadays. So let’s look at one of this problems, which has a rather simple premise and a surprisingly simple solution. The problem deals with finding stable pairing (say, … Read more

## My goals for this blog

In order to be more focused on what content will go on this blog, I think it would be wise for me to summarize my goals for this blog. 1. Have accessible, informative, articles on various topics in mathematics: The high school curriculum in math is, to put it bluntly, absolutely awful. It gives students … Read more

## A Devious Bet: The Borel-Cantelli Lemma

Suppose you are offered a bet as follows, by a totally not evil and totally not a squid monster disguised as a man casino owner. The bet will have (countably) infinitely many steps. In each you win or lose money, the only thing the totally not a squid monster tells you is that in each step, on average, you gain money. Furthermore, that average increases as the bet goes on. Do you take it?

## Why “almost surely” a math blog?

So why is this only “almost surely” a math blog? For technical reasons, it’s because maybe in the future some posts will not be about math but related subjects (or unrelated, perhaps in 2026 this blog will be about pistachios, who knows honestly). But the major reason I chose this title is as a reference … Read more

## Newton’s Method

Let’s look at a very common problem where the use of math is needed, solving equations. We have an expression using some variable x on one side of the ‘=’ sign and another expression using x on the other. We want to find for which values of x the equation holds.

## How do we choose things? (at random)

Don’t you just hate it when you are asked to pick something “at random”? No? Well let me show you what I mean.