The Gambler’s Ruin Problem

When going to a casino, most people plan on one of two outcomes being true when they leave; either they have more money than they started with, or they are leaving with their pockets empty. But did you know that there is a way to calculate the odds of these outcomes?...

The Fibonacci Word

I’m sure you’ve heard about Fibonacci numbers, but what about the Fibonacci word? Like how Fibonacci numbers are created by repeated addition, the Fibonacci word is created by the repeated concatenation of the previous numbers in the sequence. Next...

Continuity and the Popcorn Function

I will be discussing continuity and the popcorn function.  First the basic definition from pre-calc, a function you can draw smoothly without lifting up your pen. You can all picture these kinds of functions. There exists a function that breaks this intuition. It is...