Algorithms and Big O Notation

I am currently enrolled in WGU, a fully online college where I am getting a Computer Science Bachelor’s degree. To help solidify the information I learn there, I am going to reiterate things here so that I can express things in the form of teaching - a tool others can use, if not a way to find my own shortcomings or areas I need to improve upon. Recently, I finished a section of a Discrete Mathematics II course on Algorithms. This section focused on the structure of what an algorithm is, asymptotic growth of functions, analysis of algorithms, and advanced analysis of algorithms. Generally, the topics discussed in this section are not complicated - but can seem that way prior to the reading. ...

March 6, 2026 · 7 min · Earl Killingsworth

Number Theory & Modular Arithmetic

More often than not, the first mathematical object we are exposed to is Integers. Integers are whole numbers, things like 1, 2, 3. These are simple, and relatively profound in their ability to represent quantities and otherwise unrelated topics. In fact, we have studied integers, known as Number Theory, for thousands of years with no real discernable purpose — until recently. That is to say, not all science comes with some clear endgoal, but it is the search in of itself that provides us with dividends. Number Theory is one such case — where we have built out a system that allows us to encrypt large amounts of data using nothing more than prime factorization for exceptionally large numbers — something that up until today, was almost entirely pointless. ...

March 6, 2026 · 9 min · Earl Killingsworth