The topic of numeral systems is something I wanted to cover in the previous post on number theory. That post got too long before I could even get to it, however. So, here we are, talking about it now. This topic is about the concrete ways of representing the otherwise abstract notions of numbers. Both in written form, as well as when stored as information in other types of media, like computer memory.

[Continue reading]## Introduction to Number Theory: The Basic Concepts

Hi, everyone. Today I want to talk about **number theory**, one of the most important and fundamental fields in all of mathematics. This is a field that grew out of arithmetic (as a sort of generalization) and its main focus is the study of properties of whole numbers, also known as integers.

Concepts and results from this field are important enough to have implications for (and be used in) almost every branch of mathematics. And not just mathematics. Number theory is also extremely fundamental to fields like cryptography and computer science and has applications in many other sciences, like physics and chemistry.

[Continue reading]## Cryptography During World War I

Welcome to part 5 of my series on cryptography! Today, the focus is going to be on codes and ciphers used during World War I. With a special focus on the most notable ciphers, as well as a particular code and the message it was used to encode. The … [Continue reading]

## Mean and Variance of Discrete Uniform Distributions

In today's (relatively) short post, I want to show you the formal proofs for the mean and variance of discrete uniform distributions. I already talked about this distribution in my introductory post for the series on discrete probability … [Continue reading]

## Euclidean Division: Integer Division with Remainders

In today's post I want to talk about Euclidean division. This is a more general definition of division between two integers because, unlike regular division, it's defined for any pair of integers (except when the divisor is 0). I originally wanted to … [Continue reading]

## Negative Numbers and Arithmetic: Intuition

Hi everyone, and welcome to the next post from our journey in the world of numbers. Where we last left off, I was telling you about natural numbers — the objects that most naturally appear when we make our first steps in the world of Mathematics. … [Continue reading]

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