Yesterday, I had another article published for The Conversation. I wrote about the Birthday Problem, which (I think!) is well known to most mathematicians, but certainly not to the general public. Anyways, it was very well received. I guess it's a bit sad that there's a ton of crazy maths facts like this that we … Continue reading The Birthday Problem

# Author: A. W. Dudek

# A sledgehammer proof of irrationality

Mathematical proofs are a bit like people. You can choose which ones to love and which ones to spit at. The loveable proofs are undoubtably the most important, especially as a pick-me-up on those cold lonely days. I'd like to share with you all a little proof that the $latex n$th root of 2 is … Continue reading A sledgehammer proof of irrationality

# Merten’s Function

I thought that today I might write about my most favourite arithmetic function. The Moebius function $latex \mu:\mathbb{N} \rightarrow \{-1,0,1\}$ is defined as follows: $latex \mu(1)=1$, $latex \mu(n)=0$ if $latex n$ is divisible by $latex m^2$ for $latex m>1$, and $latex \mu(n)=(-1)^k$ if $latex n$ is a product of $latex k$ distinct prime numbers. So … Continue reading Merten’s Function

# The Monty Hall Problem

Another article of mine has just been published by The Conversation. Click here to get on and read it.

# The Erdős-Straus Conjecture

Here's a cute little problem.Can every number of the form $latex 4/n$ (where $latex n$ is an integer) be written as the sum of three unit fractions? (A unit fraction is a fraction of the form $latex 1/a$ where $latex a$ is an integer.)For example, if $latex n = 5$ we have$latex \frac{4}{5} = \frac{1}{2} … Continue reading The Erdős-Straus Conjecture

# Almost Twin Primes

For a quick introduction to the theory of prime numbers, see my earlier post. A mathematician by the name of Yitang Zhang made the news last week, for taking a step towards the twin prime conjecture. This conjecture asserts that there are infinitely many pairs of prime numbers that differ by 2. We call such pairs … Continue reading Almost Twin Primes

# Subspaces – A Quick and Easy Introduction

Dear MATH1115 student, Want to become a master of subspaces? Check this out! Mathematically yours, Adrian. P.S. If "Mathematically yours" is too weird, then please replace it with "yours". P.P.S. I've written the word "yours" too much, and now that thing has happened to my brain where it looks like a funny word.