Continuing my series on the interesting questions that students have asked me, in this article we look at a relatively straightforward (once you see the trick that is) algebraic problem. If you are interested, you can find all questions from this series, along with a discussion on my inspiration for…

A couple of articles ago, I discussed an interview question a student had been asked that I found interesting. An Interesting Interview Question. Very recently, one of my students had an interview for an internship at a very prestigious investment bank. They were…medium.com Recently this student came back to me with a new interview question she wanted help understanding. She claims this question has been used by companies such as Google and Microsoft. Though…

Building on my previous article, Forget The Golden Ratio, Let’s Discuss The Golden Integral! One of the first articles I ever wrote on medium discussed what I had always considered to be my favorite integral, the…medium.com we look at an alternative way to solve this integral. For more details about this integral and a quick recap on the golden ratio, please see my previous article. Just like in our first solution, we begin by setting out two important concepts which will…

Continuing my series on the interesting questions my students have asked me, in this article we look at a problem from the 1997 Polish Mathematical Olympiad. We will look at two ways to solve this problem and discuss a very useful general technique for solving problems of this form. If…

For many years, I have been using memes in my lectures. There are two main purposes for this. Firstly, they add a bit of humor to the class, something which can make a huge difference when dealing with first-year students, or when dealing with dry material. Secondly, they allow me…

One of the first articles I ever wrote on medium discussed what I had always considered to be my favorite integral, the golden integral is, however, a new contender. My favorite integral aka I don’t care what your teacher told you, π ≠ 22/7. By calculating a very simple integral we can see that π ≠ 22/7 regardless of what we were told in school.stephenwithaphd.medium.com Let’s quickly recap. The golden ratio, ϕ, is the positive solution to the equation

As some of you may have noticed, I have not published for about a month. This was because, as the title suggests, I took a break from math. This was something I had been planning to do for a while, and when the opportunity arose over December I just took…

Let’s play a game. I have 5 levels of surd-themed questions below. The game is, as you would expect, to start on level 1 (question 1) and work your way to level 5 (question 5). There is no time limit. The only rule is that you can only progress if…

Have you ever asked yourself how to calculate an irrational exponent? For example, what is the value of