Category Archives: exposition

Pace's derivation of Euler's sum of reciprocals of squares

One of my favourite identities in mathematics is the sum of the reciprocal of the squares $$1 + \frac{1}{4} + \frac{1}{9} + \frac{1}{16} + \cdots = \frac{\pi^2}{6}.$$ This summation, first derived by Euler, is known as the Basel problem. It is perhaps the most natural sum to consider after the harmonic sum $1 + 1/2 […]

How to make your own WordPress theme

This is a meta post on blogging, not mathematics. Recently, I got it into my head that I should design my own WordPress theme from scratch. As a consequence, you may have noticed that the theme of this blog has changed a little. I don't know if many other math bloggers will want to try […]

Switching the order of summation

Characteristic functions have magical properties. For example, consider a double summation: $$\sum_{k=1}^M\sum_{r=1}^k a_{r,k}.$$ How do you switch the order of summation here? A geometric way to think of this is arrange the terms out and "see" that this sum must be equal to $$\sum_{r=1}^M\sum_{k=r}^M a_{r,k}.$$ I find this unsatisfactory because the whole point of good […]

Book Review: Jayawardhana's "Neutrino Hunters"

A neutrino is a ultra low mass chargless subatomic particle that is produced in a variety of nuclear reactions such as beta decay. Neutrinos are incredibly abundant, but because of their size and lack of charge, they pass through almost anything and are extremely difficult to detect. Ray Jayawardhana's book Neutrino Hunters is a fascinating […]

Six Tips for Math Bloggers

Math blogging is a fun part of being a mathematician. For me, it's an aid to reading literature and an outlet for my writing prediliction. Blogging is cool because you write whatever you want without having to worry about the sometimes arbitrary and muddled standards of publication. But how do you do it? In this […]