Algebra – Almost Surely a Math Blog

The Paradox of Periodicity (of Functions)

July 23, 2023December 22, 2019 by VV

You know periodic functions right? Functions that after a certain place start repeating, for example sin(x): More formally, a function f is called periodic is for some constant p>0, f(x+p)=f(x). In other words, shifting by p does not affect f(x). The constant p will be called the period of the function (sometimes we say f … Read more

Necklaces and Groups. The Burnside Lemma

July 23, 2023September 18, 2019 by VV

Here is a fun riddle: suppose you have beads in n different colors, and you want to make a necklace with say, 5 beads. How many different ways are there to do this? Well, you can first look at the possible colors for the beads: Each position can have n different colors, and there are … Read more