Mathspp: mathematics and programming

Pt En Being able to do basic arithmetic calculations in your head is a great skill. Not because it is sexy but because it is useful in your daily life: it can help you check the change you are given when shopping, it can help you know if you will have enough money to pay for your groceries, it can help you estimate how much things cost after the discounts, etc... This often reduces to being able to sum and subtract decently; sometimes you need to make a couple of small multiplications, but that is it. More likely than not, you don't need to compute averages every day. But sometimes you just want the scoring average of your team for the past few games, or the average price per person of a given meal, or the average time you spent stuck in traffic this past week... And averages may appear nastier than simply adding or subtracting, because averages also require you to perform a division: in fact, you have to add all the numbers you want and then divide the total by ho...

Pt En The Hill cipher is a very simple cipher that works by using modular arithmetic and matrices. In a nutshell, your key is a matrix in some $\mathbb{Z}_m$ and you encrypt messages by breaking them up into pieces and then multiplying the pieces by the key matrix. That's it. I will be giving a workshop on this subject in a near future, and so I decided to write a Python notebook with a brief explanation of how the Hill cipher works, as well as providing an implementation of said cipher. The notebook can be downloaded and read here . I will be glad if you leave any suggestions/comments in the section below! A cifra de Hill é uma cifra simples que faz uso de noções de aritmética modular e de álgebra linear (mais concretamente, matrizes). Em duas frases, a cifra de Hill tem como chave uma matriz num dado $\mathbb{Z}_m$ e o modo como encripta mensagens é partindo-a em bocados com o mesmo tamanho e depois multiplicando a matriz chave por esses bocados. Num...