New blog!!!


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My blog is being migrated to mathspp.com!!
O meu blogue está a ser migrado para o meu novo site: mathspp.com!!

  - RGS

Popular posts from this blog

Pocket maths: how to compute averages in your head

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...
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Tutorial on programming a memory card game

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Pt En Este post vai ser um tutorial, não muito detalhado, sobre como fazer um jogo de memória com Python e pygame. O jogo que vamos implementar é um jogo comum: viramos uma série de cartas para baixo e temos que as virar duas a duas, tentando encontrar os pares. Claro que quando viramos duas cartas que não são um par, temos de as voltar de novo para baixo. Quando estou a criar um jogo, gosto de o ir desenvolvendo por etapas funcionais: partir o processo em várias fases que representem pontos nos quais eu tenho algo que posso testar. Deste modo, não só o processo se torna muito mais interessante, como posso ir controlando o aspeto do que estou a produzir. Deixo de seguida uma lista das etapas que eu pensei para este projeto; cada ponto da lista descreve a funcionalidade que o jogo já suporta: Criar um ecrã onde mostro todas as cartas dispostas, face para baixo; Clicar em cima de uma carta faz com que ela se vire para cima; Clicar na segunda carta verifica se encontrei...
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Markov Decision Processes 02: how the discount factor works

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Pt En In this previous post I defined a Markov Decision Process and explained all of its components; now, we will be exploring what the discount factor $\gamma$ really is and how it influences the MDP. Let us start with the complete example of last post: In this MDP the states are Hungry and Thirsty (which we will represent with $H$ and $T$) and the actions are Eat and Drink (which we will represent with $E$ and $D$). The transition probabilities are specified by the numbers on top of the arrows. In the previous post we put forward that the best policy for this MDP was defined as $$\begin{cases} \pi(H) = E\\ \pi(T) = D\end{cases}$$ but I didn't really prove that. I will do that in a second, but first what are all the other possible policies? Well, recall that the policy $\pi$ is the "best strategy" to be followed, and $\pi$ is formally seen as a function from the states to the actions, i.e. $\pi: S \to A$. Because of that, we must know what $\pi(H)...
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