Mathspp: mathematics and programming

Pt En I have a childhood friend that had very interesting toys... He used to play around with circuits, multimeters, LED lights, small batteries, etc. I loved going to his house and watch him play with all that. That is probably why I find circuits (in their basic form) very interesting: the current flowing and the logic gates operating on the circuits and whatnot. Because of that, in this post I will show you how to build an 8-bit addition calculator just with circuits! For that I will be using logic.ly , a circuits simulator that I can run in my browser. The best way to go about this is by starting with small components and then using a nice feature of logic.ly, which enables one to create "integrated circuits": it takes one circuit we created and transforms it into a single piece. Of course that before anything else one must know how to add two numbers in binary. It is essentially the same as in with decimal numbers, except that $1 + 1 = 10$ now. To c...

Pt En < change language In this post I want to showcase the beginning of what I think will be a really cool project. After reading a really nice book (that Bill Gates himself recommends) on machine learning, I decided to experiment with genetic algorithms. For that matter, the main goal here will be to develop a genetic algorithm that teaches a vacuum cleaner how it should move in a dirty room to clean it in the best way possible (that is what is happening in the animation above). The first step is to define what I mean by room : a room will be a rectangular grid where each cell has a number from $0$ to $1$. A cell with a $0$ is perfectly clean and a cell with a number $1$ is as dirty as a piece of floor can get. Below we see a $5\times 5$ room with a robot (in red) already in the middle of the room: As I read in The Master Algorithm (and frankly I found it very enlightening), when one is going to use genetic algorithms we must previously define the structu...