Algorithms and probabilities

Vincent Delecroix | Castell d’Estela high school | March 1, 2018

Thursday, 1 March 2018 , Olot

Algorithms and probabilities

Algorithms and probabilities

On Thursday 1st of March I went to the school of Amer to talk about algorithms and the fact that some of them use probabilities. The audience was made of roughly 40 students between 14 and 15 years old and 3 professors. I talked about 45 minutes and we had 15 minutes for questions afterwards.

During my talk, the idea I wanted to emphasize is that at a first glance the two following topics look opposite: an algorithm (or computer program) is a sequence of operations designed to answer a given problema, and probabilities deal with non-deterministic phenomena. However there is a lot of interplay between them.

In a first part I discussed the two fundamental results of probabilities that are the “law of large numbers” and the “central limit theorem” in the context of random walk ( see picture 01 | see pictures 02 ). The main point was to show that there is some regularity in the repetition of a random event (like tossing a coin).

Then I turn to algorithms and explained how to compute areas using a random sample of points and the idea behind the Page Rank algorithm that is used by the google search engine.

It is always challenging to talk to young students. We need to know what is their background in mathematics so that the talk is understandable while keeping them interested. Some of the student questions were about the talk but also one of them as about my studies.

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