Blog Archives

On Dirichlet’s approximation theorem

June 19, 2011
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On Dirichlet’s approximation theorem

This is one of my favourites: in 1840 the German mathematician Dirichlet proved an elegant theorem, known as “Dirichlet’s approximation theorem“. The proof is surprisingly simple, but the usefulness of the proposition in some fields of mathematics, such as Diophantine analysis is remarkable. It goes as follows: Let a be a real number and N

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R-bloggers

June 19, 2011
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R-bloggers

This humble blog is proudly part of R-bloggers, since a couple of weeks. I had this website as my homepage for some months now and I have found therein really inspiring and informative things. So I wish all the best to Tal Galili and his great job with...

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Always learn and never know

June 3, 2011
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Always learn and never know

I have been using R for about two years, with no previous coding background. So, I feel like the title says, “always learn and never know”. This time, I decided to use R to study a simple, non-statistical problem that came up some time ago. Suppose the exponential function 2^x and the parabola x^2. One

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Dicetributions – episode I

May 29, 2011
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Dicetributions – episode I

Suppose the following game with two players: In every round, the two players pick a random number, each. Instead of using a dice, they pick a number from an interval. Player A picks a number from and player B from . Variation 1. The greater number wins. Who is more likely to win? It

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Music file graphs with R

May 22, 2011
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Music file graphs with R

Today we will use R to extract some interesting summary statistics regarding the music files stored in the computer. For all mp3 files I keep certain metadata in their ID3 tag. We will use this information to explore the distribution of music files with respect to the year of release. All the following are done

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Smaller or greater? – episode II

May 20, 2011
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Smaller or greater? – episode II

In a previous post I introduced the following game: Suppose you play the following game: Someone holds a set of cards with the numbers {1,2,…,N} in random order, opens up the first card and asks if the next card is greater or smaller. Every time you predict correctly, you get one point, while every wrong

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