Category Archives: Computation

Grading a class

Imagine we had a class with students and each week they hand in a sheet of homework. Now, you choose a set of of them at random and correct only those . At the end, the grade assigned to a … Continue reading

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The purpose of this post is to discuss the Riemann-Lebesgue Lemma, why it makes sense, and some interesting applications among which we have , the proof of which, in my opinion, explains a lot more clearly why it should equal … Continue reading

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Higher order Newton-Raphson

In this post we shall see one way to look at the Newton–Raphson formula, and the extensions this produces. Actually, I came up with this idea a few years back, while I was studying for a Numerical Analysis exam. Introduction. … Continue reading

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The fast decay of the gamma function

The purpose of this post is to discuss the fast decay of the gamma function when along the imaginary axis. This is an interesting topic, as it is not usually discussed, we are generally more interested in the increase of … Continue reading

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Binary look-and-say sequences

A few days ago, Numberphile released a video on YouTube about the famous Look-And-Say sequence, presented by John Conway himself. Just as a reminder (if you have not watched the video, which I thoroughly recommend you do), this sequence begins … Continue reading

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Generating a random permutation

It is well-known that any permutation of can be written as a product of transpositions, that is, of permutations of the form with , where we recall that is the permutation satisfying and for . In this post however, we … Continue reading

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Symmetric random walks

Definition 1 A symmetric random walk is a homogeneous Markov chain on the set of states such that with probability , and for all . In plain terms, this means that we start off at , and at each second … Continue reading

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