Factorial Approximations


n! (and its logarithm) keep showing up in the analysis of algorithm. Unfortunately, it’s very often unwieldy, and we use approximations of n! (or \log n!) to simplify things. Let’s examine a few!

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How many bits?


In this quarantine week, let’s answer a (not that) simple question: how many bits do you need to encode sound and images with a satisfying dynamic range?

Let’s see what hypotheses are useful, and how we can use them to get a good idea on the number of bits needed.

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