On the Number of Cycles in Randomly Selected Permutations

In this article we derive the distribution, mean and variance of the number of cycles in a randomly selected permutation of the first n integers.     

On the infinitude of the prime numbers

Euclid’s elegant proof that there are infinitely many prime numbers is well known. Elder proved the same result, in fact a stronger one, byanalytical methods. This article gives an exposition of Euler’s proof introducing the necessary concepts along the way.