I just finished the book “The Monty Hall Problem” by Jason Rosenhouse, which is an exploration of one of the most counter intuitive puzzles in probability. The entire book is devoted to the basic form of the problem and a number of variations, of increasing complexity. The basic outline of ... [Read more...]

The Mandelbrot Set is possibly one of the most visually appealing mathematical visualizations. The set is defined as the set of complex numbers $c$ for which the function $f_c(z) = z^2 + c$ remains bounded when iterated – i.e. the sequence $f_c(z), f_c(f_c(z)),f_... [Read more...]

I recently read the great book Fooled By Randomness by Nicholas Nassim Taleb. There is a nice illustrative example in there on the scaling property of distributions across different time scales. The example is formulated as the hypothetical example of a dentist who has set up a home trading environment ... [Read more...]

The article https://online.wsj.com/public/resources/documents/VirtuOverview.pdf is a neat little illustration of a simple asymptotic toy distribution given an initial probability of a win or loss per-trade. It is used as an example to illustrate the basic methodology behind the working market-maker business – develop a ... [Read more...]

I was reading Simon Singh’s The Simpsons And Their Mathematical Secrets today and he mentioned a simple method for approximating e – given a uniform RNG , e can be approximated by the average number of draws required for the sum of the draws to exceed 1. This is a neat little ... [Read more...]