John D. Cook | Applied Mathematics Consulting

Suppose you've never worked at the command line and you're reading a book about the bash shell. You read that !$ is a shortcut to refer to the last word of the previous command. That little fact will almost certainly not stick in your head for a couple re

I was reading a blog post on boat names because it was on Hacker News this morning. The post contained a link to a data set on dog names in NYC and I poked around the data a little. The top names were not at all what I expected, but then again this is lim

Suppose you were able to go back in time, to an era before computers, and give someone contemporary cryptography. Encryption methods that are essentially unbreakable now would certainly be unbreakable then. But there's a catch: not only do attackers not h

The following extraordinary paragraph comes from Knuth's TAOCP Volume 4A, right before the last set of exercises. Many of the exercises below ask a modern reader to find and/or to correct errors in the literature of bygone days. The point is not to gloat

In science and engineering classes, you might describe a system using Newton's laws and end up with a differential equation. You then solve the differential equation, analytically or numerically, to see how the solutions behave. You might also do the oppo

I was reading a book on the history of the discovery of the structure of DNA 1 and was surprised by a few passing references to Bessel functions. According to Claude, When X-rays are diffracted by a helical structure, the resulting diffraction pattern bre

At the end of my post on how not to calculate cosine I said that the first step in calculating cosine, particularly cosine of a large number, would be to do range reduction. This post will present a simple range reduction method by Cody and Waite that is

I have a program that shares files between my laptop and my phone. It works well, except for apostrophes. When I type an apostrophe ' on my laptop, it becomes †on my phone. And when I type 's on my phone, it becomes 痴 on my laptop. Apparently the phone

Calculus professors with no experience in numerical computing will tell students that computers calculate trig functions with power series. They don't. I worked on the implementation of trig functions in hardware, and I can assure you we didn't just use p

The previous post pointed out that the following code such as the following unexpectedly works. from math import log, factorial log(factorial(1000)) 5912.128178488163 If you don't find this unexpected, note that if you replace math.log with numpy.log the