It doesn’t take much imagination to understand why DEN is the IATA abbreviation for the Denver airport, but the abbreviation MCO for the Orlando airport is more of a head scratcher. Here is a list of the busiest airports in the US along with a brief indication of the reason behind their abbreviations. Some require […]
Yesterday Terence Tao published a blog post on bounds for the Poisson probability distribution. Specifically, he wrote about Bennett’s inequalities and a refinement that he developed or at least made explicit. Tao writes This observation is not difficult and is implicitly in the literature … I was not able to find a clean version of […]
Is the function x ↦ x + 2 invertible? Sure, its inverse is the function x ↦ x − 2. Is the Python function def f(x): return x + 2 invertible? Not always. You might reasonably think the function def g(x): return x – 2 is the inverse of f, and it is for many […]
If your password is in the file rockyou.txt then it’s a bad password. Password cracking software will find it instantly. (Use long, randomly generated passwords; staying off the list of worst passwords is necessary but not sufficient for security.) The rockyou.txt file currently contains 14,344,394 bad passwords. I poked around in the file and this […]
A LaTeX document looks better than an HTML document, but an HTML document looks better than an awkward hybrid of HTML and inline images created by LaTeX. My rule is to only use LaTeX-generated images for displayed equations and not for math symbols in the middle of a sentence. This works pretty well, but it’s […]
It’s a curious and convenient fact that many decibel values are close to integers [1]: 3 dB ≈ 2 6 dB ≈ 4 7 dB ≈ 5 9 dB ≈ 8 Is base 10 unique in this regard? If we were to look at the analogs of decibels in other bases, would we see a […]
The previous post listed three posts I’d written before about images on the covers of math books. This post is about the image on the first edition of Dummit and Foote’s Abstract Algebra. Here’s a version of the image on the cover I recreated using LaTeX. The image on the cover appears on page 495 […]
Once in a while it’s necessary to calculate some function of the roots of a polynomial, and it may be possible to do this without first calculating the roots. Quadratics The quadratic formula gives explicit solutions to the equation The two solutions for x are where The awkward part is taking the square root of […]
There are five ways to parenthesize a product of four things: ((ab)c)d (ab)(cd) (a(b(cd)) (a(bc))d (a((bc)d) In a context where multiplication is not associative, the five products above are not necessarily the same. Maybe all five are different. This post will give two examples where the products above are all different: octonions and matrix multiplication. […]
Rings made a bad first impression on me. I couldn’t remember the definitions of all the different kinds of rings, much less have an intuition for what was important about each one. As I recall, all the examples of rings in our course were variations on the integers, often artificial variations. Entire functions I’m more […]
