Introduction After writing a post about one interesting way to arrive at a closed-form for the $n$th term of the Fibonacci sequence, a friend pointed out a few alternative ways to get there, one o...

Introduction The Fibonacci sequence is a mathematical object that has garnered much fascination over the centuries due to its simplicity and knack for rearing its head in all sorts of unexpected p...

The General Idea Over this past summer (2020), I took Stanford’s EE364A course, which is about a subdiscipline of mathematical optimization called convex optimization. I learned that it has myriad...

(This post assumes you’ve read, at least, this and this.) All of the posts on infinity that I’ve written to this point have pointed to two different infinite sizes, or cardinalities. The first is ...

Introduction In statistics, the overarching goal – in some sense – is to figure out how to take a limited amount of data and reliably make inferences about the broader population we don’t have data...

Introduction When I say that Alice is better than Bob at chess, I’m effectively asserting that barring careless mistakes, Alice should always beat Bob. This notion, of Alice “being better than” Bob...

Introduction Very often, finding exact answers is a pain; ballpark estimates usually suffice. When you’re nervous to board a plane, you don’t care to calculate the exact probability that the plane ...

Introduction This post’s title is intentionally vague. Usually, I write an introduction that describes the path the post will walk and then I meander down that path from beginning to end, and write...

Introduction In non-mathematical disciplines, it is very often the case that approaching the same question in different ways will lead you to different conclusions. One of the beautiful qualities o...

Introduction A theme of the many posts I’ve written over the last few years is that there are deep and beautiful connections we find between apparently different areas by appealing to a little bit ...