Matching Theory
Matching theory is an active field in mathematics, economics, and computer science. It ensured a Nobel memorial prize for Alvin E. Roth and Lloyd S. Shapley in 2012. The theory is applied in the real...
View ArticleMore than Infinitesimal: What is “dx”?
Problem Many people have asked this question, and many will continue to do so. It is the natural question of someone first learning the subject of calculus: what is “\(\mathrm{d}x\)”, and why is it...
View ArticleHomology: counting holes in doughnuts and why balls and disks are radically...
There are some questions that are really easily posed, have an obvious answer, but are in fact really, really hard to answer in a mathematically satisfactory way. Two examples are: How many holes does...
View ArticleDealing with Risk
Dealing With Risk Consider a small company which uses a million dollar machine as an essential part of its operations. Suppose that there is a 10% chance that the machine will break down and need...
View ArticleClimbing the ladder of hyper operators: tetration
Arguably the first math lesson we’ve had – ever – dealt with counting. Soon, we’re exposed to addition, and later, multiplication. Finally, when we’re fresh into middle school, we take on...
View ArticleWelcome the new trio of moderators of 2014
The MSE elections are over. Sure, this is a bit late, but that’s no excuse not to be excited. Welcome the new moderators! We should also take a moment to thank the retiring moderators Alex Becker and...
View ArticleAnother proof of Wilson’s Theorem
While teaching a largely student-discovery style elementary number theory course to high schoolers at the Summer@Brown program, we were looking for instructive but interesting problems to challenge our...
View ArticleWhen can we do induction?
Introduction Every so often, the question comes up (either here or elsewhere) of why induction is a valid proof technique. And this is of course a very natural question. Induction is after all rather...
View ArticleOn the Möbius function
The Möbius function is a rather useful one, especially when dealing with multiplicative functions. But first of all, a few definitions are in order. Definition 1: Let \(\omega(n)\) be the number of...
View ArticleSome Statistics on the Growth of Math.SE
(or How I implemented an unanswered question tracker and began to grasp the size of the site.) I’m not sure when it happened, but Math.StackExchange is huge. I remember a distant time when you could,...
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