a math blog
This year s NCAA basketball tournament has just ended, which means a lot of people are currently cursing their bracket picks. That also means it s a great time for a retrospective: How could one go about picking a better bracket? There Continue reading
A few years ago I answered a question on Cross Validated about the existence of a closed form for the mean residual life of the Weibull distribution, a popular distribution in reliability analysis. The short answer is that it depends Continue reading
Recently I came across the following on a site that provides questions on probability and statistics for tech interviews. I solved it, and so I thought I would give my solution here. Suppose there is a new vehicle launch upcoming. Continue reading
In this post I m going to discuss two proofs by induction. That is, they ll both be attempts at proving a statement, but they ll both have flaws in their arguments. My hope is to alert people to potential errors when attempting Continue reading
A few months ago Mathematics Magazine published a paper of mine, A Combinatorial View of Sums of Powers. In it I give a combinatorial interpretation for the power sum , together with combinatorial proofs of two formulas for this power Continue reading
The Riemann zeta function can be expressed as , for complex numbers s whose real part is greater than 1. By analytic continuation, can be extended to all complex numbers except where . The power sum is given by . Continue reading
One of the most important theoretical results in linear programming is that every LP has a corresponding dual program. Where, exactly, this dual comes from can often seem mysterious. Several years ago I answered a question on a couple of Continue reading
It s fairly well-known, to those who know it, that . In other words, the square of the sum of the first n positive integers equals the sum of the cubes of the first n positive integers. It s probably less well-known Continue reading
Today s Google doodle honors mathematician Benoit Mandelbrot. He would have been 96 today. If you re interested in learning more about his life and work, the Google doodle link contains a short summary. If you want to go deeper, you can Continue reading
Equations of the form are called Mordell equations. In this post we re going to prove that the equation has no integer solutions, using (with one exception) nothing more complicated than congruences. Theorem: There are no integer solutions to the equation Continue reading