Strange Fruit

The poem was written by Abel Meeropol, and the performance here is by Billie Holiday. A film telling the story of the song is here. Strange Fruit Southern trees bear strange fruit, Blood on the leaves and blood at the root, Black body swinging in the Southern breeze, Strange fruit hanging from the poplar trees. … Read more

An Operator Method for Solving Second Order Differential Equations, Part 2

In a previous post we discussed an operator method for solving certain second order ordinary differential equations. In this post I’ll explore this operator method a little further. I first learned about this method from an old book, Higher Mathematics for Engineers and Physicists, by Ivan S. Sokolnikoff and Elizabeth S. Sokolnikoff, McGraw-Hill, 1941. I … Read more

Proportional Reasoning

One of the most important skills in “numerical literacy” is proportional reasoning. I was reminded of this earlier today when I went out to buy a couple of pies for this evening’s family gathering. The pies came in many flavours, and two sizes, 8 inch diameter and 10 inch diameter. There was never any question … Read more

Two Nice Probability Problems

Over at Freakonometrics, here is a pair of nice probability problems. The first problem also appears here as Problem #5. A number of solutions for your consideration are here. A very elegant solution by Ted Hwa is here. (This post first appeared at my other (now deleted) blog, and was transferred to this blog on … Read more

An Operator Method for Solving Second Order Differential Equations

In talking about power series in a previous post, I mentioned one of their uses: as an aid in solving differential equations. This reminds me of a neat trick for solving some differential equations, which I will discuss in this post. A standard method for solving linear differential equations with constant coefficients is to assume … Read more

Atoms in Mathematics and Science, Part 3: Power Series

We’ve been talking about reductionism in the past couple of posts, and we’ll continue the story by discussing power series in this post. The idea behind reductionism in mathematics is to identify some elementary “objects” and to express a complicated “thing” in terms of the elementary things. The intention is either to make it easier … Read more

Atoms in Mathematics and Science, Part 2: Infinite-Dimensional Spaces

In a previous post we began to discuss the idea of a basis in mathematics. The examples given in that post are finite-dimensional vector spaces, and in this post we are going to generalize them by giving some examples of infinite-dimensional vector spaces. But before we do this, let’s play with some motivating examples not … Read more

Atoms in Mathematics and Science; The Concept of a Basis

One of the most important tools that mathematicians and scientists use to cope with the daunting complexity of the world goes by the name of reductionism. That is, one first identifies the key parts of a complex system, then one strives to understand the parts, and finally one strives to understand how the parts fit … Read more

Words, Episode 5: World Record Super-Alliteration?

Many years ago I took a course on writing led by a wonderful man (whose name I now forget) who was a veteran of the newspaper business. He remarked one day on how difficult it is to write newspaper headlines, and that most newspapers had an editor who did nothing else but write headlines. Article … Read more