In the two previous posts in this series we explored a method for solving second order linear differential equations with constant coefficients that is different from the standard textbook methods taught nowadays. I found the method in a 1941 book (or see here) by the Sokolnikoffs. The key point of the method, as we learned, … Read more
The ancient Greeks thought of atoms as the smallest, indivisible bits of matter. By the twentieth century, experiments showed that (what we nowadays call) atoms have internal structure; a key early experiment was the Geiger-Marsden experiment, performed under the supervision of Rutherford, about which we’ll have more to say in a future post. But the … Read more
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
I was driving on Highway 406 earlier today, and I noticed a passenger van ahead of me in the adjacent lane having a bumper sticker with the words in the title of this post. Provacative, wouldn’t you say? As I passed the vehicle, I saw an advertisement for a firm called “[name withheld] Blinds and … Read more
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
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
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
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
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
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