Here is another article that I hope to develop into an entry on the Tricks Wiki. It concerns the use of linear algebra to solve extremal problems in combinatorics. The method is quite easy to illustrate with some well-known examples, but what I find interesting is the question of how to recognise the kind of problem where the method is likely to apply. I have something to say about that, but I’d like to make clear that I didn’t think of it for myself. If I remember rightly, I read it in something that Noga Alon wrote. I’ll draw attention to it when I get there. (more…)
Archive for July, 2008
As may be obvious from the sudden increase in my posting rate (which I don’t expect to be able to keep up) The Princeton Companion to Mathematics is now off my hands, which gives me the chance to devote a bit of attention to other projects, of which the Tricks Wiki is one. So in this post I’m going to discuss a relatively elementary piece of university mathematics, and will do so in the form of a sample article for that site. I’ll be a little careful about predicting when the site itself will be up and running, but let me just say that I’ve put some work into it recently and I don’t want to waste that work.
In what follows, I shall adhere to what I hope will be the basic format of an article on the site. The most important elements of that format are that there is a brief description, or “slogan”, that encapsulates the basic idea, and a general discussion of the idea that is illustrated by several clearly delineated examples. (more…)
The Princeton Companion to Mathematics is even more nearly nearly finished than it was last time I said it was nearly finished. In fact, this time I can give a date — July 13th — past which it will be too late for me to do any work on it. The book will be printed in September and available in November.
As an example of the important issues we now face, here is a question about hyphens: I’m fairly sure there will be a small but passionate minority of mathematicians who care about these, and a question has come up. I am curious to know what other people think, so I’m not going to say what I think: I’ll just try to present the question as neutrally as possible. And here it is. (more…)