## Archive for July, 2012

### What are dense Sidon subsets of {1,2,…,n} like?

July 13, 2012

The short answer if you don’t feel like reading a post with some actual mathematics in it is that I don’t know.

Now for the longer answer. A subset $A$ of $\{1,2,\dots,n\}$ is called a Sidon set if the only solutions of the equation $a+b=c+d$ with $a,b,c,d\in A$ are the trivial ones with $a=c$ and $b=d$ or $a=d$ and $b=c$. Since the number of pairs $a\leq b$ with $a,b\in A$ is $|A|(|A|+1)/2$ and $2\leq a+b\leq 2n$ whenever $a,b\in A$, it is trivial that if $A$ is a Sidon set, then $|A|(|A|+1)/2\leq 2n$, which gives an upper bound for $|A|$ of around $2\sqrt{n}$.
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### A trip to Watford Grammar School for Boys

July 7, 2012

As I said would happen in my post about a possible approach to teaching maths to non-mathematicians aged 16-18, I went last Wednesday to Watford Grammar School for Boys to try the approach out. The headmaster there, Martin Post, was remarkably helpful and assembled a usefully varied group of pupils, some from his school, some from the equivalent school for girls, and some from a nearby mixed comprehensive school (I wasn’t told which one) whose pupils receive some of their teaching in scientific subjects from Watford Grammar School. What’s more, some of the people there were doing maths and further maths, some were doing just maths, and some were not doing either. The one thing that was not representative about the group was that they were much brighter than average: for example, the non-mathematicians there had been chosen by their teachers as clever people who could have done maths but decided that they were more interested in other things. For most of the rest of this post, I’ll say what questions I discussed and how the discussions went. All but two of them were taken from the list in the earlier post.
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### A new open-access venture from Cambridge University Press

July 2, 2012

The formal launch has just taken place at the European Congress of Mathematicians in Krakow of the Forum of Mathematics, which to a first approximation is a new open-access electronic journal. However, the singular “journal” is misleading, because in some ways it is more like a whole set of journals. But there will be considerable interdependence between the elements of the set, so “journals” is misleading too. We need an intermediate number between singular and plural. Also, although the journal(s) is/are primarily electronic, there will be a print-on-demand option if anyone wants it.

What is the Forum of Mathematics?

Terminological questions aside, how will this new journal-like object work? I think the easiest way of explaining it is to describe the process for submitting an article, which is similar to the process for submitting an article to a conventional maths journal, but with one or two unusual aspects.
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