Mathigon

This is a guest post from Philipp Legner, the creator of Mathigon an interactive maths education platform.

Every year, thousands of students around the world ask themselves why they have to learn mathematics. Calculators can do long division. You can look up the quadratic formula on the internet. And when will you ever need calculus in everyday life? It seems like they have a point.

In fact, the maths curriculum has not changed significantly in the last 50 years. Its primary focus is on memorising rules and procedures which can be used to solve standardised exam questions. I created Mathigon because I strongly believe we need to change this – not only to make mathematics more enjoyable for students, but also to teach different skills that are much more useful in life: problem-solving, abstraction, logical reasoning, creativity, and curiosity.

Talking Maths in Public

In 2017, the University of Bath hosted the first Talking Maths in Public conference, a gathering for UK maths communicators. As part of the event, attendance bursaries were awarded to students interested in maths outreach, and the recipients of the bursaries wrote about their experiences. To celebrate the fact that a second TMiP conference will be happening this year (booking is open now, and we’re all going to be there!), we’re sharing their report of TMiP 2017. You can find out more about this year’s event (which also includes a bursary scheme) at talkingmathsinpublic.uk.

This post was jointly written by Imogen Morris, (University of Edinburgh), David Nkansah (University of Glasgow) and Olivia Sorto (University of Edinburgh).

Elwyn Berlekamp has left us

In memory of Elwyn Berlekamp, who passed away on 9th April, Colin Wright has shared with us this post from his blog.

I remember meeting Elwyn Berlekamp.

Scientists call for an end to statistical significance

A group of over 800 scientists have signed their names to an article published in Nature, explaining why statistical significance shouldn’t be relied on so heavily as a measure of the success of an experiment. We asked statistics buff Andrew Steele to explain.

realhats: Writing a $\LaTeX$ Package

A few months ago, Adam Townsend went to lunch and had a conversation. I wasn’t there, but I imagine the conversation went something like this:

Smitha: Hello.
Smitha: You know how the \hat command in LaTeΧ puts a caret above a letter?… Well I was thinking it would be funny if someone made a package that made the \hat command put a picture of an actual hat on the symbol instead?
Adam: (After a few hours of laughter.) I’ll see what my flatmate is up to this weekend…
Jeff: What on Earth are you two talking about?!

As anyone who has been anywhere near maths at a university in the last ∞ years will be able to tell you, LaTeΧ (or $\LaTeX$) is a piece of maths typesetting software. It’s a bit like a version of Word that runs in terminal and makes PDFs with really pretty equations.

By default, LaTeΧ can’t do very much, but features can easily added by importing packages: importing the graphicsx package allows you to put images in your PDF; importing geometry allows you to easily change the page margins; and importing realhats makes the \hat command put real hats above symbols.

Changing the behaviour of \hat

By default, the LaTeΧ command \hat puts a pointy “hat” above a symbol:

After Adam’s conversation, we had a go at redefining the \hat command by putting the following at the top of our LaTeΧ file.

\renewcommand{\hat}[1]{     % We put our new definition here }

After a fair amount of fiddling with the code, we eventually got it to produce the following result:

We were now ready to put our code into a package so others could use it.

How to write a package

A LaTeΧ package is made up of:

• a sty file, containing a collection of commands like the one we wrote above;
• a PDF of documentation showing users how to use your package;

It’s quite common to make the first two of these by making a dtx file and an ins file. And no, we have no idea either why these are the file extensions used or why this is supposedly simpler than making a sty file and a PDF.

The ins file says which bits of the dtx should be used to make up the sty file. Our ins file looks like this:

\input{docstrip.tex}\keepsilent\usedir{tex/latex/realhats}\preamble  *License goes here*\endpreamble\askforoverwritefalse\generate{   \file{realhats.sty}{\from{realhats.dtx}{realhats}} }\endbatchfile

The most important command in this file is \generate: this says that that the file realhats.sty should be made from the file realhats.dtx taking all the lines that are marked as part of realhats. The following is part of our dtx file:

%\lstinline{realhats} is a package for \LaTeX{} that makes the \lstinline{\hat}%command put real hats on symbols.%For example, the input \lstinline@\hat{a}=\hat{b}@ will produce the output:%[\hat{a}=\hat{b}]%To make a vector with a hat, the input \lstinline@\hat{\mathbf{a}}@ produces:%[\hat{\mathbf{a}}]%%\iffalse%<*documentation>\documentclass{article}\usepackage{realhats}\usepackage{doc}\usepackage{listings}\title{realhats}\author{Matthew W.~Scroggs \& Adam K.~Townsend}\begin{document}\maketitle    \DocInput{realhats.dtx}\end{document}%</documentation>%\fi%\iffalse%<*realhats>\NeedsTeXFormat{LaTeX2e}\ProvidesPackage{realhats}[2019/02/02 realhats]\RequirePackage{amsmath}\RequirePackage{graphicx}\RequirePackage{ifthen}\renewcommand{\hat}[1]{    % We put our new definition here}%</realhats>%\fi

The lines near the end between <*realhats> and </realhats> will be included in the sty file, as they are marked at part of realhats.

The rest of this file will make the PDF documentation when the dtx file is compiled. The command \DocInput tells LaTeΧ to include the dtx again, but with the %s that make lines into comments removed. In this way all the comments that describe the functionality will end up in the PDF. The lines that define the package will not be included in the PDF as they are between \iffalse and \fi.

Writing both the commands and the documentation in the same file like this means that the resulting file is quite a mess, and really quite ugly. But this is apparently the standard way of writing LaTeΧ packages, so rest assured that it’s not just our code that ugly and confusing.

What to do with your package

Once you’ve written a package, you’ll want to get it out there for other people to use. After all, what’s the point of being able to put real hats on top of symbols if the whole world can’t do the same?

First, we put the source code of our package on GitHub, so that Adam and I had an easy way to both work on the same code. This also allows other LaTeΧ lovers to see the source and contribute to it, although none have chosen to add anything yet.

Next, we submitted our package to CTAN, the Comprehensive TeΧ Archive Network. CTAN is an archive of thousands of LaTeΧ packages, and putting realhats there gives LaTeΧ users everywhere easy access to real hats. Within days of being added to CTAN, realhats was added (with no work by us) to MikTeX and TeX Live to allow anyone using these LaTeΧ distributions to seemlessly install it as soon as it is needed.

We figured that the packaged needed a website too, so we made one. We also figured that the website should look as horrid as possible.

How to use realhats

So if you want to end fake hats and put real hats on top of your symbols, you can simply write \usepackage{realhats} at the top of your LaTeΧ file.

Buzz in when you think you know the answer

Aperiodical guest author Andrew Taylor writes about an intriguing piece of number theory which turns out to also be something else.

How many ways are there of writing some natural number $n$ as the sum of two squares?

$$n = p^2 + q^2$$

I don’t want an answer for some particular $n$. I don’t even want a general formula. I just want to know… on average.