A while ago I was helping out at an open day. The material presented gave some information about the range of assessment types we use. A potential applicant asked me “how can you do coursework for maths?”. She felt that (what she understood as) maths could only be assessed by examination. (This is presumably because her experience of the English school system has not exposed her to anything but exams for maths.)
I thought it might be interesting (to me, at least) to list the types of assessment I’ve been involved in marking in the 2015/16 academic year.
I rediscovered this nice paper by Kenneth P. Bogart in my Interesting Esoterica collection, and decided to read through it. It turned out that, while the solution presented is very neat, there’s quite a bit of hard work to do to along the way. I’m not particularly experienced with combinatorics, so the little facts that the paper skips over took me quite a while to verify.
Once I was happy with the proof, I decided to record a video explaining how it works. Here it is:
I probably made mistakes. If you spot one, please write a polite correction in the comments.
The Winton Beauty of Mathematics Garden was an entry in this year’s Chelsea Flower Show. It looks like this:
Apparently those symbols winding their way around the garden are “plant growth algorithms”, whatever those are.
There’s also a golden-ratio-thingy water feature, of course.
You can thank Winton Capital, sponsors of all sorts of worthy maths projects, for this bit of mathsy art.
Theorem: every 5-connected non-planar graph contains a subdivision of $K_5$.
The above statement, conjectured independently by Alexander Kelmans and Paul Seymour in the 70s, is very easy to say. And the video below, starring Dawei He, Yan Wang, and Xingxing Yu, makes it look very easy to prove:
It’s like they got Wes Anderson to film an academic PR video. In the normally uninspiring world of maths press releases, it’s quite refreshing. And the written press release is pretty snappy, too. Let’s not make this a thing, though.
(For once I can use an exclamation mark next to a number without wise alecks making the canonical joke)
Maths and stats! On BBC Radio 1! Who’d’ve though it!
DJ Clara Amfo and the ubiquitous Hannah Fry have got a new series on the UK’s top pop station, looking at music from a mathematical perspective.
Music by Numbers (excuse me, Music by Num83r5), is currently being broadcast at 9pm each Tuesday, and there are a couple of episodes already on iPlayer Radio to catch up on. The first is about Coldplay (records sold: millions; distinct tunes composed: 1) and the second looks at a few numbers to do with Iggy Azalea’s career.
It’s mostly a very easy listen, more a biography hung off a list of numbers than any real maths, but that might be your cup of tea. And Dr Fry’s segments do go into a little bit of depth about subjects like how the top 40 chart is calculated.
I’ll warn you now that each episode is an hour long, with a lot of music breaks. If you’re like me, your tolerance for some of the featured artists might not be sufficient to get through a whole episode in one go.
Listen: Music by Numbers on BBC Radio 1.
Since 2010, I’ve been maintaining a list of “interesting esoterica” – papers, books, essays and poems that I find interesting entirely on their own merits. It’s mainly bits of esoteric maths – hence the name – but I’ve also included quite a few things just because they have amusing titles. The main idea is that when I’m talking to someone and want to show them a cool thing that I’ve half-remembered, I can look up the exact reference: I’ve shared the paper “Orange peels and Fresnel integrals” more times than I can count (probably the same as the number of times I’ve eaten an orange).
Here are a few of the stories that we didn’t get round to covering in depth this month.
Turing’s Sunflowers Project – results
Manchester Science Festival’s mass-participation maths/gardening project, Turing’s Sunflowers, ran in 2012 and invited members of the public to grow their own sunflowers, and then photograph or bring in the seed heads so a group of mathematicians could study them. The aim was to determine whether Fibonacci numbers occur in the seed spirals – this has previously been observed, but no large-scale study like this has ever been undertaken. This carries on the work Alan Turing did before he died.
The results of the research are now published – a paper has been published in the Royal Society’s Open Science journal, and the findings indicate that while Fibonacci numbers do often occur, other types of numbers also crop up, including Lucas numbers and other similarly defined number sequences.