Watch mathematician and entrepreneur Anne-Marie Imafidon MBE explain binary numbers. Anne-Marie studied for an MSc in mathematics at Oxford University, and founded the social enterprise Stemettes to encourage more women and girls into STEM careers.
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Watch mathematician and data scientist Jonny explain mathematical modelling of networks.
The Further Maths Support Programme is an organisation in the UK that supports students wishing to take an A-level in Further Maths. Since this isn’t offered in all schools and colleges, the Programme helps organise tuition for people who can’t do it through their school, but also encourages students at younger ages to consider taking the A-level through workshops and university visit days. They also run excellent training courses for teachers, and have a number of resources on their website for students and teachers, including problem solving materials, videos, podcasts and maths competitions.
According to a recent blog post by maths teacher Jo Morgan, a government review has made the FMSP’s future precarious. Their funding through the Department for Education will be removed next April, and they’ll be replaced by the “Level 3 Maths Support Programme”. The L3MSP will support Core Maths as well as A level mathematics and further mathematics, but will focus on only certain geographical areas, meaning many will lose access to the resources currently provided.
Two of the programmes previously supported by the same funding have already had their funding stopped – the Core Maths Support Programme, and Underground Maths – but the FMSP hasn’t finished yet, and Jo hopes that by contacting the DfE we could convince the government to continue funding it. As they point out in the blog post, the FMSP has made a huge difference to the numbers of students taking maths and has had a direct impact in classrooms supporting teachers all over the UK.
In September, Katie and Paul spent a week blogging from the Heidelberg Laureate Forum – a week-long maths conference where current young researchers in maths and computer science can meet and hear talks by top-level prize-winning researchers. For more information about the HLF, visit the Heidelberg Laureate Forum website.
At the start of his HLF lecture on Asymptotic Group Theory on Thursday morning, Fields medalist Efim Zelmanov described the ‘group’ as: “the great unifying concept in mathematics,” remarking “if you go for a trip, and you are allowed to take only two or three mathematical concepts with you, give serious consideration to this one.” Very loosely defined, a group is a set of things (its ‘elements’) that you can ‘multiply’ together, with this multiplication behaving in certain helpful ways. Think of numbers being added, functions composed together or rotations and reflections of a shape being carried out one after the other. I doubt any mathematician would accuse Zelmanov of overstating their importance in mathematics.
In his talk he discussed residually finite groups. These are groups which are infinite in size but still just a little bit finite-y. In technical terms, the group has a set of homomorphisms with finite kernels having trivial intersection. Although the group is too large to see all at once, as Zelmanov put it, we have “photos from all sides of the group”. He contrasted this to “hopelessly infinite groups”, for which no such photo album is possible.
A common way to look at a group is to find a set of ‘generators’: these are elements of the group which you can multiply together to create any element of a group (the elements ‘generate’ the entire group). Some infinite groups can’t be generated from a finite set — consider trying to find a set of rational numbers that you can multiply together to create any rational number. Those that can be generated from a finite set are unexcitingly called ‘finitely generated’. Of course, finite groups are also finitely generated.
Zelmanov considered under what circumstances finitely generated groups can be proved to be finite. One immediate way this won’t happen is if one of the generators is not periodic: if you keep multiplying it by itself you keep getting new elements forever, never ‘looping back’ to the original generator. (Imagine starting with 1 and continually adding 1…) The Burnside problem asks whether there are any other ways to make a finitely-generated, yet infinite, group. In 1991, Zelmanov proved that for residually finite groups, there aren’t. However, this isn’t the case for the ‘hopelessly infinite’ groups.
In his lecture Zelmanov, accompanied by his excellent hand-drawn slides, discussed this before moving on to related topics such as the growth of groups (if you start with a generating set, and create new elements by multiplying them together, how quickly does the set grow?) and ‘approximate groups’ (which, as the name suggests, are things that are like, but not quite, groups).
You may by now have seen the image below knocking around on Twitter and other social medias, in which a maths question appears to be almost a parody of itself:
The text reads:
An orchestra of 120 players takes 40 minutes to play Beethoven’s 9th Symphony. How long would it take for 60 players to play the Symphony? Let P be the number of players and T the time playing.
Well, once you’re done laughing, we’ve done some investigative journalism and found the origin of this question. And it turns out it’s quite nice!
I wrote this!! How did you get this??? I am a maths teacher in Nottingham UK. Wrote this 10 years ago. Here is the original whole worksheet pic.twitter.com/jYX55GSBKz
— Claire Longmoor (@LongmoorClaire) October 11, 2017
The question is from a worksheet developed by maths teacher Claire Longmoor (who is, based on current evidence, brilliant) ten years ago. Claire put together a selection of example questions with relationships in direct and inverse proportion, and deliberately included the orchestra question as an example of something where it doesn’t work that way. It’s a nice activity to help reinforce the difference, and in context the question works nicely.
Other examples on the sheet include a bricklaying example with creditably diverse gender representation, a car with terrifyingly low fuel efficiency, good cow names and a delightful insight into the bygone world of fruit picking.
Ritangle, a maths competition aimed at A-level and equivalent maths students in the UK, is open for registration. The first set of preliminary questions has already been released, but the main competition starts on 9th November and there’s still time to register a team.
Comprising 21 questions over 21 days, the competition requires no maths beyond A-level and the winning teams gets a hamper and a trophy.
Marcus du Sautoy has tweeted about a mathematics and music project he’s involved in, called The Sound of Proof. Five classical proofs from Euclid’s Elements have been interpreted by composer Jamie Perera into musical pieces, and they’ve put together an app/game to see if you can work out which one corresponds to which.
They’ll be announcing the results at an event as part of Manchester Science Festival in October. The project is a collaboration with PRiSM, the research arm of the Royal Northern College of Music in Manchester.