How to attract teen boys to mathematics?

September 14th, 2014 by ajb

Putting a porn star on the front of your textbooks could be one method…

porno

Link
Porn Star Accidentally Ends Up on Math Book Cover

The future of Scottish research?

September 13th, 2014 by ajb
Flag I have not yet really thought about this, but Scottish independence must bring with it the question of the role of the UK research councils in Scotland. I imagine that Scotland would have to set up its own research councils independently of the UK councils.

This then brings in the question of the future of science in Scotland, especially in the short to mid term during a transition period. It would then be a question of if the Scottish government and the people see science as a worthwhile investment. Coupled with that must be the long term stability of science funding.

Nearly everybody that has spoken to me is very worried if there’s a yes vote.

Prof Sir Paul Nurse, President, Royal Society talking to the BBC

There are some fantastic people in Scotland working in mathematical physics and related subjects, for example there is the Edinburgh Mathematical Physics Group, which part of the Maxwell Institute for Mathematical Science. It would be a shame if the already tough job of getting funding becomes harder for mathematicians and physicists working in Scotland.

Worrying times for researchers based in Scotland I would say.

Link
Scottish independence: Future of science contested, BBC News.

Linearisation & linear duals of graded bundles and weighted algebroids

September 2nd, 2014 by ajb
I have now placed a preprint on the arXiv entitled “Linear duals of graded bundles and higher analogues of (Lie) algebroids” (arXiv:1409.0439 [math-ph],) which is joint work with J. Grabowski and K. Grabowska.

In this preprint (which we will shortly submit for publication) we develop some technology based on n-tuple graded bundles as first studied by Grabowski & Rotkiewicz, to define the notion of a linear dual of a graded bundle. As graded bundles are not simply vector bundles, they are polynomial bundles, the notion of a dual is not immediately obvious. We propose that the linear dual of a graded bundle be a particular reduction of the cotangent bundle of the said graded bundle. Related to the linear dual is the notion of the linearisation functor which takes a graded bundle and produces a double graded bundle for which the two side bundles are vector bundles. The linearisation can also be understood in terms of a particular reduction of the tangent bundle of the graded bundle.

From there we define the notion of a weighted skew/Lie algebroid, which is loosely a skew/Lie algebroid carrying some extra gradings. Interestingly, these objects are closely related to higher Lie algebroids as defined by Voronov in terms of a weight-one homological vector field on a non–negatively graded supermanifold and the $latex \mathcal{VB}$-algebroids as studied by Mackenzie, Gracia-Saz & Mehta and most recently by Brahic, Cabrera & Ortiz.

There are plenty of canonical examples of weighted algebroids including tangent bundles of graded bundles, the linearisation of higher order tangent bundles and in particular the reduction of higher order tangent bundles on Lie groupoids, again via linearisation.

For all the details and proper references consult the preprint.

This work is purely theoretical mathematics, though we are now looking towards applications in geometric mechanics. So watch this space…

Look who I bumped into in Warsaw!

August 30th, 2014 by ajb

Just thinking about some mathematical problems related to sigma models and string theory wandering round the new physics building in Warsaw…there are some nice views of the city from the 5th floor

warsaw window 1
View from the 5th floor

close up
Pałac Kultury i Nauki

Then just around the corner I met this man…

einstein

However, much like Banach, he was not very talkative… my regular coffee guy is a much better conversationalist and knows a thing or two about sigma models.

My brother on Knotweed News report

August 29th, 2014 by ajb

My brother, Dr G.W. Bruce appeared on the local news in relation to the Japanese knotweed (Fallopia Japonica) problem. Scientists at Swansea University are conducting the largest field trials in Europe to find new ways of killing knotweed.

weed
Fallopia Japonica

Follow the link below for the news report.

Link
Swansea University scientists trial knotweed killers BBC Wales News

UPDATE You can read more about the project, and see a picture of my little younger brother here.

Assume spherical sheep in vacuum…

August 27th, 2014 by ajb
sheep Scientists have now used GPS to uncover the rules that describe how sheepdogs are able to herd sheep.

Strömbom et al [1] have shown that there are surprisingly few rules here; in fact they suggest just two rules.

  1. The sheepdog learns how to make the sheep come together in a flock.
  2. Whenever the sheep are in a tightly knit group, the dog pushes them forwards.

The sheepdogs make the most of what is know as “selfish herd theory”, that is the tendency of a given sheep to want to be near the centre of the flock when under threat.

There is a Welsh connection here. One of the authors, Dr. A. King is based at Swansea University, which is where I studied for my undergraduate degree.

Now, anyone know any good jokes about Welsh people and sheep? Can’t say that I have herd many…

References
[1] Strömbom et al, Solving the shepherding problem: heuristics for herding autonomous, interacting agents, J. R. Soc. Interface 11(100) (2014).

How to make my maths classes more interesting…

August 17th, 2014 by ajb
sleep I was thinking about how to make my lectures more interesting. However, I have decided not to follow the lead of Ramil Buenaventura…

In my class you see me rapping, singing, dancing on the tables—I even made a music video about math to grab their attention.

Buenaventura

But then if it works…

Link
US-based Filipino teacher cited for making algebra cool

The Polish breaking of the Enigma code

August 9th, 2014 by ajb
Bomba
The working rebuilt bombe at Bletchley Park Image courtesy of Wikipeda.
Mathematicians from the Polish Cipher Bureau, Marian Rejewski, Jerzy Różycki and Henryk Zygalski broke the German Enigma cipher machine codes in the 1930′s.

Working with engineers from the AVA Radio Manufacturing Company, they built the “Bomba”, which was the first machine to break Enigma codes. By working with a commercially available version of the Enigma machine, they laid down the mathematical foundations that were essential for the British work at Bletchley Park in breaking the German military codes. In particular Alan Turing helped develop the British version of the Bomba and the story from here is well-known.

The efforts of Rejewski, Różycki and Zygalski are far less well-known and were never really appreciated in their lifetimes. There is a small memorial at Bletchley Park in honour of these three.

In August 2014 the Institute of Electrical and Electronics Engineers (IEEE), as part of their Milestones commemorations have honoured Rejewski, Różycki and Zygalski with a plaque outside the Institute of Mathematics of the Polish Academy of sciences. I was lucky enough to be present at the unavailing ceremony which was hosted by IEEE President Prof. J. Roberto B. de Marca. There were several diplomats and representatives from the Polish military. Janina Sylwestrzak, the daughter of Marian Rejewski, was also present and gave a short speech (in Polish of course).


The Rejewski, Różycki and Zygalski memorial stone.

The plaque reads as follows;

plaque

You can find out more about the Polish work on breaking the Enigma codes by following the links below.

Links
Milestones:First Breaking of Enigma Code by the Team of Polish Cipher Bureau, 1932-1939 IEEE website.

The Breaking of Enigma by the Polish Mathematicians
, Virtual Bletchley Park.

Poland’s overlooked Enigma codebreakers, BBC News.

Smoking supercapacitors!

August 6th, 2014 by ajb
scientists from South Korea have converted cigarette butts into a high-performing material that could be used to coat the electrodes of supercapacitors [1].

The material is produces via the heat treatment of used cigarette butts in a nitrogen rich environment.

The article states that the processed cigarette filter material stored a higher amount of electrical energy than commercially available carbon. Also the material stored more energy than the more experimental materials graphene and carbon nanotubes.

If the process can be made economically viable then this process could be used to ecologically recycle cigarette butts.

Reference
[1] Minzae Lee, Gil-Pyo Kim, Hyeon Don Song, Soomin Park and Jongheop Yi, Preparation of energy storage material derived from a used cigarette filter for a supercapacitor electrode, 2014 Nanotechnology 25 345601.

Link
Cigarette butts offer energy storage solution IOP News

I am sure this was known about for donkey’s years

August 5th, 2014 by ajb
Researchers at the University of Sussex have published their research on how horses communicate [1]. It seems that they use their swiveling ears to aid in communication.

Talking to someone who is not a scientist, but has lots of experience of working with horses, said that the horse riding community knew this already. However, a scientific study was needed as anecdotal evidence is not enough.

That said, this was known about for donkey’s years*!

*Non-native speakers may find this link useful.

Link
Horses’ mobile ears are ‘communication tool’ BBC News

Reference
Jennifer Wathan & Karen McComb, The eyes and ears are visual indicators of attention in domestic horses, Current Biology , Volume 24, Issue 15, 4 August 2014, Pages R677–R679.