News

Wednesday, 30 November 2016

Levelling the access playing-field

Oxford Mathematics and Imperial College have joined forces to co-pilot a new programme aimed at levelling the playing-field for bright young mathematicians.

The two universities use the Maths Admission Test (MAT) as the basis for undergraduate assessment. It’s meant to be fair to all, particularly as it is not based on the Further Maths syllabus which many schools do not offer. But is it? How can it take in to account all the other factors that determine a candidate’s preparedness for such a potentially daunting challenge?

The Problem Solving MATters programme is designed to prepare students from less advantaged backgrounds for achieving success in the MAT. It comprises three face-to-face study days, focussing on specific problem-solving skills, with a short practice exam in the final session; three summer assignments to further develop thinking skills and technique; and five online follow-up sessions, designed to consolidate new skills in the run up to the MAT itself. Crucially, participants are supported by student mentors who offer feedback throughout the process.

The course has been made possible by the generosity of Oxford Mathematics Alumnus Tony Hill.

“My aim”, says Tony, "is that the programme will continue and be rolled out to other Russell Group Universities, so we can get the best people into Maths departments, not just the best-prepared. This programme gives young people from less advantaged backgrounds an opportunity to see what Imperial and Oxford are actually like. As well as being taught by experts and mentored by undergraduates, they have a chance to look around, see people like them from all over the country and to visualise themselves in such a place."

Tony himself grew up on a council estate and was the first from his family to go to university. He understands the issues and he's passionate about helping talented young people overcome common stumbling blocks, in particular "those kids from lower socio-economic backgrounds or whose families don't value education; those whose school isn't very good generally or at teaching Maths, or where they have the attitude of kids from round here don't go to that type of university...Compare that to a kid coming from a good school that's strong in maths and with a strong tradition of getting their students into good universities. In one sense it's equal and in another, it's not."

If you would like to know more about the courses for 2017 please email external-relations@maths.ox.ac.uk.

Thanks to Jean Bywater at Imperial College for researching and writing the original article.

 

Tuesday, 29 November 2016

Improving the quality and safety of x-rays

X-ray imaging is an important technique for a variety of applications including medical imaging, industrial inspection and airport security. An X-ray image shows a two-dimensional projection of a three-dimensional body. The original 3D information can be recovered if multiple images are given of the same object from different viewpoints. The process of recovering 3D information from a set of 2D X-ray projections is called Computed Tomography (CT).

Traditional CT scanners are based on a single moving source, rotating around the object to reconstruct. In this set-up, images are taken sequentially and the resulting reconstruction problem gives rise to a linear system of equations.

The innovation of X-ray emitter arrays allows for a novel type of X-ray scanning device with faster image acquisition due to multiple simultaneously emitting sources. Acquisition speed is an important factor in medical imaging because it can help to avoid artefacts from motion of the analysed tissue. Another major advantage of emitter arrays is that they result in light weight, highly mobile 3D imaging systems that can be taken to the patient rather than having to move the patient to a radiology suite.

However, two or more sources emitting simultaneously can yield measurements from spatially and temporally overlapping rays. This imposes a new type of image reconstruction problem based on nonlinear constraints that traditional linear image reconstruction methods cannot cope with.

Oxford Mathematicians Raphael Hauser and Maria Klodt have derived a mathematical model for this new type of image reconstruction problem, and developed a reconstruction method that allows the recovery of images from measurements with overlapping rays. Based on compressed sensing, the method allows for reconstruction from undersampled data, which means that the number of reconstructed densities is higher than the number of measurements, which enables reduced doses (see the full paper).

The method has been successfully applied to real X-ray measurements in cooperation with Gil Travish and Paul Betteridge from industrial partner Adaptix, an Oxford-based start-up company. The Adaptix scanners acquire images with a flat panel of comparatively small emitters with small opening angles of the emitter cones, arranged in a fixed grid which can allow for small devices with reduced doses.

The new image reconstruction method opens new possibilities for X-ray scanner design, because it allows for a new class of hand-held X-ray scanning devices, where emitter and detector positions cannot be aligned exactly, and overlapping of emitter cones cannot be avoided.

Friday, 25 November 2016

Maria Bruna wins the Women of the Future Science award

Oxford Mathematician Maria Bruna has won the Women of the Future Science award. The Women of the Future Awards, founded by Pinky Lilani in 2006, were conceived to provide a platform for the pipeline of female talent in the UK. Now in their 11th year they recognise the inspirational young female stars of today and tomorrow. They are open to women aged 35 or under and celebrate talent across categories including business, culture, media, technology and more.

Maria's work focuses on partial differential equations, stochastic simulation algorithms and the application of these techniques to the modelling of biological and ecological systems. 

Thursday, 24 November 2016

Random Walks 3 – The beauty and symmetry of ancient tiles

Beauty is in the eye of the beholder, but what about symmetry? In our final feature on mathematicians let loose in the Ashmolean Museum, Oxford Mathematician Balázs Szendrői investigates the beauty of symmetry in the Museum's Islamic art works. As he explains, no matter what the tile pattern may look like, its underlying symmetry configuration belongs to a small set of possibilities. 

If you are interested in the Random Walks series have a look at the previous films.

 

 

 

 

 

 

 

Friday, 18 November 2016

Random Walks 2 – Navigating the globe

From gigantic hanging tapestries to small pocket globes, the Ashmolean covers a whole range of navigational equipment. In the second of our Random Walks films featuring mathematicians let loose in the Ashmolean Museum, Vicky Neale from Oxford Mathematics demonstrates that she knows her place in the world. Through interactive examples that can be imitated at home, Vicky demonstrates the difficulties that cartographers have faced throughout the centuries.

 

 

 

 

 

Monday, 14 November 2016

Mitigating the impact of buy-to-let on the housing market

Much has been written about the buy-to-let sector and its role in encouraging both high levels of leverage and increases in house prices. Now Oxford Mathematician Doyne Farmer and colleagues from the Institute for New Economic Thinking at the Oxford Martin School and the Bank of England have modelled that impact. By looking at a large selection of micro-data, mostly from household surveys and housing market data sources, the team were able to model the individual behaviour and interactions of first-time buyers, home owners, buy-to-let investors, and renters from the bottom up, and observe the resulting aggregate dynamics in the property and credit markets. In turn a series of comparative statics exercises investigated the impact of the size of the rental/buy-to-let sector and different types of buy-to-let investors on housing booms and busts.

The results suggest that an increase in the size of the buy-to-let sector may amplify both house price cycles and increase house price volatility. Furthermore, in an effort to illustrate how this might be mitigated at a macro prudential level, the team modelled a loan-to-income portfolio limit which, encouragingly for policy-makers, attenuates the house price cycle. 

 

Friday, 11 November 2016

Random Walks: the Art of the Ashmolean through a mathematician’s eyes

The University of Oxford’s Ashmolean Museum is not only an exhibitor of art, but home to vital artistic research. The museum’s collections are investigated by some of the world’s leading historians, archaeologists, anthropologists and… mathematicians?

Throughout November 2016, the Ashmolean Museum and Oxford Mathematics proudly present Random Walks, a series of short films that present the historical world through mathematical eyes.

Our aim is to bring the humanities and sciences closer together, whilst demonstrating that historical museums are extremely useful for providing context to the development of logical thinking. What problems did humanity face throughout the millennia? How did science develop to surmount these problems? Why do remnants of these ideas remain important to this very day?

Join us as we answer these and many other questions and, hopefully, by the end, we will demonstrate that while mathematics may tell us how the universe began, it takes a museum to show us our place within it.

In our first film, Oxford Mathematics’ Thomas E. Woolley, takes you on a tour through the Ashmolean’s collection of mathematical tablets from the time of the ancient Babylonians. Thomas investigates how mistakes in mathematics can be just as illuminating as correct answers.

If you want to know more about the calculations presented in the film please click here

Friday, 11 November 2016

How can we understand our complex economy - Doyne Farmer Public Lecture now online

We are getting better at predicting things about our environment - the impact of climate change for example. But what about predicting our collective effect on ourselves? We can predict the small things, but we fail miserably when it comes to many of the big things. The financial crisis cost the world trillions, yet our ability to forecast and mitigate the next economic crisis is very low. Is this inherently impossible? Or perhaps we are just not going about it the right way? 

The complex systems approach to economics, which brings in insights from the physical and natural sciences, presents an alternative to standard methods. Doyne explains this new approach and give examples of its successes. He presents a vision of the economics of the future as it confronts the serious problems that our world will face.
 
J. Doyne Farmer is Director of the Complexity Economics programme at the Institute for New Economic Thinking at the Oxford Martin School and Professor in the Mathematical Institute at the University of Oxford.

 

Tuesday, 1 November 2016

Gui-Qiang Chen elected Fellow of the American Mathematical Society

Oxford Mathematician and Fellow of Keble College, Gui-Qiang G. Chen has been elected a Fellow of the American Mathematical Society in recognition of his contribution to partial differential equations, nonlinear analysis, fluid mechanics, hyperbolic conservation laws, and shock wave theory.

Professor Chen is Statutory Professor in the Analysis of Partial Differential Equations and Director of the EPSRC Centre for Doctoral Training in Partial Differential Equations in Oxford.

 

Tuesday, 1 November 2016

North meets South - helping mathematicians to understand each other

Mathematics can look like a foreign language to those who have not studied it in depth. Even for mathematicians, it can be difficult to understand the work of colleagues in other branches of mathematics, or indeed to know what questions they are seeking to answer in their research, because the vocabularies are so specialised and technical. A huge success of modern mathematics is that it is both broad and deep: mathematicians study a wide range of topics, and our knowledge in many of these areas is now so great that in order to work at the cutting edge of research one must specialise a lot. 

There is a tension, though, because while mathematicians need to immerse themselves in their research areas in order to make progress, at the same time they also need to be aware of developments in other areas that might help their work. Above all, and perhaps contrary to some perceptions, mathematics is highly interconnected and collaborative, and very often progress happens by making connections between research areas.

Oxford Mathematics seeks to address this in a number of ways. At the physical level, the splendid new home of the department, the Andrew Wiles Building, has been designed to facilitate both deliberate collaboration and also spontaneous exchanges of mathematical ideas through communal spaces (not least the excellent Café π).

Last year, Oxford Mathematics went one step further with a new initiative aimed at helping mathematicians to get to know what their Oxford colleagues are working on, and to give early career researchers the opportunity to share their work.

The new Fridays@4 project involves a programme of weekly sessions, aimed primarily but not exclusively at graduate students and postdocs, including a mix of colloquia, skills training, and advice on personal and career development. Part of this programme is the new ‘North meets South’ colloquium, organised by early career researchers and with early career researchers as invited speakers.

The colloquia happen once or twice each term. Each features two speakers, one from the north wing of the Andrew Wiles Building (roughly corresponding to pure mathematics, although that is a rather crude way to subdivide mathematics), and one from the south wing (roughly corresponding to applied mathematics). The speakers are asked to ensure that their talks are accessible to all the mathematicians in the department, not only those in their research areas.  Last year saw talks on a selection of topics: cluster algebras, modelling data streams, topological quantum field theory and defects in liquid crystals. This week (November 4) sees the first North meets South colloquium for this academic year, featuring Emilie Dufresne and Robert Van Gorder talking about their work. Interestingly, while both are working in Applied Mathematics, much of their work has also been in Pure Maths and Emilie's talk on separating sets in Invariant Theory is indeed Pure Mathematics. She and Robert are perhaps the ultimate North meets Southers, today's modern mathematicians. 

Heather Harrington and Brent Pym were instrumental in the setting up of North meets South. “We created this internal colloquium to learn what other young mathematicians here in Oxford are working on, and to form a network of early career researchers. Last year's speakers showed great skill, delivering exciting and accessible talks about research-level mathematics - and in only 30 minutes each! As organisers, we have observed that this experience is rewarding for the speakers, but even more so for Oxford Mathematics, as it brings together mathematicians from many subfields. We hope that North meetsSouth is another example of how such events can spark interactions that cross mathematical lines.”

The success of the North meets South colloquium is in itself a reminder of why mathematicians need to talk to each other, both to ensure that they make the most of the ideas and expertise around them, and, above all, to motivate them in their work. This is not a recreational add-on, but a core component of a modern mathematician's life.

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