Tag Archives: maths

How the generosity of donors transforms the lives of students

On 13 July 2017 Birkbeck welcomed donors, volunteers, students and staff for an ‘An Evening of Thanks’ for all they give to the College. Aziza Sentissi, a PhD candidate in Mathematics and Statistics, spoke at the event, and reflects on what the generosity of donors means for students like her, who may otherwise be unable to undertake their studies. aziza850x450My interest in Mathematics dates back to an early age at primary school. I achieved good academic results in Mathematics and I never felt that it was an effort to tackle my math homework or any math puzzle. I have always enjoyed the thrill of the mathematical challenge. It was (and it is still) like going on an adventure where your only tools are your logic and your instinct. I believe that we all have naturally a set of skills in which we reach our optimal potential. It is just matter of finding, nurturing and using them. In my case, it is definitely Mathematics.

Most of my academic and professional decisions were motivated by the need to use Mathematics on a daily basis. I studied industrial engineering for my undergraduate degree, focused on financial engineering when I studied for my MBA and spent more than a decade working in market risk management in both Toronto and London. My career allowed me to gain an expert-level experience in the field while using the mathematical finance skills I acquired through education and experience.

I know that I should have felt a certain degree of contentment with my academic and professional progression, but in reality, I felt frustration that I was still far from my intellectual potential. I felt that I needed to get back to ‘core Mathematics’. It was just about finding the right programme so that I could reconcile studies and work. Finding out about Birkbeck’s MSc programmes was already a big step toward my goals. Indeed, Birkbeck offered the best opportunity to join a recognized programme taught by an outstanding faculty while working in London.  A few years later, I graduated with distinction from the MSc Applied Statistics (2013) course, and with merit from MSc Mathematics (2015).

Studying at Birkbeck by far exceeded all my expectations. It has competitive programmes with strong curriculums, an outstanding faculty, and dedicated staff. Some companies I’ve worked at have spent a lot of money persuading employees to buy into their mission. Well, at Birkbeck, it is an achieved goal. You can sense the commitment to the university’s mission at each one of your interactions either with the professors or with the staff. I have always been amazed that everybody will make that extra effort to help you thrive in your studies and achieve your goals as you are trying to balance your work life and your studies.

My story with Birkbeck did not stop at the end of my second masters. Indeed, as I expressed my interest in joining the full-time PhD programme while highlighting my financial constraints, my supervisors suggested applying to few scholarships which I eagerly did. After a few weeks, I was approved for the Winton STEM PhD Studentship, which aims to promote gender equality in STEM subjects.

The support from Winton has indeed made it possible for me to join the full-time PhD programme in Mathematics. There are no words that really capture how grateful I am to Winton for their support and for giving me the opportunity to pursue a long-term ambition which is to build a career in research in Mathematics either within the academic world or within a research firm. The subject of my PhD is about optimizing one of the advanced approximation methods (Meshfree method) in multivariate setting.  It is a cutting-edge subject with multiple applications in several fields such as engineering, machine learning and artificial intelligence. I am extremely proud to be working on this subject with my supervisors who are experts in the field.

Through my PhD, I have also had the opportunity to take part in an outreach conference jointly organised by Birkbeck and Winton. At the conference, we encouraged young women from schools in disadvantaged London boroughs to consider studying mathematics at university. It was a privilege and an amazing experience to see the impact of the conference on these girls and to see how it changed their perspective on using their mathematical talent.

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Escher and Coxeter: a mathematical conversation

On Monday 5 June 2017, Professor Sarah Hart from Birkbeck’s Department of Economics, Mathematics and Statistics gave a prestigious Gresham Lecture at the Museum of London. Andrew Silverman, Learning Development Tutor in the School of Business, Economics and Informatics reports on the lecture.

Gresham College crest in hyperbolic geometry. Credit: Sarah Hart

Gresham College crest in hyperbolic geometry. Credit: Sarah Hart

Gresham College was founded in 1597 and has been providing free lectures within the City of London for over 400 years. Walking down from the dusty roads of the Barbican into the cool and quiet of the Weston Theatre, the audience was transported into a conversation between an artist and a mathematician, Escher and Coxeter. Told with infectious excitement and humour, Professor Hart wove the story of the lives of these two figures and their friendship through the mathematics and the artwork that fed into one another.

Born on 17 June 1898 in Leeuwarden, Holland, the youngest of five brothers and moving with his family to Arnhem when he was five, Maurits Cornelis Escher would eventually go on to study at the School for Architecture and Decorative Arts in Haarlem. His father was a civil engineer and his brothers all became scientists. Escher himself almost became an architect before switching to graphic arts. He later quipped that it was only by a hair’s breadth that he escaped becoming a useful member of society.

Escher began by producing woodcuts and lithographs featuring mainly landscapes. An example of this was the 1931 lithograph Atranti, Coast of Amalfi. But in 1936 his work went in a new direction, becoming more abstract; according to Escher, he had replaced landscapes with mindscapes. The woodcut Metamorphosis I, produced in 1937, exemplifies this change and is clearly a ‘mindscape’ adapted from the 1931 piece.

What could have triggered this change? In 1922, Escher visited the Alhambra palace in Granada, Spain; his second visit was in 1936. The buildings we know today were constructed in the mid-11th century by the Moorish king Mohammed ben Al-Ahmar. One of the key points about Moorish art, and Islamic art more generally, is that it is not permitted to contain images of living things; it is instead rich in symmetry and tessellations of tiles. Escher was able to combine this richness of geometric design with images of ‘living’ things (albeit at times mythical living things), thereby leading to works such as Angel and Devils (1941), produced in ink rather than wood.

Donald Coxeter, or Harold Scott Macdonald Coxeter, was born on 9 February 1907. His name was originally going to be Harold Macdonald Scott Coxeter, until they realised that this would have been HMS Coxeter, more a ship name than a baby name, and so the name was changed. As a schoolboy, Coxeter became so engrossed in geometry, at the expense of other subjects, that one teacher told him he was only allowed to think in four dimensions on Sundays.

In 1936, the year Escher’s art took a new direction, Coxeter took up a post at the University of Toronto. When asked what the point of pure mathematics is, Coxeter responded: “No one asks artists why they do what they do. I’m like any artist; it’s just that the obsession that fills my mind is shapes and patterns.”

In 1954, the International Congress of Mathematicians was held in Amsterdam. To coincide with this, a major exhibition of Escher’s work was held in the Stedelijk Museum in Amsterdam. It was here that Coxeter and Escher first met, when Coxeter bought a couple of Escher’s prints.

Incidentally, another mathematician who visited the exhibition was Roger Penrose, who was a Reader and then Professor of Applied Mathematics at Birkbeck from 1964 to 1973, and later became Professor of Geometry at Gresham College, London. After seeing an impossible staircase in Escher’s Relativity print, he came up with the concept of a ‘Penrose triangle’.

Professor Hart explained the mathematics behind the regular tilings in three geometries: plane (Euclidean), spherical and hyperbolic geometry. She managed to put the concepts across in such a way that even someone with no prior knowledge could walk away with a good basic understanding, and the images presented were an excellent way of getting a more intuitive sense of what was really going on.

Escher learnt a great deal from Coxeter, to the extent that when Escher created a picture based on a new geometrical concept, he would refer to it as ‘Coxetering’. But in turn, Coxeter also learnt from Escher. For example, Escher’s 1959 work, Circle Limit III, led Coxeter to a new understanding of the hyperbolic disc. By looking at the spines of the fish in the image, Coxeter realised that Escher had found equidistant curves and produced them incredibly precisely. In this way their friendship was a true exchange of ideas – a mathematical conversation.

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Academia’s gender inequality problem

This post was contributed by Professor Helen Lawton-Smith of Birkbeck’s Department of Management. Professor Lawton-Smith is organising Improving gender equality in work – what can we learn from London’s business and policy organisations? on Wednesday 18 March, 2pm-5pm.

laboratoryWomen are under-represented in senior positions in science, engineering, maths and medicine disciplines at UK universities. Initiatives including Athena SWAN and the Aurora Women’s leadership programme have been set up to address this problem, yet such initiatives by themselves are not enough to tackle the problem of the current gender bias. What is needed is institutional embedding, so that gender and other diversity issues are integrated into an equality framework of decision-making processes and structures within organisations, which cannot be side-stepped by those in positions of power.

The four-year Transforming Institutions by Gendering contents and Gaining Equality in Research (TRIGGER) project at Birkbeck is championing the role of female academics in scientific subjects as part of a five-country European project. This initiative is testing a blueprint designed to raise the status of women in scientific and technological organisations such as universities. The nine action areas are designed to identify barriers to equality in the workplace, including the impact of research. The project builds on Birkbeck’s existing commitment to promoting female academics. Results and reactions have been very interesting.

Equality issues have been tackled in a variety of ways by companies and by policy making bodies such as local authorities and government agencies. According to the New York Times in October 2014, Silicon Valley also has a diversity problem – one which is being tackled head on by companies such as Google and Facebook.

Academia has a lot to learn from how other kinds of large organisation have identified the nature and causes of gender inequality. On Wednesday 18 March the TRIGGER project and the BEI School are hosting a networking event designed to explore which institutional changes work best in supporting gender equality in large organisations. The panel’s speakers will reflect on why changes were necessary, what changes have been introduced, the outcome of those changes, and what still needs to happen to improve gender equality. The diversity of speakers will ensure there are opportunities for learning for all.

Interested? Find out more

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