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Asymptopia - Centre for Mathematical Sciences Newsletter


A new vision for Mathematics


Charles Clarke

The Rt Hon Charles Clarke MP, Secretary of State for Education and Skills, visited the Centre for Mathematical Sciences on 6 November.

I have to admit to a serious prejudice in favour of the study of Mathematics. From very early days, I was encouraged to enjoy Mathematics by my parents (my father obtained a first in Mathematics from Cambridge in the 1930s) and I was fortunate enough to do well in Maths at school - where I had some outstanding teachers - so that eventually I did two Maths 'A' levels and was admitted to read Maths at Cambridge University.

I didn't do so well thereafter, and discovered my interest (and ability) in the subject waning through the first year of the Tripos, so that I changed to do my Part II in Economics, for which it has to be said that my Mathematics background was of value.

After leaving University, I did some secondary Maths teaching as well as teaching the Mathematics component of a Higher Education Access course for people who had mainly left school at 15 or 16, which proved to be one of the most fulfilling things I have ever done. The students came to see that mathematics was exciting and engaging rather than remote and alienating.

Moreover, it has also become clear to me that very many people lack the basic numeracy skills that really should be a sine qua non of modern life. Similarly, they lack the logical framework that ought to be the basis of modern thought, whether in the political field where I am now engaged or in other parts of life. While it is of course possible to study subjects other than Mathematics and to retain these attributes, too many people do not.

Worse than this, many people retain a fear of Mathematics and its methods which verges on the irrational. I think this can only come from early educational experiences which led them to feel that their failures to grasp some aspects of the language of mathematics, or to be confident in carrying out certain mathematical techniques represented a personal inadequacy or incapacity which is for them demotivating and depressing.

Ironically, at the same time, most people do acknowledge that mastering a range of mathematical skills is essential for a rewarding career. For example, a recent study into mathematical skills in the workplace found that jobs at all levels in seven sectors of the economy needed 'mathematical literacy', particularly at the inter-face between Information Communication Technology and decision-making.

Charles Clarke on the roof of the CMS.

Whatever the reasons for this state of affairs, I have personally been keen in the various roles that I have played in educational policy-making to encourage far higher standards of comprehension and command of mathematics that now exist across the population.

This is, however, a difficult task, as the explanation for why this state of affairs has arisen is ambiguous and the remedies are not always easy to identify. This problem is not unique to the UK; it is shared by many other countries.

This is, however, a difficult task, as the explanation for why this state of affairs has arisen is ambiguous and the remedies are not always easy to identify. This problem is not unique to the UK; it is shared by many other countries.

These are the reasons why the Government established a large scale review of mathematics post-14 under the leadership of Professor Adrian Smith. His report, 'Making Mathematics Count', was published on 24th February 2004. The Inquiry makes recommendations on changes to the curriculum and qualifications for those aged 14 and over - in schools, colleges and higher education institutions - to enable those students to acquire mathematical knowledge and skills necessary to meet the requirements of employers and of further and higher education. He also makes related recommendations on teacher supply and continuing professional development. This will be set within the context of Mike Tomlinson's wider review into 14-19 education more generally.

The publication of this report now gives us the opportunity to get this right, so that more children and young people acquire confidence in mathematical disciplines and their related subjects and that more young people study these subjects in depth.

Some elements of the solution are now widely understood, and are beginning to be put into effect. I will give just three examples.

First, it is obviously right to focus strongly on raising achievement in numeracy at the earliest stages. Children need key building blocks in place as they leave primary school. That is why since 1998 we have had a numeracy strategy and there has been a significant improvement at both Key Stage 2 and Key Stage 3.

Charles Clarke takes part in a video conferencing session as part of the work of the Millenium Mathematics Project.

Secondly, it is clearly necessary to focus on providing stronger support for Mathematics teachers, and their teaching and learning methods. There needs to be far more regular and systematic access to the latest thinking and, so, closer ties between the discipline of mathematics itself and those who teach it. There is beginning to be a rich and creative supply of resources, such as NRICH at the Millenium Maths Project, but teachers need better access and more encouragement to take advantage of them. This is why I announced the establishment of a new National Centre for Excellence in Mathematics last Spring, and I am carefully considering Adrian Smith's recommendations on the best way of developing this.

Thirdly, the increasing availability of, and confidence in, Information and Communications Technology is a massive opportunity. This is critical to the future of Mathematics teaching, to aid grasp of mathematical concepts and to enthuse the learner by engaging them in new and innovative ways.

These are just three areas where some progress has been made but a great deal remains to be done. Adrian Smith's report provides us with a far more comprehensive analysis.

I know from my visit last year that the Cambridge Centre for Mathematical Sciences is an outstanding inspiration for what can be achieved. Developing stronger Mathematics disciplines across the country can only strengthen the achievements of the Centre.

That means establishing a virtuous circle in which more school students desire to study mathematical subjects, leading to more undergraduates in those disciplines. Thus leading to an increasing number of undergraduates who want to undertake research in these disciplines, leading to greater standing for these disciplines in the academic world and more widely, leading to more interest in these subjects amongst those at school.

I believe that it is indeed possible to create such a virtuous circle and I hope that the Government, in first setting up and then in responding to Adrian Smith's enquiry can help to make it happen.

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News from the CMS

Congratulations to Peter Gershon, chairman of the mathematics fundraising committee, on the award of a knighthood in the New Year's Honours List. Sir Peter heads the Office of Government Commerce, which works with government to improve procurement and project/programme management. One of the lecture rooms at the CMS bears his name.

The CMS has won an important award: it is the British Construction Industry's Major Project of the Year. Warm congratulations to Edward Cullinan Architects and all the construction team.

Congratulations to Professor Michael Green, who has been awarded the Dirac Medal of the Institute of Physics for his crucial role in the development of superstring theory as a credible new framework for physics.

Professor Michael Green and the Dirac Medal.

Professor A.S.Fokas has been awarded the Aristeion prize of the Academy of Athens (which is the Greek analogue of the Royal Society). This is the most prestigious prize of the Academy, it is given every four years to a single scholar chosen from Science, Engineering or Medicine. It is the first time that it is given in Applied Mathematics.

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Cambridge-MIT Exchange Program


Dan Abramson

The University of Cambridge and the Massachusetts Institute of Technology (MIT) have established the Cambridge-MIT Institute (CMI), funded by Her Majesty's Government and private industry, to create a new form of academic enterprise.

The CMI has established an exchange program, allowing undergraduates to spend a year at the other institution. Mathematics is one of the subject areas that permits students to spend a year abroad. Students from Cambridge University spend their 2nd year at MIT, studying a program decided by themselves, in discussion with their subject coordinator in Cambridge and their advisor at MIT. Students are able to choose courses from a broader subject range and are also able to participate in research projects.

I spent my second year at MIT. It was the first year that Cambridge had sent undergraduates over the Atlantic, and of the thirty that went, two of us were doing maths. I had jumped at the chance to go, finding the offer of a year abroad highly attractive. Plus I had always wanted to meet a real American.

The approach to undergraduate mathematics in America is somewhat different to the way we do things. First of all, it is rare to devote all of your energies to one subject - to graduate from MIT you need to have taken courses from a range of subjects, including options in the humanities. Can you imagine? Maths students being forced to write essays? It looked to be a strange world. My advisor (similar to a Director of Studies) was rather shocked at the idea that one might spend more than two-thirds of your time on just one subject. In the end I took his advice; I even took a course in welding.

It is interesting that when candidates apply for MIT, they do not have to specify a subject that they wish to study. This is partly because they come to university from a lower level of specialisation, and spend their first year doing a range of basic courses to bring them up to the level require to study more advanced courses. But it is also because at the undergraduate level, students are encouraged to have a broader outlook; after all, if they do choose to persue a career in academia there is plenty of time to hone their skills. They are also encouraged to involve themselves in research. I ended up on an undergraduate research team at Harvard in my second semester; our results have been published. However, I admit that mathematics is a particularly difficult subject to do research in without an awful lot of background, and this idea of undergraduate involvement was really most successful in the engineering department. It is one of the reasons that MIT outputs such brilliant engineers.

The teaching itself also differs. A semester lasts fourteen weeks, so courses are less dense than in Cambridge. The lecturers tend to explain what they are teaching in much greater detail, and spend less time strictly expounding the subject. Proofs that do not help to enlighten the subject are likely to be omitted from the lectures - they are in the book and who follows them in lectures anyway? The lecturers expect their students to say something if they are confused. The idea is that everyone taking the course understands what is going on. If they do not, simply ploughing on will not help. There is also no intensive exam period at the end of the year. Courses are modular, and work is graded regularly. These marks often contribute to the final grade. There are no supervisions either; if confused, I went to the lecturer for help. This created a close link between the undergraduate community and the department itself, one that is lacking in Cambridge.

The system at MIT is by no means faultless. I worked for many more hours a week that year than I have done before or since, but the work was less challenging. It was frustrating that you could not just skip bits you thought were a waste of time as your work was marked and this would determine your grade. Working long hours is expected at MIT, and this did create a less pleasant atmosphere.

Undergraduates at MIT pay around $30,000 a year in tuition fees. I was lucky. I didn't have to. And I had a great time.

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Computational molecular biology in the Department of Applied Mathematics and Theoretical Physics


Simon Tavaré

Recent technological advances in molecular biology and computational science are allowing us to study biology and medicine with a precision hitherto unknown. Many universities around the world, as well as many pharmaceutical and biotechnology companies, are actively building research groups in computational molecular biology and bioinformatics. It is clear that the mathematical sciences - in particular probability, statistics and computer science - have already played a major role in recent successes in molecular biology. This is sure to continue, as new experimental technologies generate new data that in turn need new mathematics for their synthesis and interpretation.

A major impetus for computational molecular biology and bioinformatics is coming from applications to human health. The ability to use high throughput molecular techniques (for example, DNA sequencing, single nucleotide polymorphism genotyping, expression analysis using microarrays, and mass spectrometry for proteomics) to elucidate a variety of molecular mechanisms and pathways promises to make medicine a more predictive discipline. Prerequisites for the effective use of such data include the development of methods for statistical and computational analysis and the curation, storage and mining of disparate databases.

False colour image (kindly provided by Dr. Paul Edwards) showing chromosomes from a breast cancer cell. Several of the chromosomes have been formed by translocations, which join fragments from different chromosomes.

The Centre for Mathematical Sciences (CMS) is playing an important role in the development of this new, more quantitative, biology. The University has recently formed the Cambridge Computational Biology Institute (CCBI), based in pavilion G of the CMS, to serve as the bridge between clinical and biological research on the one hand and mathematical sciences on the other. The CCBI is a priority of the University's Schools of Biology, Clinical Medicine, Physical Sciences, and Technology. Almost every department in each of these Schools has expressed a wish to be a participant in the Institute, as have the European Bioinformatics Institute and the Wellcome Trust Sanger Institute at Hinxton and the Babraham Institute. The Institute is developing a consortium of large computer and pharmacology companies to support the Institute and collaborate in its work. It is hoped also to draw in some of the numerous small high-technology companies in the Cambridge region. The Institute is working closely with the Cambridge eScience Centre. Scientists participating in the CCBI will have access to massive computing resources, including those of the Cambridge-Cranfield High Performance Computing Facility, and to expert advice in their use.

I am the first appointment in CCBI. My research is in probabilistic and statistical aspects of biology and medicine, in particular population genetics, genomics and stochastic computation. I am one of three new Cambridge University-Cancer Research UK professors based in the Oncology Department at Addenbrookes. The cancer genomics program there addresses basic questions in cancer biology and therapy. The CCBI has recently appointed a director, Gos Micklem, primarily based at the Genetics Department and also have an executive director, Karen Smith, based at the Corporate Liaison Office, where her responsibilities include the development of the industrial component of CCBI.

CCBI recently received its first major funding, a collaborative project in systems and stem cell biology, informatics and drug development funded by the Cambridge-MIT Institute (CMI). In addition to supporting this research the CMI is also supporting the development of an MPhil program in Computational Biology, due to start in October 2004. Two lecturers have been hired, Dr. Johan Paulsson, a systems biologist and Dr. Stephen Eglen, a computational neuroscientist. We are keen to develop in DAMTP a strong research program in computational biology. The CCBI staff join Professor Tim Pedley and Dr Natalia Berloff who already represent aspects of computational biology in DAMTP. We are planning a seminar series for next term, where we can highlight aspects of this fascinating field.

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For information on making a donation in support of any aspect of Mathematics at Cambridge, please contact Professor Peter Landshoff or Mr Christopher Hesketh