The MSc by Research in Mathematics of Complex Systems is aimed at students with a good degree in a numerate subject who want to use their mathematical ability to pursue high level professional careers, and who are interested in developing their research skills in the field of complex systems hands-on.
Run within a stimulating research environment (the
Non-linearity & Complexity Research Group), the programme enables students to develop through doing research. The topics reflect a wide range of active research interests in the group, ensuring that both the course material and projects include the latest developments at the forefront of current research.
The programme offers the combination of a concentrated taught component where the students are introduced to a wide variety of techniques in a principled way, and an extensive research project in which they learn how to apply these techniques to real problems, and in which they get a good taste of all the aspects that research (in academia or industry) entails.
The nine month individual research project may involve analysis of new theoretical insights, or gaining practical experience of developing new methods and applying them to real-world problems. It can be taken in collaboration with an external commercial or industrial organisation and could be jointly supervised. The projects are chosen from many put forward by researchers at the forefront of their field. The project is
assessed by a substantial written thesis together with an oral examination with external and internal examiners and may result in a refereed publication.
The programme offers the possibility to extend the MSc into a PhD.
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Mathematics, Algorithms and Computational Methods (10 credits)
The module prepares students with a principled approach to numerical computation essential for research. In particular: techniques from linear algebra and multivariate calculus, fundamental principles of mathematical computation and numerical analysis to analyse algorithms, algorithms for differentiation, interpolation, integration, optimisation and linear algebra, and the implementation and application of algorithms to complex systems applications.
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Introduction to Methods of Statistical Physics (10 credits)
The module introduces students to important concepts and modern methods of Statistical Physics and their application to problems in related areas. It provides an in-depth analysis of some selected topics from Statistical Physics. It also provides the students with a clear understanding of the need for independent thinking and the difficulties that may arise when selecting/applying these methods to concrete problems and enables them to carry out research in this area.
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Statistical Pattern Analysis and Probabilistic Modelling (15 credits)
The module introduces the main concepts of probabilistic models and Bayesian methods to postgraduate students, enabling them to carry out research in this area as part of an MSc by Research programme. For statistical pattern recognition it covers topics such as classification, Bayesian inference and decision theory, and general linear models, while for probabilistic modelling it covers topics such as Gaussian mixture models, graphical models, inference in belief networks, Markov processes, the Bayesian approach, and Monte Carlo methods.
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Stochastic and Non-Linear Dynamic Systems (15 credits)
This module gives a concise introduction to modern methods and concepts of dynamic systems. This will expound two views, based on deterministic partial differential equations and stochastic differential equations. The emphasis of the course is on the application of mathematical methods rather than deep mathematical rigour. Both analytical and numerical methods will be considered with applications to physics, finance, earth sciences, biology etc. Practical work will be included.
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Research Project (130 credits)
The individual research project is a substantial piece of research in the general field of complexity, the specifics of which will be worked out in collaboration with the supervisor. Note that as an integral part of the research project, the students are required to follow a Research Skills module and complete individual assignments (pass/fail) on specific topics. In addition students may be required by their project supervisor to attend some short course(s) from the Research Skills Training Programme.
Applicants must produce evidence of being awarded a minimum of a 2:2 Honours degree in a numerate science from a UK University, or equivalent qualification. The Programme Director may conduct an (telephone) interview.
International students whose native language is not English will also need to demonstrate English Language ability (e.g. IELTS 6.5,
TOEFL score of 600 or equivalent).
This MSc requires the student to undertake 4 taught modules, together with the completion of a major project. The taught modules involve 22-33 teaching hours (depending on whether it is a 10 or 15 credit module), and may include tutorials, case studies and guest lectures. The programme runs from October to September with all taught modules being taught in term 1 (October to December). Upon successful completion of the taught component the project starts in January, and occupies nine months, being submitted in September.
Assessment methods are designed to meet the particular requirements of each module, but all taught modules are 100% continuous assessment. The research project is assessed by the research thesis and an oral presentation (viva) and counts for 130 of the 180 credits required for successful completion of the degree.
On successful completion of this programme, students will be able to understand and use a wide range of techniques from Complex Systems which they can interpret in a principled framework. They will understand the whole research process including non-technical issues, have developed independent learning and self-management skills, and transferable skills in numerical computing and oral and written communication. They will have carried out research in collaboration with an academic (and possibly industrial) partner, and have contributed to an active research programme.
The programme has been specifically designed to meet the huge demand for mathematically skilled experts in complexity science. Graduates may be employed in a broad range of positions: research and development teams as a part of a large company, in start-ups, or as consultants. We expect a substantial fraction of graduates from this programme to join research teams in high-tech engineering and IT sectors. Previous evidence suggests that such employment prospects are good. Projects in collaboration with an industrial partner have proven to be an excellent opportunity to forge links with industry that may result in subsequent employment, and students interested in such projects will be encouraged.
Dr Amit Chattopadhyay
Dr Amit Chattopadhyay is the Programme Director for the Masters Degree in the Mathematics of Complex Systems.
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