In addition to being a science in its own right, mathematics plays a fundamental role in the quantitative areas of practically all other academic disciplines, particularly in the natural sciences, engineering, business administration, economics, medicine and psychology. Mathematical results permeate nearly all facets of life and are a necessary prerequisite for the vast majority of modern technologies – and as our IT systems become increasingly powerful, we are able to mathematically handle enormous amounts of data and solve ever more complex problems.
Special emphasis is placed on developing students' ability to formalise given problems in a way that facilitates algorithmic processing as well as enabling them to choose or develop, and subsequently apply, suitable algorithms to solve problems in an appropriate manner. The degree programme is theoretical in its orientation, with strongly application-oriented components. Studying this programme, you can gain advanced knowledge in the mathematical areas of Cryptography, Computer Algebra, Algorithmic Algebra and Geometry, Image and Signals Processing, Statistics and Stochastic Simulation, Dynamical Systems and Control Theory as well as expert knowledge in Computer Science fields such as Data Management, Machine Learning and Data Mining.
Furthermore, you will have the chance to learn how to apply your knowledge to tackle problems in areas as diverse as Marketing, Predictive Analytics, Computational Finance, Digital Humanities, IT Security and Robotics.
The core modules consist of two mathematics seminars and the presentation of your master's thesis.The compulsory elective modules are divided into eight module groups:
1) Algebra, Geometry and Cryptography
This module group imparts advanced results in the areas of algebra and geometry, which constitute the fundament for algorithmic calculations, particularly in cryptography but also in many other mathematical areas.
2) Mathematical Logic and Discrete Mathematics
The theoretical possibilities and limitations of algorithm-based solutions are treated in this module group.
3) Analysis, Numerics and Approximation Theory
Methods from the fields of mathematical analysis, applied harmonic analysis and approximation theory for modelling and approximating continuous and discrete data and systems as well as efficient numerical implementation and evaluation of these methods are the scope of this module group.
4) Dynamical Systems and Optimisation
Dynamical systems theory deals with the description of change over time. This module group is concerned with methods used for the modelling, analysis, optimisation and design of dynamical systems, as well as the numerical implementation of such techniques.
5) Stochastics, Statistics
This module group deals with methods for modelling and analysing complex random phenomena as well as the construction, analysis and optimisation of stochastic algorithms and techniques used in statistical data analysis.
6) Data Analysis and Data Management and Programming
This module group examines the core methods used in computer science for the analysis of data of heterogeneous modalities (e.g. multimedia data, social networks and sensor data) and for the realisation of data analysis systems.
In this module group, you will practise applying the mathematical methods learned in module groups 1 to 6 to real-world applications such as Marketing, Predictive Analytics and Computational Finance.
8) Key Competencies and Language Training
In this module group, you will choose seminars that develop your non-subject-specific skills, such as public speaking and academic writing and other soft skills; you may also undertake internships. This serves to complement your technical expertise gained during your degree studies and helps to prepare you for your professional life after university.
The Master of Science in Mathematics (120 ECTS) is a research-based master’s programme in which you can specialize in the following fields of mathematics: Pure Mathematics: Algebra, Analysis and Geometry; and Applied Mathematics: Statistics, Financial Mathematics, Computational Mathematics, Plasma-Astrophysics.
Besides a solid, all-round education in mathematics, the programme offers you the possibility to focus on either pure or applied mathematics. This allows you to acquire both breadth of knowledge and depth in your own areas of interest. Pure and applied mathematics courses are firmly grounded in the core research activities of the Department of Mathematics. Gradually, you will gain experience and autonomy in learning how to cope with new concepts, higher levels of abstraction, new techniques, new applications, and new results. This culminates in the Master’s thesis, where you become actively involved in the research performed in the various mathematical research groups of the Departments of Mathematics, Physics, Astronomy and Computer Sciences.
This is an initial Master's programme and can be followed on a full-time or part-time basis.
The programme of the Master of Science in Mathematics consists of 120 ECTS. You choose one of the two profiles – Pure Mathematics or Applied Mathematics (54 ECTS) – and one of the two options – Research Option or Professional Option (30 ECTS). The profile allows you to specialize either in pure mathematics (algebra, geometry, analysis), or in applied mathematics (statistics, computational mathematics, fluid dynamics).
There is one common course: ‘Mathematics of the 21st Century’ (6 ECTS). To complete the programme, you carry out a research project that results in a master’s thesis (30 ECTS).
All staff members of the Department of Mathematics are actively involved in the two-year Master of Science in Mathematics programme. The academic staff at the Department of Mathematics consists of leading experts in their fields. Researchers in pure mathematics focus on algebraic geometry, group theory, differential geometry, functional analysis, and complex analysis. Researchers in mathematical statistics deal with extreme values, robust statistics, non-parametric statistics, and financial mathematics. Research in the applied mathematics group is in computational fluid dynamics and plasma-astrophysics.
Mathematicians find employment in industry and in the banking, insurance, and IT sectors. Many graduates from the research option pursue a career in research and start a PhD in mathematics, mathematical physics, astrophysics, engineering, or related fields.
Computational Mathematics, in particular the physical applied areas and the theory and implementation of numerical methods and algorithms, have wide-ranging applications in both the public and private sectors. More recently, in this era of ubiquitous and cheap computing power, there has been an explosion in the number of problems that require us to understand processes by modelling them, and to use data sets that are large. Thus the subject of Computational Mathematics has become increasingly prominent. Consequently there is high demand also for computational modellers and data scientists. This programme concentrates on the overlap and synergy between these fields.
The programme consists of 120 credits of courses in total during Semesters 1 and 2, followed by a 60 credit dissertation which is completed during the Summer. The courses taken will be dependent on the availability of courses each year which may be subject to change as curriculum develops to reflect a modern degree programme.
The first semester is composed of a combination of compulsory and optional courses. The compulsory courses will build strong applied mathematical and computational foundations. The curriculum is completed with optional courses in related subjects such as statistics and optimization.
The second semester is again composed of a combination of compulsory and optional courses, building on the skills gained in Semester 1. The compulsory courses include Research Skills, which will prepare you for the Summer Dissertation Project. The optional courses cover a wide range of areas including, for example, data science, high performance computing, and related disciplines such as Informatics and Physics.
The 60 credit individual dissertation will take the form of a supervised research-style project on a topic proposed by a staff member of the Applied and Computational Mathematics group. The aim of the project is to provide practical experience and skills for tackling scientific problems which require both computational approaches and mathematical insight. This will include identifying and applying appropriate mathematical and numerical techniques, interpreting the results, and presenting the conclusions.
This programme will provide training in the tools and techniques of mathematical modelling and scientific computing, and will provide students with skills for problem solving using modern techniques of applied mathematics.
Visit our website for more information on fees, scholarships, postgraduate loans and other funding options to study Erasmus Mundus Computational Mechanics at Swansea University - 'Welsh University of the Year 2017' (Times and Sunday Times Good University Guide 2017).
Swansea University has gained a significant international profile as one of the key international centres for research and training in computational mechanics and engineering. As a student on the Master's course in Erasmus Mundus Computational Mechanics, you will be provided with in-depth, multidisciplinary training in the application of the finite element method and related state-of-the-art numerical and computational techniques to the solution and simulation of highly challenging problems in engineering analysis and design.
The Zienkiewicz Centre for Computational Engineering is acknowledged internationally as the leading UK centre for computational engineering research. It represents an interdisciplinary group of researchers who are active in computational or applied mechanics. It is unrivalled concentration of knowledge and expertise in this field. Many numerical techniques currently in use in commercial simulation software have originated from Swansea University.
The Erasmus Mundus MSc Computational Mechanics course is a two-year postgraduate programme run by an international consortium of four leading European Universities, namely Swansea University, Universitat Politècnica de Catalunya (Spain), École Centrale de Nantes (France) and University of Stuttgart (Germany) in cooperation with the International Centre for Numerical Methods in Engineering (CIMNE, Spain).
As a student on the Erasmus Mundus MSc Computational Mechanics course, you will gain a general knowledge of the theory of computational mechanics, including the strengths and weaknesses of the approach, appreciate the worth of undertaking a computational simulation in an industrial context, and be provided with training in the development of new software for the improved simulation of current engineering problems.
In the first year of the Erasmus Mundus MSc Computational Mechanics course, you will follow an agreed common set of core modules leading to common examinations in Swansea or Barcelona. In addition, an industrial placement will take place during this year, where you will have the opportunity to be exposed to the use of computational mechanics within an industrial context. For the second year of the Erasmus Mundus MSc Computational Mechanics, you will move to one of the other Universities, depending upon your preferred specialisation, to complete a series of taught modules and the research thesis. There will be a wide choice of specialisation areas (i.e. fluids, structures, aerospace, biomedical) by incorporating modules from the four Universities. This allows you to experience postgraduate education in more than one European institution.
Modules on the Erasmus Mundus MSc Computational Mechanics course can vary each year but you could expect to study the following core modules (together with elective modules):
Numerical Methods for Partial Differential Equations
Advanced Fluid Mechanics
Finite Element Computational Analysis
Entrepreneurship for Engineers
Finite Element in Fluids
Nonlinear Continuum Mechanics
Computational Fluid Dynamics
Dynamics and Transient Analysis
Reservoir Modelling and Simulation
The Erasmus Mundus Computational Mechanics course is accredited by the Joint Board of Moderators (JBM).
The Joint Board of Moderators (JBM) is composed of the Institution of Civil Engineers (ICE), the Institution of Structural Engineers (IStructE), the Chartered Institution of Highways and Transportation (CIHT), and the Institute of Highway Engineers (IHE).
This degree is accredited as meeting the requirements for Further Learning for a Chartered Engineer (CEng) for candidates who have already acquired an Accredited CEng (Partial) BEng(Hons) or an Accredited IEng (Full) BEng/BSc (Hons) undergraduate first degree.
See http://www.jbm.org.uk for further information.
This degree has been accredited by the JBM under licence from the UK regulator, the Engineering Council.
Accreditation is a mark of assurance that the degree meets the standards set by the Engineering Council in the UK Standard for Professional Engineering Competence (UK-SPEC). An accredited degree will provide you with some or all of the underpinning knowledge, understanding and skills for eventual registration as an Incorporated (IEng) or Chartered Engineer (CEng). Some employers recruit preferentially from accredited degrees, and an accredited degree is likely to be recognised by other countries that are signatories to international accords.
On the Erasmus Mundus MSc Computational Mechanics course, you will have the opportunity to apply your skills and knowledge in computational mechanics in an industrial context.
As a student on the Erasmus Mundus MSc Computational Mechanics course you will be placed in engineering industries, consultancies or research institutions that have an interest and expertise in computational mechanics. Typically, you will be trained by the relevant industry in the use of their in-house or commercial computational mechanics software.
You will also gain knowledge and expertise on the use of the particular range of commercial software used in the industry where you are placed.
The next decade will experience an explosive growth in the demand for accurate and reliable numerical simulation and optimisation of engineering systems.
Computational mechanics will become even more multidisciplinary than in the past and many technological tools will be, for instance, integrated to explore biological systems and submicron devices. This will have a major impact in our everyday lives.
Employment can be found in a broad range of engineering industries as this course provides the skills for the modelling, formulation, analysis and implementation of simulation tools for advanced engineering problems.
“I gained immensely from the high quality coursework, extensive research support, confluence of cultures and unforgettable friendship.”
Prabhu Muthuganeisan, MSc Computational Mechanics
Visit our website for more information on fees, scholarships, postgraduate loans and other funding options to study Mathematics at Swansea University - 'Welsh University of the Year 2017' (Times and Sunday Times Good University Guide 2017).
The MSc Mathematics course has been designed for students who wish to build on their BSc, extending their range of mathematics expertise across a broader spread of topics, and demonstrating their literature research skills through an extended dissertation.
Such a qualification will mark graduates out as having a broader and deeper understanding of mathematics, and the skills required to pursue a significant project with a high level of independence, presenting their results in a written report. This will give MSc Mathematics graduates an edge in the ever more competitive jobs market.
On the Mathematics course you will study different elements of mathematics in a broad sense - including mathematical elements of computing if desired - in addition to developing your research, project management, and written communication skills through a project you will undertake. As a student of MSc in Mathematics, you will be fully supported to ensure that your project further develops an excellent foundation for your future career plans.
Modules on the MSc Mathematics include:
• Algebraic coding theory
• Black-Scholes theory
• Data science
• Differential geometry
• Fourier analysis
• Ito calculus
• Lie theory
• Numerical analysis
• Partial differential equations
• Stochastic processes
• Statistical mechanics
Please visit our website for a full description of modules for the MSc Mathematics.
On top of the Mathematics modules you study, you will also complete a dissertation as part of your studies.
The Aubrey Truman Reading Room, located in the centre of the Department of Mathematics, houses the departmental library and computers for student use. It is a popular venue for students to work independently on the regular example sheets set by their lecturers, and to discuss Mathematics together.
Our main university library, Information Services and Systems (ISS), contains a notably extensive collection of Mathematics books.
Mathematics students will benefit from the £31m Computational Foundry for computer and mathematical sciences which will provide the most up-to-date and high quality teaching facilities featuring world-leading experimental set-ups, devices and prototypes to accelerate innovation and ensure students will be ready for exciting and successful careers. (From September 2018)
The ability to think rationally and to process data clearly and accurately are highly valued by employers. Mathematics graduates earn on average 50% more than most other graduates. The most popular areas are the actuarial profession, the financial sector, IT, computer programming and systems administration, and opportunities within business and industry where employers need mathematicians for research and development, statistically analysis, marketing and sales.
Some of our Mathematics students have been employed by AXA, BA, Deutsche Bank, Shell Research, Health Authorities and Local Government. Teaching is another area where Mathematics graduates will find plenty of career opportunities.
The results of the Research Excellence Framework (REF) 2014 show that our research environment (how the Department supports research staff and students) and the impact of our research (its value to society) were both judged to be 100% world leading or internationally excellent.
All academic staff in Mathematics are active researchers and the department has a thriving research culture.
"Further to my studies at Swansea University as a Master of Science graduate in Financial Mathematics, I am currently working at Deutsche Bank in London as part of the Structured Financial Services team providing client services for corporate lending and debt portfolios. The complex nature of the Mathematics course has helped me become a logical decision maker and a highly skilled problem solver. These transferable skills are very useful in the world of Finance since the role is highly challenging working towards deadlines and structured transaction targets. My studies at Swansea University have also enriched me with leadership, motivational skills and have enhanced my communication skills. I work in a close team of 10 people within a large department which encourages a culture that strives towards learning and effective teamwork. I thoroughly enjoyed my time at Swansea University and cherish the many fond memories. I am so pleased to be expanding my horizon within a major financial centre."
Rhian Ivey, BSc Mathematics, MSc Mathematics and Computing for Finance
This programme is now closed but you may want to consider other courses such as the Mathematics MSc.
The Financial Mathematics MSc programme enables graduates and professionals with a strong mathematical background to research, develop and apply quantitative and computational techniques to investment and risk management. Based in the Department of Mathematics, this course has a superb reputation for research-led teaching and strong links to industry.
Financial Mathematics studies problems of optimal investment and risk management, and this course covers a diverse range of topics, from classical options pricing to post-crisis investment and risk management
Like any branch of applied mathematics, financial mathematics analyses a given problem by first building a mathematical model for it and then examining the model. Both steps require detailed knowledge in different areas of mathematics, including probability, statistics, optimisation, computer science and many more traditional fields of mathematics.
Our Financial Mathematics MSc course is a unique study pathway that encompasses the essential skills required for successful risk management, trading and research in quantitative finance: probability, statistics, optimisation, computing and financial markets. You will explore probability theories, risk neutral valuation, stochastic analysis as well as interest rate and credit risk modules. We also offer you the opportunity to study an additional zero-credit supportive module called mathematical analysis for financial mathematics.
The Financial Mathematics MSc programme offers you the choice to study either full or part-time and is made up of optional and required modules. You must take modules totalling 180 credits to complete the course. If you are studying full-time, you will complete the course in one year, from September to September. If you are studying part-time, your programme will take two years to complete, you will study the required modules in the first year, and a further selection of required and optional modules including the 60-credit financial mathematics report module in your second year.
Bloomberg terminal laboratory
King’s is one of only a few academic departments in the UK that offers full access to Bloomberg terminals. These terminals will provide you access to live financial data. They are heavily used within the financial industry, and the data they provide is critical in assisting traders in making investment decisions and for risk managers monitoring investment probabilities. We have 13 Bloomberg terminals available for exclusive use by the Financial Mathematics MSc programme.
You will use the Bloomberg terminals to:
The skills you will learn from using the terminals are highly valued by employers. King’s is part of a strong network of financial mathematics in London with connections both in academia and in the industry.
We are also members of the University of London and by arrangement, you can enrol in optional modules at other institutions within the University of London, which includes Birkbeck, London School of Economics and Political Sciences, University College London and many others.
This programme is suitable for students or professionals with a strong mathematical background. It covers the principles and techniques of quantitative finance to prepare students for advanced work in the financial sector or research in mathematical finance.
We use lectures, seminars and group tutorials to deliver most of the modules on the programme. You will also be expected to undertake a significant amount of independent study.
Average per week: Three hours for 11 weeks per each 15 credit module.
You are expected to spend approximately 10 hours of effort for each credit (so for a typical module of 15 credits this means 150 hours of effort).
The primary method of assessment for this course is a combination of written examinations, essays, coursework and individual or group projects and oral presentations.
Our graduates are highly sought after by investment banks, corporate risk management units, insurance companies, fund management institutions, financial regulatory bodies, brokerage firms, and trading companies. Recent employers of our graduates include, Capital Investment, Credit Suisse, European Bank for Reconstruction & Development, Fitch Ratings, HSBC and Morgan & Stanley. Some graduates have pursued research degrees in financial mathematics.