Masters degrees in Computational Mathematics involve the application of advanced mathematical concepts to the computational processes which are in use across a range of industries.
Related subjects include Computational Applied Mathematics and Computational Finance. Entry requirements normally include an undergraduate degree in an appropriate Mathematics subject.
Computational Mathematics is essential for the use of many machines, systems and practices. Courses in this field emphasise increasing your understanding of modelling and algorithms, numerical methods and symbolic computations (the creation of algorithms and software for manipulating mathematical expressions).
You may wish to specialise your studies in a particular area of Computational Mathematics, such as computational optimisation and the development of networks and algorithms. These techniques may be applied to industries like robotics and aerospace.
Alternatively, you might specialise in mathematical modelling for purposes such as financial forecasting across a range of industries, particularly banking and insurance. Operational research is also a key component of the day-to-day running of most large corporations. You may be employed to assess the operations of business activities on a national or global scale, with the goal of increasing profits and reducing risk.
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
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.
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 basis of natural sciences is the modelling of phenomena and solving these models. The Master’s programme in theoretical and computational methods will give you a strong basis in the theoretical methods, modelling, and mathematical and numerical analysis within physics, mathematics, chemistry and/or computer science. The special feature of this programme is that you can combine the above disciplines into a comprehensive programme. It is well suited for the needs of fundamental and applied research. This programme requires a strong commitment from you to develop your own skills and plan your degree. You can tailor your programme according to your existing knowledge and interests, in cooperation with the programme professors.
The programme’s strong scientific emphasis makes it a natural gateway to further studies in physics, mathematics, chemistry, and computer science. This will usually take place within one of the research groups working on the Kumpula campus.
Upon completing the Master’s programme, you will:
As a graduate of this Master’s programme you can work as an expert in many kinds of scientific jobs in the private and the public sectors. The employment rate in this field is good.
Further information about the studies on the Master's programme website.
The special feature of this programme is its great scope: it consists of several modules in physics, mathematics, chemistry, and/or computer science. Out of these, you may select a suitable group of subjects according to your interests and the courses you took for your Bachelor's degree. The programme incorporates modules from e.g. the following areas:
The courses include group and lecture instruction, exercises, literature, and workshops. Most courses also include exams or project assignments. In addition, you can complete some courses independently, by taking exams.
The MSc in Computational Mathematical Finance (CMF) is a dynamic new programme with the aim to deliver high quality training in the theory of Mathematical Finance with strong emphasis on computational methods.
Currently graduates in this field are expected to have a working knowledge of advanced computational finance (including construction of algorithms and programming skills) as well as a sound knowledge of the theory of Probability and Stochastic Analysis. These are the core theories needed in the modern valuation of complex financial instruments.
This MSc programme delivers:
You must obtain a total of 180 credits to be awarded the MSc. Over semesters 1 and 2, you will take compulsory courses worth a total of 85 credits and optional courses worth a further 35 credits. Successful performance in these courses (assessed through coursework or examinations or both) allows you to start work on a three-month dissertation project, worth 60 credits, for the award of the MSc degree.
There are two streams: the Financial stream and the Computational stream.
Compulsory courses previously offered include (both streams):
Additional compulsory courses for Computational Stream previously offered include:
Additional compulsory courses for Financial stream previously offered include:
Optional courses previously offered include:
We work closely with the Scottish Financial Risk Academy (SFRA) to offer a number of short courses led by industry (part of our Research-Linked Topics) and to provide the opportunity to our best students to write their dissertations during placements with financial services companies.
At the end of this programme you will have:
Graduates can expect to go on to work in major financial institutions or to continue their studies by joining PhD programmes.
This Masters degree provides you with knowledge of advanced finance concepts, whilst developing your quantitative, mathematical and research skills.
Taught by experienced academics based in both Leeds University Business School and the School of Mathematics, you’ll cover key topics including financial derivative pricing, discrete and continuous time models, risk management and portfolio optimisation, as well as statistical methods for finance.
You will be equipped with a rare combination of mathematical skills and the latest business finance knowledge, which is highly sought after in the financial sector by banks, investment and consultancy companies. It’s also excellent preparation if you’re interested in pursuing further academic research.
This course is ideal if you’ve previously studied finance, economics, mathematics, physics or computing, and are interested in applying your skills to financial markets.
As a student, you will be able to access the knowledge of our advanced specialist research units, which also have strong links with leading institutions in the US, Europe and Asia. These include the Centre for Advanced Study in Finance (CASIF), the Institute of Banking and Investment (IBI) and the Credit Management Research Centre (CMRC).
This research makes an important contribution to your learning on the MSc Financial Mathematics; you will benefit from a curriculum that is informed by the latest knowledge and critical thinking.
You will also benefit from our strong relationships with the finance, credit and accounting professions. This provides a connection to the latest practitioner and policy developments, giving you a masters degree that is relevant to the contemporary environment.
In your first semester you’ll develop a broad understanding of corporate finance and how financial theory relates to practice in business and financial markets. This will put your mathematical studies into context while you develop your skills in applied statistics and probability, optimisation methods and discrete time finance.
You’ll build on these skills in topics such as continuous time finance, risk management and computational methods. You’ll also gain specialist knowledge in topics that suit your career ambitions such as risk and insurance, actuarial science and behavioural finance.
The programme will improve your research skills and allow you to study different research methodologies, including those employed by our own leading academics. This will prepare you for your dissertation – an independent research project on a topic of your choice that you’ll submit by the end of the year.
You'll also take two optional modules.
We use a variety of teaching and learning methods to help you make the most of your studies. These will include lectures, seminars, workshops, online learning and tutorials. Independent study is also vital for this course allowing you to prepare for taught classes and sharpen your own research and critical skills.
In addition to the assessed modules and research dissertation, you benefit from professional training activities and employability workshops. Thanks to our links with major companies across the business world, you can also gain a practical understanding of key issues.
Recent activities have included CV building and interview sessions, professional risk management workshops and commercial awareness events. For example, students have developed their knowledge of financial markets through a one-week trading simulation. Read more about professional development activities for postgraduate finance students.
Assessment methods emphasise not just knowledge, but essential skills development too. They include formal exams, group projects, reports, computer simulation exercises, essays and written assignments, group and individual presentations.
This diversity enables you to develop a broad range of skills as preparation for professional life.
You have various opportunities open to you as a Financial Mathematics graduate, including: quantitative analysis, risk management, investment banking, financial consultancy, insurance, accounting and academia.
Previous graduates have gone on to secure employment with Allianz (London), AstraZeneca, Barclays, Cathay Life Insurance, CITIC Group, Commerzbank, Deloitte, First Direct, Gaz de France, HSBC, KPMG, Moody’s, PricewaterhouseCoopers, Royal Bank of Scotland, RSA and UK Government Actuary’s Department.
We help you to achieve your career ambitions by providing professional development support and training as part of the course. You benefit from the support of a professional development tutor, who will work with you to develop the important professional skills that employers value.
Read more about our careers and professional development support.
The University of Leeds Careers Centre also provides a range of help and advice to help you plan your career and make well-informed decisions along the way, even after you graduate. Find out more at the Careers website
This MSc teaches advanced analytical and computational skills for success in a data rich world. Designed to be both mathematically rigorous and relevant, the programme covers fundamental aspects of machine learning and statistics, with potential options in information retrieval, bioinformatics, quantitative finance, artificial intelligence and machine vision.
The programme aims to provide graduates with the foundational principles and the practical experience needed by employers in the area of machine learning and statistics. Graduates of this programme will have had the opportunity to develop their skills by tackling problems related to industrial needs or to leading-edge research.
Students undertake modules to the value of 180 credits.
The programme consists of two core modules (30 credits), four to six optional modules (60 to 90 credits), up to two elective modules (up to 30 credits) and a research project (60 credits). Please note that not all combinations of optional modules will be available due to timetabling restrictions.
Students must choose 15 credits from Group One Options. Of the remaining credits, students must choose a minimum of 30 and a maximum of 60 from Group Two, 15 credits from Group Three and a maximum of 30 credits from Electives.
Group One Options (15 credits)
Group Two Options (30 to 60 credits)
Group Three Options (15 credits)
Please note: the availability and delivery of optional modules may vary, depending on your selection.
A list of acceptable elective modules is available on the Departmental page.
All MSc students undertake an independent research project, which culminates in a dissertation of 10,000-12,000 words.
Teaching and learning
The programme is delivered through a combination of lectures, discussions, practical sessions and project work. Student performance is assessed through unseen written examinations, coursework, practical application and the project assessment process.
Further information on modules and degree structure is available on the department website: Computational Statistics and Machine Learning MSc
There is a strong national and international demand for graduates with skills at the interface of traditional statistics and machine learning. Substantial sectors of UK industry, including leading, large companies already make extensive use of computational statistics and machine learning techniques in the course of their business activities. Globally there are a large number of very successful users of this technology, many located in the UK. Areas in which expertise in statistics and machine learning is in particular demand include: finance, banking, insurance, retail, e-commerce, pharmaceuticals, and computer security. Graduates have gone on to further study at, for example, the Universities of Cambridge, Helsinki, Chicago, as well as at UCL. The MSc is also ideal preparation for a PhD, in statistics, machine learning or a related area.
Recent career destinations for this degree
Scientific experiments and companies now routinely generate vast databases and machine learning and statistical methodologies are core to their analysis. There is a considerable shortfall in the number of qualified graduates in this area internationally. CSML graduates have been in high demand for PhD positions across the sciences. In London there are many companies looking to understand their customers better who have hired our CSML graduates. Similarly graduates now work in companies in, amongst others, Germany, Iceland, France and the US in large-scale data analysis. The finance sector has also hired several graduates recently.
Careers data is taken from the ‘Destinations of Leavers from Higher Education’ survey undertaken by HESA looking at the destinations of UK and EU students in the 2013–2015 graduating cohorts six months after graduation.
The Centre for Computational Statistics and Machine Learning (CSML) is a major European Centre for machine learning having coordinated the PASCAL European Network of Excellence.
Coupled with the internationally renowned Gatsby Computational Neuroscience and the Machine Learning Unit, and UCL Statistical Science, this MSc programme draws on world-class research and teaching talents. The centre has excellent links with world-leading companies in internet technology, finance and related information areas.
The programme is designed to train students in both the practical and theoretical sides of machine learning. A significant grounding in computational statistics is also provided.
The Research Excellence Framework, or REF, is the system for assessing the quality of research in UK higher education institutions. The 2014 REF was carried out by the UK's higher education funding bodies, and the results used to allocate research funding from 2015/16.
The following REF score was awarded to the department: Computer Science
96% rated 4* (‘world-leading’) or 3* (‘internationally excellent’)
Learn more about the scope of UCL's research, and browse case studies, on our Research Impact website.
Postgraduate degree programme in Financial Engineering Masters/MSc:
MSc Financial Engineering is a multi-disciplinary field that involves the application of the computational engineering, software engineering, and computer programming skills, as well as the underlying mathematical and statistical theories to the analysis and management of financial opportunities. Students will receive the most advanced computational and programming techniques which help them advance quickly in the field.
Financial engineering is a multi-disciplinary field that involves the application of computational engineering, software engineering, and computer programming skills, as well as the underlying mathematical and statistical theories to the analysis and management of financial opportunities.
The programme is for strong (1st, 2.1 or equivalent) graduates from programmes in mathematics, or programmes with advanced mathematical components, and who wish to pursue a career in quantitative analysis in economic or financial sectors with state-of-art mathematical methods, computational skills and programming expertise.
In the Autumn and Spring semesters, you will take masters-level courses in both computational methods and programming and statistical methods in economics, as well as computer science courses such as the Computer Science Workshop, in addition to the core quantitative finance and further quantitative finance modules which are needed for a career in financial engineering and computational finance.
In the summer you will undertake a project, working with research leaders in mathematics and computer sciences. This will provide directly relevant training for a career in academic, and quantitative analysis in financial industry. A key component will be training specifically in independent study and research, an essential skill for quantitative analyst.
This programme gives an ideal preparation for a career in quantitative analysis in economic or financial sectors with state-of-art mathematical methods, computational skills and programming expertise. The School’s graduates work in a wide variety of fields in governmental and multi-national organisations.
University Careers Network
Preparation for your career should be one of the first things you think about as you start university. Whether you have a clear idea of where your future aspirations lie or want to consider the broad range of opportunities available once you have a Birmingham degree, our Careers Network can help you achieve your goal.
Our unique careers guidance service is tailored to your academic subject area, offering a specialised team (in each of the five academic colleges) who can give you expert advice. Our team source exclusive work experience opportunities to help you stand out amongst the competition, with mentoring, global internships and placements available to you. Once you have a career in your sights, one-to-one support with CVs and job applications will help give you the edge.
If you make the most of the wide range of services you will be able to develop your career from the moment you arrive.
The MSc in Mathematics and Foundations of Computer Science, run jointly by the Mathematical Institute and the Department of Computer Science, focuses on the interface between pure mathematics and theoretical computer science.
The mathematical side concentrates on areas where computers are used, or which are relevant to computer science, namely algebra, general topology, number theory, combinatorics and logic. Examples from the computing side include computational complexity, concurrency, and quantum computing. Students take a minimum of five options and write a dissertation.
The course is suitable for those who wish to pursue research in pure mathematics (especially algebra, number theory, combinatorics, general topology and their computational aspects), mathematical logic, or theoretical computer science. It is also suitable for students wishing to enter industry with an understanding of the mathematical and logical design and concurrency.
The course will consist of examined lecture courses and a written dissertation. The lecture courses will be divided into two sections:
Each section shall be divided into schedule I (basic) and schedule II (advanced). Students will be required to satisfy the examiners in at least two courses taken from section B and in at least two courses taken from schedule II. The majority of these courses should be given in the first two terms.
During Trinity term and over the summer students should complete a dissertation on an agreed topic. The dissertation must bear regard to course material from section A or section B, and it must demonstrate relevance to some area of science, engineering, industry or commerce.
It is intended that a major feature of this course is that candidates should show a broad knowledge and understanding over a wide range of material. Consequently, each lecture course taken will receive an assessment upon its completion by means of a test based on written work. Students will be required to pass five courses, that include two courses from section B and two at the schedule II level - these need not be distinct - and the dissertation.
The course runs from the beginning of October through to the end of September, including the dissertation.