The Applied Mathematics group in the School of Mathematics at the University of Manchester has a long-standing international reputation for its research. Expertise in the group encompasses a broad range of topics, including Continuum Mechanics, Analysis & Dynamical Systems, Industrial & Applied Mathematics, Inverse Problems, Mathematical Finance, and Numerical Analysis & Scientific Computing. The group has a strongly interdisciplinary research ethos, which it pursues in areas such as Mathematics in the Life Sciences, Uncertainty Quantification & Data Science, and within the Manchester Centre for Nonlinear Dynamics.
The Applied Mathematics group offers the MSc in Applied Mathematics as an entry point to graduate study. The MSc has two pathways, reflecting the existing strengths within the group in numerical analysis and in industrial mathematics. The MSc consists of five core modules (total 75 credits) covering the main areas of mathematical techniques, modelling and computing skills necessary to become a modern applied mathematician. Students then choose three options, chosen from specific pathways in numerical analysis and industrial modelling (total 45 credits). Finally, a dissertation (60 credits) is undertaken with supervision from a member of staff in the applied mathematics group with the possibility of co-supervision with an industrial sponsor.
The course aims to develop core skills in applied mathematics and allows students to specialise in industrial modelling or numerical analysis, in preparation for study towards a PhD or a career using mathematics within industry. An important element is the course regarding transferable skills which will link with academics and employers to deliver important skills for a successful transition to a research career or the industrial workplace.
The course features a transferable skills module, with guest lectures from industrial partners. Some dissertation projects and short internships will also be available with industry.
Students take eight taught modules and write a dissertation. The taught modules feature a variety of teaching methods, including lectures, coursework, and computing and modelling projects (both individually and in groups). The modules on Scientific Computing and Transferable Skills particularly involve significant project work. Modules are examined through both coursework and examinations.
Assessment comprises course work, exams in January and May, followed by a dissertation carried out and written up between June and September. The dissertation counts for 60 credits of the 180 credits and is chosen from a range of available projects, including projects suggested by industrial partners.
Course unit details
CORE (75 credits)
* Introduction to Uncertainty Quantification
* Mathematical Methods
* Partial Differential Equations
* Scientific Computing
* Transferable Skills for Applied Mathematicians
OPTIONAL (3 modules, 45 credits)
* Applied Dynamical Systems (IM)
* Continuum Mechanics (IM)
* Stability theory (IM)
* Transport Phenomena and Conservation Laws (IM)
* Advanced Uncertainty Quantification (IM,NA)
* Approximation Theory and Finite Element Analysis (NA)
* Numerical Linear Algebra (NA)
* Numerical Optimization and Inverse Problems (NA)
Students registered on the Numerical Analysis pathway must select modules marked NA, and those registered on the Industrial Modelling pathway must select modules marked IM.
Syllabuses for the modules Introduction to Uncertainty Quantification and Advanced Uncertainty Quantification are currently being finalized and details will be added here as soon as possible.
Modern computing facilities are available to support the course.
Practical support and advice for current students and applicants is available from the Disability Advisory and Support Service. Email: [email protected]
The programme will prepare students for a career in research (via entry into a PhD programme) or direct entry into industry. Possible subsequent PhD programmes would be those in mathematics, computer science, or one of the many science and engineering disciplines where applied mathematics is crucial. The programme develops many computational, analytical, and modelling skills, which are valued by a wide range of employers. Specialist skills in scientific computing are valued in the science, engineering, and financial sector.
This one-year master's course provides training in the application of mathematics to a wide range of problems in science and technology. Emphasis is placed on the formulation of problems, on the analytical and numerical techniques for a solution and the computation of useful results.
By the end of the course students should be able to formulate a well posed problem in mathematical terms from a possibly sketchy verbal description, carry out appropriate mathematical analysis, select or develop an appropriate numerical method, write a computer program which gives sensible answers to the problem, and present and interpret these results for a possible client. Particular emphasis is placed on the need for all these parts in the problem solving process, and on the fact that they frequently interact and cannot be carried out sequentially.
The course consists of both taught courses and a dissertation. To complete the course you must complete 13 units.
There are four core courses which you must complete (one unit each), which each usually consist of 24 lectures, classes and an examination. There is one course on mathematical methods and one on numerical analysis in both Michaelmas term and Hilary term. Each course is assessed by written examination in Week 0 of the following term.
Additionally, you must choose at least least one special topic in the area of modelling and one in computation (one unit each). There are around twenty special topics to choose from, spread over all three academic terms, each usually consisting for 12 to 16 lectures and a mini project, which culminates in a written report of around 20 pages. Topics covered include mathematical biology, fluid mechanics, perturbation methods, numerical solution of differential equations and scientific programming.
You must also undertake at least one case study in modelling and one in scientific computing (one unit each), normally consisting of four weeks of group work, an oral presentation and a report delivered in Hilary term.
There is also a dissertation (four units) of around 50 pages, which does not necessarily need to represent original ideas. Since there is another MSc focussed on mathematical finance specifically, the MSc in Mathematical and Computational Finance, you are not permitted to undertake a dissertation in this field.
You will normally accumulate four units in core courses, three units in special topics, two units in case studies and four units in the dissertation. In addition, you will usually attend classes in mathematical modelling, practical numerical analysis and additional skills during Michaelmas term.
In the first term, students should expect their weekly schedule to consist of around seven hours of core course lectures and seven hours of modelling, practical numerical analysis and additional skills classes, then a further two hours of lectures for each special topic course followed. In addition there are about three hours of problem solving classes to go through core course exercises and students should expect to spend time working through the exercises then submitting them for marking prior to the class. There are slightly fewer contact hours in the second term, but students will spend more time working in groups on the case studies.
In the third term there are some special topic courses, including one week intensive computing courses, but the expectation is that students will spend most of the third term and long vacation working on their dissertations. During this time, students should expect to work hours that are equivalent to full-time working hours, although extra hours may occasionally be needed. Students are expected to write special topic and case study reports during the Christmas and Easter vacations, as well as revising for the core course written examinations.
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.
Visit our website for more information on fees, scholarships, postgraduate loans and other funding options to study Mathematics and Computing for Finance at Swansea University - 'Welsh University of the Year 2017' (Times and Sunday Times Good University Guide 2017).
The MSc Mathematics and Computing for Finance course has been designed to meet the growing demand for specially trained mathematicians to work in the world’s financial markets and insurance.
Despite the current volatile nature of the banking industry, many banks still have a pressing need for employees with advanced mathematical skills who can further their understanding of turbulence in financial markets.
On the Mathematics and Computing for Finance course you will study different elements of both mathematics and computing in addition to developing your communication and presentational skills through a project you will undertake. As a student of the MSc in Mathematics and Computing for Finance programme you will be fully supported to ensure that your project is best suited to support your future career plans.
Have in depth knowledge in stochastic analysis and parts of advanced real analysis. (Fourier analysis and Partial Differential Equations) as well as parts of numerical analysis which are central for applications to finance.
Have developed advanced computing skills being essential for handling problems relevant for a job on the finance markets.
Have, as a mathematician, a good understanding of finance markets.
Have developed skills needed to work in a highly inter-disciplinary profession, including advanced programming techniques and communication skills across the borders.
Please visit our website for a full description of modules for the MSc Mathematics and Computing for Finance.
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 students have been employed by AXA, BA, Deutsche Bank, Shell Research, Health Authorities and Local Government. Teaching is another area where maths 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 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