Masters degrees in Mathematical Modelling equip postgraduates with the skills to apply mathematical methods in the construction (or simulation) of real-world processes. From these simulations, calculations and predictions may then be made.
Related postgraduate specialisms include Data Visualisation and Predictive Modelling. Entry requirements typically include an undergraduate degree in a relevant Mathematics subject.
Mathematical Modelling is essential in our understanding of many of the day-to-day processes and systems we know and utilise.
For example, modelling is a useful way of understanding different economies. You may work on behalf of government departments, dealing with big data to assess where crucial changes are needed, or to record activity.
This could include analysing the number of organisations involved with certain trade deals and transactions, or how certain economic operations will fare under different circumstances, such as recession.
These techniques also help understand industries such as transport or finance, whereby current figures may be used to assess supply and demand of different products and services.
Alternatively, you could be employed to undertake operational research on behalf of an organisation, calculating budgets, profits, pay scales and stocks.
This MSc provides an ideal foundation for students wishing to advance their mathematical modelling skills. The programme teaches students the basic concepts which arise in a broad range of technical and scientific problems and illustrates how these may be applied in a research context to provide powerful solutions.
Students develop an understanding of the processes undertaken to arrive at a suitable mathematical model and are taught the fundamental analytical techniques and computational methods used to develop insight into system behaviour. The programme introduces a range of problems - industrial, biological and environmental - and associated conceptual models and solutions.
Students undertake modules to the value of 180 credits.
The programme consists of five core modules (75 credits), three optional modules (45 credits), and a research dissertation (60 credits).
The part-time option normally spans two years. The eight taught modules are spread over the two years. The research dissertation is taken in the summer of the second year.
All MSc students undertake an independent research project, which culminates in a dissertation of approximately 15,000-words and a project presentation.
Teaching and learning
The programme is delivered through seminar-style lectures and problem and computer-based classes. Student performance is assessed through a combination of unseen examination and coursework. For the majority of courses, the examination makes up between 90–100% of the assessment. The project is assessed through the dissertation and an oral presentation.
Further information on modules and degree structure is available on the department website: Mathematical Modelling MSc
Our graduates have found employment in a wide variety of organisations such as Hillier-Parker, IBM, Swissbank, Commerzbank Global Equities, British Gas, Harrow Public School, Building Research Establishment and the European Centre for Medium-Range Weather-Forecasting.
Recent career destinations for this degree
Finance, actuarial and accountancy professionals are constantly in demand for their high-level mathematical skills and recent graduates have taken positions in leading finance-related companies such as UBS, Royal Bank of Scotland, Societe Generale, PricewaterhouseCoopers, Deloitte, and KPMG.
In the engineering sector, one recent graduate has progressed to a mathematical modelling role at a leading transportation planning consultancy; another became a graduate trainee at a business segment of Schlumberger that provides reservoir imaging, monitoring, and development services.
In addition, a number of graduates have remained in education either progressing to a PhD or entering the teaching profession.
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.
UCL Mathematics is internationally renowned for its excellent individual and group research that involves applying modelling techniques to problems in industrial, biological and environmental areas.
The department hosts a stream of distinguished international visitors. In recent years four staff members have been elected fellows of the Royal Society, and the department publishes the highly regarded research journal Mathematika.
This MSc enables students to consolidate their mathematical knowledge and formulate basic concepts of modelling before moving on to case studies in which models have been developed for issues motivated by industrial, biological or environmental considerations.
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: Mathematics
82% 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.
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.
MathMods is a 2-year Joint MSc programme which can be taken in 5 EU universities: University of L’Aquila in Italy (UAQ), Vienna University of Technology in Austria (TUW), Autonomous University of Barcelona in Spain (UAB), Hamburg University of Technology (TUHH) & University of Hamburg in Germany (UHH), and University of Nice - Sophia Antipolis in France (UNS).
What makes MathMods so special is its peculiar mobility scheme, that is the fact that our students will be spending their postgrad years in two or even three different European countries. You'll be indeed studying in central Italy for your first semester, then move to Austria or Germany for the second term, and finally move again to 1 of our 5 partners for your second year, based on the mobility path you'll be assigned.
Upon graduation students will be awarded a Joint Master's degree (or double, depending on where they spend their Year2).
Since its establishement in 2008 MathMods was funded by the EU Commission firstly through the Erasmus Mundus programme action 1 A (project no. 2008-0100), and later through the Erasmus+ Key Action 1 programme, project no. 2013-0227. We're currently applying for the Erasmus+ Call for Proposals 2018 to continue awarding Erasmus Munuds scholarships to our future generations. No matter the outcome, MathMods will still be running with the aid of Consortium grants and other local grants. Visit the sections Apply and Program Structure to learn more.
Semester 1 focuses on Theory and is to be spend in L'Aquila (Italy)
Semester 2 focuses on Numerics and can be taken in Vienna (Austria) or Hamburg (Germany).
Then for Year2 each partner institution offers a specific curriculum or study path:
Semester4 is dedicated to thesis work.
Mathematical modelling refers to the use of mathematics and related computational tools to bring real-world, challenging and important socio-economic and industrial problems into a form simple enough so that a good solution can be found in a reasonable time, while keeping the relevant features of the problem. Constructing models requires knowledge of enough mathematical theory, methods of solution which are really effective and efficient, computational tools at hand to do it, some knowledge of the field of application, and communicative skills to understand the important elements from experts in that field. Our master's programme tries to put together all these elements to produce professionals able to work in different relevant fields with the highest intellectual level and state-of-the-art tools.
Effective modelling and simulation is an art that require a lot of practice, so that problem solving, project development and team work are aspects that should be highlighted in any training programme, as our Consortium knows perfectly. On the other hand, the abstraction behind the specific application is necessary to realise that the same base tools can be applied, with the needed changes, to very different situations in various engineering fields.
The language of the whole course is exclusively English at each of our five universities. Students must also attend (and acquire the relating credits of) a course of basic Italian language (first semester) and German language (second semester). Students will also have the opportunity to attend local language courses during their second year (spent at one of the five partners).
The area of applied mathematics on which this project is focused is a fundamental scientific field for a number of key technologies and sciences. The areas of the proposed tracks connect very well with various branches of the European high-tech industry, and one of the goals of the project is to enhance these connections by means of the release of well prepared professionals and researchers.
Career opportunities for graduates will typically arise in research and development laboratories, especially those defining and testing numerical models and procedures, either working for an specific sector or with a broader scope. Also, in big or medium size enterprises possessing their own research department or a division with an orientation towards research, in public or privately held Sector Technology Centres, and at computing centres involved in data processing or the creation of numerical codes for the industry.
Click here to view the results of a recent survey taken by our graduates about their overall experience in our MSc and their work experience after having graduated.
The graduates will be able to apply successfully for PhD programmes if they wish so, as has happened for the three already completed cycles. In all the countries of the Consortium members, the programme has been validated as enabling the holder of the MSc degree to enter a local PhD programme. A good percentage of our students seem indeed to prefer pursuing a PhD before going to the industry or returning to their countries of origin. The intended level of the programme, together with the initial selection of the students, allows affirming that most of them could follow a successful academic career, after a suitable PhD.
Postgraduate degree programme in Mathematical Modelling Masters/MSc:
Most things in the real world are complex and difficult to understand, from biological systems to the financial markets to industrial processes, but explaining them is essential to making progress in the modern world. Mathematical modelling is a fundamental tool in the challenge to understand many of these systems, and is an essential part of contemporary applied mathematics. By developing, analysing and interpreting mathematical and computational models we gain insight into these complex processes, as well as giving a framework in which to interpret experimental data.
To fully capitalise on these tools, there is a fundamental need in both academic research and industry for a new generation of scientists trained to work at the interdisciplinary frontiers of mathematics and computation. These scientists require the ability to assimilate and understand information from other disciplines, communicate with and enthuse other researchers, as well as having the advanced mathematical and computational skills needed.
In the Autumn and Spring semesters, you will take masters-level courses in both advanced mathematical modelling and computation, in addition to the core interdisciplinary skills needed for a career in this field. In the summer you will undertake a research skills project, working with research leaders in a related area such as biosciences, systems biology, chemical engineering or medicine, alongside mathematics and computation. This will provide directly relevant training for a career in academic, industrial or clinical research, for example biotechnology, industrial engineering or the pharmaceutical industry. A key component will be training specifically in multidisciplinary research and communication, a vital skill for whichever career path the MSc leads you to.
In the Autumn and Spring semesters, you will take masters-level courses in both advanced mathematical modelling and computation, in addition to the core interdisciplinary skills needed for a career in this field.
In the summer you will undertake a research skills project, working with research leaders in a related area such as biosciences, systems biology, chemical engineering or medicine, alongside mathematics and computation. This will provide directly relevant training for a career in academic, industrial or clinical research, for example biotechnology, industrial engineering or the pharmaceutical industry.
A key component will be training specifically in multidisciplinary research and communication, a vital skill for whichever career path the MSc leads you to.
This course is tailored to train students for careers in scientific research, and for employment in a wide range of industrial contexts, for example biotechnology, industrial engineering or the pharmaceutical industry. There is a considerable need for scientists with a strong mathematical and computational background who can communicate with experimental scientists; this MSc will provide you with specialised training, and through your research skills project, evidence that you can work in this multidisciplinary context.
Further transferrable skills developed through this course include team-working, oral and written presentation, problem-solving and time-management, particularly developed through the summer research skills project. Additional careers support is available through the School of Mathematics and from the University's career support team.
Self-learning systems are an important and newly emerging technique in many areas of applied science such as Applied Mathematics, Engineering, Computer Science and Statistics. In particular, self-learning systems are a disruptive approach to mathematical modelling which use differential equations at their foundation. A particular strength of this approach is that it combines numerical learning algorithms such as dynamic machine learning with differential equations to design applications that can adapt to a changing environment. This approach is new and unique because it explicitly takes into account the dynamic aspects of data and allows for fast and accurate modelling of self-learning systems. This is a new and rapidly developing area at the interface between applied mathematics and machine-learning (for example see here).
The primary aim of this course is to provide training in the use and development of modern numerical methods and self-learning software. Graduates will develop and apply new skills to real-world problems using mathematical ideas and techniques together with software tailored for complex networks and self-learning systems. While there is a strong focus on modern applications, graduates will gain in-demand skills in mathematical modelling, problem-solving, scientific computing, dynamic machine learning, complex networks and communication of mathematical ideas to a non-technical audience.
More general hands-on skills include mathematical typesetting, mathematical writing, desktop and web-based mathematical software development, and the use of computer languages and packages such as C#, R, Python and TensorFlow.
The course places great emphasis on hands-on practical skills. There is a computer laboratory allocated solely for the use of MSc students. PCs are preloaded with all the required software and tools. Teaching hours, tutorials and practical demonstrations, usually take place in the morning. The rest of the time, you are expected to do exercises, assignments and generally put in the time required to acquire key skills. For online modules, students are advised to have access to a laptop/home computer with internet connection, modern browser, word processing and spreadsheet software.
This MSc reflects a philosophy of cutting edge teaching methods and pragmatism. As well as providing you with a host of abilities which are in demand in industry, this MSc provides skills which are complementary to most scientific and engineering undergraduate courses. The MSc not only opens up new possibilities, you also gain a set of skills that sets you apart from the crowd in your original field of study. The final project is an excellent opportunity for you to showcase your abilities to future employers or to undertake a detailed study in a new area of interest. The course is extremely flexible in helping you realise your ambitions.
Graduates with quantitative skills and expertise in self-learning algorithms are in high demand in industry according to the Governments Expert Group on Future Skills Needs. Demand for these skills is projected to rise over the coming years not just in Ireland but in the EU and globally. Graduates from a similar MSc have secured jobs in the following areas: banking, financial trading, consultancy, online gambling firms, software development, logistics, data analysis and with companies such as AIB, McAfee, Fexco, DeCare Systems, MpStor, the Tyndall Institute, Matchbook.com, First Derivatives and KPMG.
Visit the Institute for Transport Studies at our Masters Open Days.
Mathematical models are fundamental to how we understand, analyse and design transportation systems, but these models face challenges from the rapidly changing nature of mobility.
Innovative technologies are being harnessed to deliver new approaches to transport services, and huge volumes of data create new opportunities to examine how patterns of movement are evolving.
If you’re a highly numerate graduate with a desire to apply your quantitative skills to the real world, or a practitioner working in the sector, this course will take you to the next level and prepare you for a career as a transport modelling specialist.
97% of our graduates find employment in a professional or managerial role, or continue with further studies.*
Experience a course designed in collaboration with employers, learning skills the industry desperately needs to unlock the full potential of big data.
Learn to think creatively, beyond the standard application of established solutions, and use your technical expertise across multiple scenarios.
Develop and apply mathematical models to analyse and improve the performance of transportation networks and flows:
Experience what it is like to be part of a project team working across disciplinary boundaries within the transport sector. Through this, gain insights into how modelling, environmental science, planning, economics and engineering can work together to develop sustainable solutions to global challenges. This industry-inspired approach will enable you to apply your knowledge to real-world issues in the field.
Your colleagues will be among the best and brightest from the UK and across the globe. Together you will learn mathematical modelling skills that can be applied to design smarter transport solutions founded on robust methods.
With a strong focus on industry needs, our degrees will prepare you for employment in your chosen field. They will also address the multi-disciplinary nature of transport – enabling you to make effective decisions for clients, employers and society.
Other Study Options
This programme is available part time, allowing you to combine study with other commitments. You can work to fund your studies, or gain a new qualification without giving up an existing job. We aim to be flexible in helping you to put together a part-time course structure that meets your academic goals while recognising the constraints on your study time.
The Complex Systems Modelling - From Biomedical and Natural to Economic and Social Sciences MSc programme will teach you to apply mathematical techniques in the rapidly developing and exciting interdisciplinary field of complex systems and examine how they apply to a variety of areas including biomedicine, nature, economics and social sciences. This research-led course is suitable for graduates who wish to work in research and development in an academic or industrial environment.
The Complex Systems Modelling MSc is an innovative study programme that explores the latest research in the rapidly developing and exciting interdisciplinary field of cpmplex systems.
Modern societies rely on a broad range of infrastructures, institutions and technologies, and their complexities have grown dramatically in the recent past. Consequently, there is a rapidly expanding demand for expertise in complex systems modelling as a foundation for understanding, maintaining and further developing of such systems.
The programme offers you the choice to study either full or part-time. You must take a combination of required and optional 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 complex systems modelling module in your second year.
You will study key natural and biomedical scientific topics as well as economic and social sciences. We also offer the opportunity to study an additional zero-credit module called foundations for complex systems modelling and cross-disciplinary approaches to non-equilibrium systems and is designed as a refresher module covering vital mathematics and physics skills.
For graduates in mathematics, or in other suitable scientific disciplines with a strong background in mathematics, who want to work in research and development in an academic or industrial environment. The programme aims to develop a knowledge and understanding of complex systems modelling and their uses, and to enable students to use mathematical techniques to quantify, predict and improve such systems.
Primarily written examinations, some with coursework element, in eight lecture modules, plus an oral presentation and assessed report on the research project.
Our graduates are highly sought after: the applicability of complex systems modelling to areas as diverse as biomedical, natural, economic and social sciences, results in a broad range of opportunities. Some graduates are employed by the companies or laboratories that supervise their MSc research projects, or continue to PhD study.
Other career destinations include:
In this MRes Mathematical Sciences course, you will gain deep knowledge of a chosen topic in mathematics or statistics and develop your research skills in project planning, reviewing literature, group discussions, research presentations and writing publications.
You can choose to work with experts from a range of areas including quantum cryptography, graph theory, statistical analysis, bioinformatics and mathematical modelling.
You will take three taught modules each providing you with the underpinning theory to support your research work.
Visit us on campus throughout the year, find and register for our next open event on http://www.ntu.ac.uk/pgevents.
This programme reflects and benefits from the strong research activities of the Department of Mathematics.
The taught modules and dissertation topics are closely aligned with the interests of the Department’s four research groups:
During the first two semesters you will take a range of taught modules from an extensive list of options, followed by an extended research project conducted over the summer under the supervision of a member of the department, culminating in the writing of a dissertation.
This programme is studied full-time over one academic year. It consists of eight taught modules and a dissertation.
Example module listing
The following modules are indicative, reflecting the information available at the time of publication. Please note that not all modules described are compulsory and may be subject to teaching availability and/or student demand.
Mathematics is not only central to science, technology and finance-related fields, but the logical insight, analytical skills and intellectual discipline gained from a mathematical education are highly sought after in a broad range of other areas such as law, business and management.
There is also a strong demand for new mathematics teachers to meet the ongoing shortage in schools.
As well as being designed to meet the needs of future employers, our MSc programme also provides a solid foundation from which to pursue further research in mathematics or one of the many areas to which mathematical ideas and techniques are applied.
Knowledge and understanding
Intellectual / cognitive skills
Professional practical skills
Key / transferable skills
We often give our students the opportunity to acquire international experience during their degrees by taking advantage of our exchange agreements with overseas universities.
In addition to the hugely enjoyable and satisfying experience, time spent abroad adds a distinctive element to your CV.
This programme gives you a flexible syllabus to suit the demands of employers that use modern financial tools and optimization techniques in areas such as the financial sector and energy markets.
We will give you sound knowledge in financial derivative pricing, portfolio optimization and financial risk management.
We will also provide you with the skills to solve some of today’s financial problems, which have themselves been caused by modern financial instruments. This expertise includes modern probability theory, applied statistics, stochastic analysis and optimization.
Adding depth to your learning, our work placement programme puts you at the heart of financial organisations such as Moody's Analytics, Standard Life Investment and Lloyds Banking Group.
This programme involves two taught semesters of compulsory and option courses, followed by a dissertation project. You must obtain a total of 180 credits to be awarded the MSc. Over semesters 1 and 2, you will take a number of compulsory courses and optional courses. 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, possibly with one of our industry partners, for the award of the MSc degree.
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 have gone on to work in major financial institutions or to continue their studies by joining PhD programmes.