MSc Industrial Mathematical Modelling degree

Qualifications available: MSc

Entry requirements
2:1 +
Full-time
1 year
Part-time
Not available
Start date
September 2020
UK / EU fee
£9,300
International fee
£19,100
Location
Loughborough
Application status
Open

Overview

Our MSc Industrial Mathematical Modelling will equip you with the skills and techniques required by industrial mathematics, including the real world problem-solving abilities in applied mathematics that are highly sought after within industry and commerce.

Industrial mathematics is a branch of applied mathematics that focuses on a modelling, simulating and solving problems of relevance to industry.

Our master's degree in industrial mathematics modelling enables you to explore mathematical models of real-world processes and their formulation, with a strong emphasis on how these techniques can be applied in industry, culminating in a 12-week summer project which is usually carried out within a local business. Your project is supported by our well-established links to industry and will give you a practical, real-life insight into how mathematical theory and technique is applied in organisational scenarios.

MSc Industrial Mathematical Modelling will see you work in small groups to solve industry-based problems using mathematical models and statistics, whilst also covering areas such as regular and chaotic dynamics, partial differential equations and fluid mechanics.

As a postgraduate student within the Department of Mathematical Sciences, your studies will be enhanced by the research insights of our international staff, as well as our recently refurbished building with dedicated modern facilities for mathematics.

Who should study this programme?

Mathematical modelling is a valuable skill for solving the real problems and challenges faced by companies and provides a useful language to describe, solve and validate the problem. As such, our industrial mathematics master's is especially suitable if you have undertaken a 3-year bachelor's degree in mathematics, science or engineering and wish to apply your enhanced skills in an industrial context. The programme also also provides excellent preparation for PhD study.

Why you should choose us

Why you should study this degree

What makes this programme different?

  • 12 week summer project - often carried out in a local company
  • provides mathematical techniques required by industry
  • learn the skills to solve partial differential equations.

What you'll study

Our MSc Industrial Mathematical Modelling provides a solid foundation in the core areas of mathematics relevant to industry.

The following information is intended as an example only and is based on module information for the 2019/20 year of entry. Modules are reviewed on an annual basis and may be subject to future changes. Updated Programme and Module Specifications are made available ahead of each academic year. Please see Terms and Conditions of Study for more information.

Regular and Chaotic Dynamics

In this module you will study dynamical systems from a modern viewpoint, emphasising the rich behaviour of nonlinear systems.

Module content

Topics covered may include:

  • Hamiltonian formalism
  • integrable systems
  • Kepler's system and harmonic oscillator
  • phase plane analysis
  • linearisation
  • stability
  • bifurcations
  • chaos
  • fractals and strange attractors
  • baker's map
  • Feigenbaum universality.

Learning outcomes

On completion of this module you will be able to:

  • define the Liouville integrability and describe its dynamical consequences
  • analyse stability of nonlinear differential equations and maps
  • describe bifurcations of nonlinear differential equations and maps
  • explain the role of fractals in chaotic systems
  • analyse Kepler system and derive Kepler's laws of planetary motion
  • apply linearisation techniques
  • use stability tests
  • explain different types of Hopf bifurcations
  • analyse simple integrable and chaotic systems

Teaching and learning

  • seminars: 12 hours
  • lectures: 24 hours
  • guided independent study: 114 hours

Assessment

  • 1 x 3-hour exam

Programming and Numerical Methods (15 credits)

This module will introduce you to the basic concepts of programming, as well as introducing and explaining numerical methods for solving ordinary and partial differential equations.

Module content

Topics studied may include:

  • programming in a standard language
  • numerical methods for the solution of ordinary differential equations (ODEs): linear multi-step and Runge-Kutta methods for scalar ODEs and systems of ODEs
  • numerical methods for the solution of partial differential equations: finite difference and finite element methods.

Learning outcomes

On completion of this module, you will be able to:

  • program a numerical method in a standard programming language
  • use numerical methods to find the solutions of ordinary and partial differential equations
  • apply numerical methods for solving ordinary and partial differential equations
  • derive numerical methods for solving ordinary and partial differential equations
  • program competently.

Teaching and learning

  • practical classes and workshops: 12 hours
  • lectures: 24 hours
  • guided independent study: 114 hours

Assessment

  • 1.5-hour in-class computer-based programming test: 50%
  • 2-hour written exam: 50%

Mathematical Modelling (15 credits)

This module will develop your skills in the mathematical modelling of real life situations, along with your ability to work effectively in a group.

Module content

Your introductory lectures will describe the general principles of mathematical modelling, with additional ones presenting case histories and sampling modelling problems.

A large part of the module involves working on group tasks - you will be involved in two modelling tasks chosen from a range of topics in the areas of mechanics, heat transfer and fluid mechanics. The direction of these modelling tasks is supervised through weekly meetings between each group and your module coordinators.

The tasks do not require sophisticated solution procedures but do often involve solving mathematical models on a computer. They are aimed at developing your ability and confidence in the modelling process and working effecively in a group.

Learning outcomes

On completion of this module you will be able to:

  • evaluate the role that mathematical modelling plays in the investigation of real life problems
  • formulate mathematical models for simple systems
  • determine appropriate solution methods
  • obtain solutions and interpret results
  • prepare a research report and briefing.

Teaching and learning

  • lectures: 15 hours
  • seminars: 21 hours
  • guided independent study: 114 hours

Assessment

  • group project 1: 40%
  • group project 2: 60% 

Optional modules (choose one)

Stochastic Models in Finance (15 credits)

This module will:

  1. introduce you to basic discrete models in finance
  2. provide you with the mathematical background in the security market and derivative industry
  3. introduce you to the mathematical tools needed to deal with financial problems.

Module content

Topics studied may include:

  • discrete stochastic process modelling of stock prices
  • portfolios
  • martingale and arbitrage opportunity
  • martingale measure
  • pricing and hedging European options
  • complete markets
  • binomial models
  • optimal stopping problem and American options
  • optimal portfolio and dynamic programming.

Learning outcomes

On completion of this module you will be able to:

  • explain the essential role that the random processes and martingales play in the mathematical modelling of a stock price
  • describe variety of contingent claims and their relevance to real world problems
  • apply mathematics to study option pricing and hedging
  • use discrete stochastic process to model a stock price
  • use martingales to study arbitrage and risk neutral probability measures
  • use risk neutral probability measure and martingales to study pricing and hedging portfolios of contingent claims
  • use optimal stopping to study American options
  • use martingale method to solve optimal portfolio problems
  • construct rigorous mathematics argument (proof)
  • build stochastic models for some simple real world problems.

Teaching and learning

  • practical classes and workshops: 12 hours
  • lectures: 24 hours
  • guided independent study: 114 hours

Assessment

  • 1 x 3-hour exam: 100%

Mathematical Methods for Interdisciplinary Sciences (15 credits)

This module will help you to develop the mathematical skills needed for your research projects. It will also introduce some of the mathematical methods that can be applied to models in a range of interdisciplinary sciences. Students who complete the module should be able to comprehend an extended range of advanced mathematical methods, including ordinary differential and partial differential equations, integral equations and the use of variational technique.

The module will enable you to have improved skills in solving differential equations and have an enhanced ability to use specific analytical and numerical physical methods. You'll also be able to apply a range of mathematical methods to various interdisciplinary problems.

Topics studied may include:

  • Ordinary and partial differential equations
  • Integral equations
  • Qualitative analysis of differential equations
  • Variational techniques

Elements of PDEs (15 credits)

This module will develop your familiarity with modern qualitative theory of linear Partial Differential Equations (PDEs), with particular emphasis on second-order equations. You will also study selected aspects of modern methods for simple nonlinear PDEs.

Learning outcomes

  • On completion of this module you be able to:
  • recognise the significance of uniqueness and existence results
  • recognise the need for qualitative methods for PDEs
  • apply the basic qualitative methods for Laplace's equation, the heat equation and the wave equation
  • use characteristics to analyse first and second order nonlinear PDEs

Module content

  • linear theory:
    • classification of second-order linear PDE into elliptic, parabolic and hyperbolic types
  • methods of characteristics
  • basic questions of well-posedness
  • fundamental solutions and Green's functions
  • Laplace's equation:
    • fundamental solution
    • maximum principle
    • sub- and superharmonic functions
    • mean-value theorems
    • regularity theory for solutions
  • heat equation:
    • fundamental solution
    • maximum principle
    • infinite speed of propagation
    • smoothing properties
    • energy estimates
  • wave equation:
    • transport of information at finite speeds
    • solution by spherical means
    • Euler-Poisson-Darboux equation
    • Kirchhoff's and Poisson's formulae
    • distinction between odd and even dimensions
    • energy estimates
  • nonlinear theory:
    • similarity and travelling-wave solutions of non-linear equations.

Teaching and learning

  • seminars: 12 hours
  • lectures: 24 hours
  • guided independent study: 114 hours

Assessment

  • 1 x 3-hour exam: 100%

Static and Dynamic Optimisation (15 credits)

This module will develop your familiarity with theory and techniques of static optimisation and dynamic optimisation.

Learning outcomes

On completion of this module you will be able to:

  • identify appropriate methods for solving optimisation problems exactly and numerically
  • interpret solutions to optimisation problems in applied situations
  • resolve subtle difficulties that arise in implementation of optimisation algorithms
  • describe basic properties of and implement methods for unconstrained static optimisation
  • apply methods for optimising under constraints
  • write computer code which implements numerical optimisation algorithms
  • analyse dynamic optimisation problems using the calculus of variations
  • solve optimal control problems.

Module content

Topics covered may include:

  • static optimisation:
    • definition of the nonlinear program
    • modelling practical problems as nonlinear programs
  • Karush-Kuhn-Tucker conditions and constraint qualifications
  • General form of an optimisation algorithm, descent property, stopping conditions and convergence
  • algorithms for single and multi-variable unconstrained function optimisation
  • dynamic optimisation: the calculus of variations
  • the principle of optimality and dynamic programming
  • applications to the optimal control problem
  • the linear regulator and the Riccati equation
  • pontryagin's Maximum Principle

Teaching and learning

  • lectures: 15 hours
  • seminars: 15 hours
  • guided independent study: 120 hours

Assessment

  • coursework: 30%
  • 1 x 2-hour exam: 70%

Mathematical Modelling (15 credits)

This module is a continuation of that of the same name in semester 1. It will develop your skills in the mathematical modelling of real life situations and your ability to work effectively in a group.

Module content

You will be involved in two modelling tasks chosen from a range of topics in the areas of mechanics, heat transfer and fluid mechanics, material science, and logistics. The direction of the modelling tasks is supervised through weekly meetings between each group and the module coordinators.

You may use numerical techniques studied in other modules to develop solutions for these tasks.

Learning outcomes

On completion of this module you will be able to:

  • evaluate the role that mathematical modelling plays in the investigation of real life problems
  • formulate mathematical models for simple systems
  • determine appropriate solution methods
  • obtain solutions and interpret results
  • prepare a research report and briefing.

Teaching and learning

  • lectures: 16 hours
  • seminars: 20 hours
  • guided independent study: 114 hours

Assessment

  • 2 x group projects: 100%

Fluid Mechanics (15 credits)

This module will:

  1. provide you with knowledge of the fundamental equations of fluid mechanics
  2. develop your expertise in solving simplified forms of these equations applicable to a variety of fluid flows
  3. teach you about some of the industrial and environmental applications of fluid mechanics.

Learning outcomes

On completion of this module you will be able to:

  • describe the significance of the various terms in the equations of fluid motion
  • describe the dependence of flow on Reynolds number
  • model a variety of flows using appropriate forms of the equations of fluid motion
  • relate mathematical equations to physical processes.

Module content

Topics studied may include:

  • conservation laws for:
    • mass (continuity equation)
    • passive tracer (advection-diffusion equation)
    • momentum (Navier-Stokes equation)
    • energy
  • exact solutions of the equations of fluid motion
  • low-Reynolds-number flows
  • boundary layer theory
  • vorticity dynamics.

Teaching and learning

  • seminars: 12 hours
  • lectures: 24 hours
  • guided independent study: 114 hours

Assessment

  • 1 x 3 hour exam: 100%

Industrial Mathematical Modelling Research Project (60 credits)

This module will provide you with experience of independent work in mathematics and its applications, especially those of an industrial nature.

Learning outcomes

On completion of this module, you will be able to:

  • define a research programme in the field of industrial mathematics and its applications
  • identify and explain research approaches appropriate to the area in question
  • present results clearly and accurately and use them to draw appropriate conclusions
  • take a practical solution arising in and out of interest to industry and represent it by a mathematical model
  • apply theoretical and/or practical knowledge to solve the specific problem
  • write-up the solution in a clear and convincing manner
  • identify the limitations, where applicable, of the chosen model, and draw relevant conclusions.

Module content

Departmental staff provide project specifications annually covering a wide range of mathematical interests within which they are able to supervise projects. A limited number of projects supplied by external sponsors may also be available. In the case of external projects, you will be expected to work primarily under the supervision of the external supervisor and be present on a normal work day basis.

Teaching and learning

  • guided independent study: 600 hours

Assessment

  • oral presentation: 25%
  • project report: 75%

How you'll be assessed

You will be assessed by a combination of exams, reports, individual and group projects, and verbal presentations. You will spend approximately 14 weeks at the end of the programme devoted to an individual project, either in an industrial or engineering company, or at the University. For full details, please see the module descriptions above.

How you'll study

  • Lectures
  • Seminars
  • Independent study
  • Group work
  • Supervision
  • Workshops
  • Practical sessions

Your personal and professional development

The Department of Mathematical Sciences is committed to helping you develop the skills and attributes you need to progress successfully in your chosen career.

Future career prospects

Graduate employment spans a wide range of industries encompassing aerospace, automotive electronics and computer interests, as well as software houses, insurance companies and research establishments and institutions.

Graduate destinations

Recent graduate destinations include:

  • lecturer in higher education
  • modeller in the Energy technology Institute
  • PhD study in plasma liquid interactions
  • software Engineer in New Zealand

Your personal development

Our industrial mathematics master's will support your personal development by equipping you with industry-relevant skills. In particular, you will be introduced to a range of analytical, qualitative and numerical techniques, and instructed in the application of computer software to the solution of mathematical problems. You will develop in both independent working and group work, whilst growing your time management, organisational, IT, presentation and communication skills.

Entry requirements

Our entry requirements are listed using standard UK undergraduate degree classifications i.e. first-class honours, upper second-class honours and lower second-class honours. To learn the equivalent for your country, please choose it from the dropdown below.

Entry requirements for United Kingdom

A 2:1 honours degree (or equivalent international qualification) in mathematics or an engineering or science subject with a high mathematical content.

Afghanistan

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Masters 95% 85% 70%

Albania

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Diplomë e Nivelit të Pare (First Level (University) Diploma (from 2010) 9.5 8.5 8

Algeria

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Licence (4 year) / Diplome d'Inginieur d'Etat / Diplôme d'Etudes Supérieures 16 14 12

Argentina

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Argentina 8.5 7.5 6.0

Armenia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Bakalavri Kochum 90% 80% 70%
Magistrosi Kochum 3.9 3.5 3.0

Australia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Honours degree (AQF level 8) First Class, 80% Upper Second, 70%, H2A Lower Second, 60%, 2B
Ordinary degree - AQF Level 7 pass (mark 46 or 50) High Distinction (80% or 85%) Distinction (75% or 80%) Distinction (70% or 75%)

Austria

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Degree/ Diplomstudium / Magister degree A (or 1.5) mit Auszeichnungbestanden 60% or B or 3.0 (or 2) 50% or C or 2.7 (or 3)

Azerbaijan

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Bakalavr Diplomu 4.5 4 3.5
Diplomu (Specialist Diploma) 90% 80% 70%

Bahamas

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Degree from University of the West Indies only 1st (GPA 3.6) 2:1 (GPA 3.0) 2:2 (GPA 2.5)

Bahrain

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
GPA 4.0 scale 3.5 3.0 2.8

Bangladesh

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
BUET or 'Good Private' University - 4 year degree BUET - 1st (70%) / 3.5 BUET - 2nd (60%) / 3.0 BUET - 2nd (55%) / 2.75
Other universities - Masters (1-2 years) following a 3 or 4 year degree 80% / 4.0 65% / 3.25 50% / 2.5

Barbados

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Barbados - Degree from University of the West Indies only 1st (GPA 3.6) 2:1 (GPA 3.0) 2:2 (GPA 2.5)

Belarus

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Specialist Diploma (5Yr) 9 7 5

Belgium

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Bachelor degree Magna Cum Laude Cum Laude 60%/12
Licenciaat 80% 70% 60%
Licencie 17 14 12

Belize

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Degree from University of the West Indies only 1st (GPA 3.6) 2:1 (GPA 3.0) 2:2 (GPA 2.5)

Benin

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Maitrise 18 15 or Bien 12 or Assez Bien

Bermuda

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Degree from University of the West Indies only 1st (GPA 3.6) 2:1 (GPA 3.0) 2:2 (GPA 2.5)

Bolivia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
A Licenciado, 4 years Private (public/private) 85/78 75/66 67/55

Bosnia and Herzegovina

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Diploma Visokog Obrazovanja / Diplomirani 10 9 8

Botswana

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Master's degree A or 80% B or 70% C or 60%

Brazil

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Brazil - 4 yr Bacharel or Licenciado/Licenciatura or Título Profissional 8.5 (A) 7.5 6.0

Brunei

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Brunei First Upper Second (60%/B/3.1) Lower Second (50%/C/2.7)

Bulgaria

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
5 yr Diploma za Zavarsheno Visshe Obrazovanie (Diploma of Completed Higher Education) 6 5 4

Cambodia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
4 years 90% or 9 or 4.0 80% or 8 or 3.5 70% or 7 or 3.0

Cameroon

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Bachelor degree or Diplome d'Etudes Superiures de Commerce 1st or 15 2:1 or 14 2:2 or 12.5
Diplome d'Ingenieur or Diplôme d'Ingénieur de Conception or a Maitrise or a 4 year Licence 20 or GPA 3.7 20 or Bien (GPA 3.4) 20 or Assez Bien (GPA 3.1)

Canada

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
GPA 4.0/percentage scale 3.7/85% 3.3/75% 2.7/68%
Out of 9 8 6 5
Out of 12 10 8 6

Chile

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Grado de Licenciado / Título (Profesional) de [subject area] (4 years) 6 5.5 5

China

Students are required to have a bachelor degree (4 years) for entry to a postgraduate programme. The University uses the Shanghai Academic Ranking of World Universities to identify the required final mark, as outlined on the table below:

First class (70%) Mid 2:1 (65%) 2:1 (60%) Mid 2:2 (55%) 2:2 (50%)
Shanghai Rank Top 250 85% 81% 80% 78% 77%
Shanghai Rank 251-500 89% 84% 83% 81% 80%
Shanghai Rank 501+ 92% 87% 86% 85% 82%

Affiliated colleges

The University will consider students from Affiliated Colleges in the following way:

Applicants from colleges affiliated to universities in the top 250 Shanghai rankings will considered if they have achieved or are likely to achieve final marks of 80%-84%.

Applicants from colleges affiliated to universities which are 251-500 in the Shanghai rankings will considered if they have achieved or are likely to achieve final marks of 82%-87%.

Applicants from colleges affiliated to universities which are above 500 in the Shanghai rankings will considered as follows:

  • School of Business and Economics: not considered
  • All other programmes if they have achieved or are likely to achieve final marks of 82%-87%.

Universities given special consideration

Applicants from a small number of Chinese universities that specialise in business, management, finance or creative arts will be given special consideration by the University. The full list of these universities and the Shanghai band under which they will be considered can be found in the PDF below.

Download the list of Chinese universities given special consideration here

Students who do not meet the above requirements may occasionally be considered if they have a relevant degree, can show good grades in relevant subjects, and/or have substantial relevant work experience.

Colombia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Licenciado / Título de [subject area] 4.5 3.75 3.2

Costa Rica

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Licenciado 9 8 or 80 7 or 75

Croatia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Baccalaureus / Prvostupnik 4.5 3.8 3.0

Cuba

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
4-year Titulo de Licenciado / Licenciatura 5 4 3

Cyprus

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Cyprus 8.5 7.0 6.5

Czech Republic

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Bakalár (after 2001) 6 yr integrated Magistr 1 1.5 2

Denmark

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
5 year Candidatus/Candidata Magisterii or Bachelor degree (7 point scale) 12 10 7

Dominican Republic

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
4 year Licenciado 3.8 Magna Cum Laude 3.5 Cum Laude 3.2
Título de [subject area] - 85% 82%

Ecuador

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Título de Licenciado 8.5 8 7
Título de [subject area] 85% 80% 70%

Egypt

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Egypt 3.5 3.2 2.8
Universities only BA 90%, BSc 85% BA 80%, BSc 75% BA 65%, BSc 65%

El Salvador

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
5 year Licenciado 8.5 7.5 6.5
Título de Ingeniero 85% 75% 65%
Arquitecto - Muy Bueno Bueno

Estonia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Bakalaureusekraad or Magister or Magistrikraad 5 or A 4 or B 3 or C

Ethiopia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Master's A/GPA 4.0 A/GPA 3.5 B/GPA 2.8

Finland

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Kandidaattii/Kandidat (out of 3) 3 2 1
Maisteri/Magister (out of 5) 4.5 3 2.5

France

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Licence (3 years)/ Maitrise/ Diplôme d'Ingénieur 14 12 11

Georgia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
4-year degree (% = new system) 5 (95%) 4.5 (85%) 4 (75%)

Germany

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
German Bachelor/ Diplom, Magister Artium / Zeugnis über den Zweiten Abschnitt der Ärztlichen Prüfung 1.5 2.5 3.0

Ghana

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Ghana First Upper second/60% Lower second/50%

Greece

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
AEI 8.5 7.0 6
TEI 8.5 7 6.5

Grenada

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Degree from University of West Indies - classification 1st 2:1 2:2
Degree from University of West Indies - grade / percentage A B / 75% C / 55%
Degree from University of West Indies - GPA 3.6 3.0 2.0

Guatemala

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Liceniado / Titulo de (subject area) - 4years 90% (public university) / 95% (private university) 80% (public university) / 85% (private university) 60% (public university) / 70% (private university)

Guyana

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Master's GPA 4 GPA 3.5 3.0

Honduras

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Título de Licenciado / Grado Académico de Licenciatura (4 year degree) - GPA out of 5 GPA 5 or 90% GPA 4 or 80% GPA 3.5 or 70%

Hong Kong

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
GPA 4.0 scale 3.5 3.0 2.5

Hungary

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Alapfokozt or Egyetemi Oklevel / Bachelor 5 4 3

Iceland

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Baccalaurreatus degree or Kandidatsprof/Candidatus Mag 8.5 7.5 6.5

India

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Institutions listed on the Indian Ranking of Higher Educational Institutions Framework 65% (First) 60% (First) 55% (Upper second)
All other Indian institutions 70% (First with distinction) 65% (First) 60% (First)

Indonesia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Sarjana I (S1) from A (or B) credited Universities 3.7 (4.0) 3.3 (3.7) 3 (3.3)

Iran

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Iran 17 15 13

Iraq

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Iraq 80% 75% 70%

Ireland

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Republic of Ireland First (70%) Upper second (60%) Lower second (50%)

Israel

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
3 yr Bachelor Degree 90% 80% 70%

Italy

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Diploma di Laurea 109/110 104/110 (or 27) 100/110 (or 26)

Ivory Coast

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Diplome d'Etude Approfondies, Diplome d'Etude Superieures or Diplome d'Etude Superieures 16 14 (Bien) 12 (Assez Bien)

Jamaica

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
For degrees studied at The University of West Indies or degrees accredited by UCJ and CCCJ 1st (GPA 3.6) 2:1 (GPA 3.0) or B 2:2 (GPA 2.0) or C

Japan

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Japan 85% 80% or B or 3.0 70% or C or 2.0

Jordan

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
GPA 4.0 scale 3.5 3 or 3.5/5 or 75% 2.8 or 65%

Kazakhstan

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
GPA 5.0/percentage scale 4.5 or 90% 4 or 85% 3.5 or 80%
GPA 4.33 scale 3.9 3.7 3.2
GPA 4.0 scale 3.7 3.4 3

Kenya

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Kenya First / 70% / A Upper second / 60% / B Lower second / 50% / C

Kosovo

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Kosovo 10 9 8

Kuwait

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
GPA 4.0 scale 3.6 3.0 2.8

Latvia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Latvia 9 7 6

Lebanon

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
American 90% (3.5) 80% (3.2) 70% (2.8)
French 18 15 12

Liberia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Master's 4.0 or 90% 3.5 or 85% 3 or 80%

Libya

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
BSc Engineering, Architecture, Medicine 85 (3.6) 75 (3.0) 65 (2.5)
Other bachelor's degree from a university 90 (4.0) 85% (3.6) 75% (3.0)

Lithuania

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Lithuania 9 8 7

Macau

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Macau 1st or GPA 3.7 2:1 or GPA 3.0 2:2 or GPA 2.5

Macedonia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Macedonia 10 9 8

Malawi

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Master's only MSc 75% MSc 70% MSc 65%

Malaysia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Classification First Class 2.1 2.2
GPA 4.0 scale 3.5 3.0 2.8

Malta

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Malta 1st (80%) 2:1 (70%) 2:2 (55%)

Mauritius

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Mauritius 1st or 70% 2:1 or 60% 2:2 or 50%

Mexico

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Mexico 9 8 7

Moldova

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Diploma de Licenţă (Diploma of Licentiate) 10 9 8

Mongolia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Диплом Специалиста (Specialist Diploma) 90% or 3.5 80% or GPA 3.2 70% or GPA 3.0

Morocco

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Morocco 17 15 13

Mozambique

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
4 year Licenciatura 16 14 12

Myanmar (Burma)

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
2 year Master's degree 5 or 85% 5 or 75% 4.5 or 65%

Namibia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Namibia 80% or A 70% or B 60% or C

Nepal

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Master's (after 3 year bachelor degree) 90% or 3.9 GPA 80% or 3.8 GPA 65% or 3.3 GPA

Netherlands

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Netherlands 8 7 6

New Zealand

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
4 Year Honours degree (480 credits) - Level 8 First (7.0) Upper Second (6.0) Lower Second (4.0)

Nicaragua

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Licenciatura (4 year) 90% 80% 70%

Nigeria

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
7 point Scale 6 5 4
5 point scale 4.5 3.8 3.5
4 point scale 3.5 3 2.5

Norway

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Norway A B C

Oman

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
GPA 4.0 scale 3.5 3.0 2.5

Pakistan

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Public Universities 4 Year degree only First with distinction (75%) / 4.0 First (65%) / 3.2 Second (59%) / 2.6
Private Universities 4 Year degree only First with Distinction (85%) First (75%) First (65%)
2 or 3 year bachelor's plus Master's First (60%) Second (55%) Second (50%)

Palestine

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Bachelor Degree A / 90% / 3.7 B+ / 85% / 3.3 B / 80% / 3.0

Panama

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
4 Year Licenciado / Título de [subject area] 91 (A) 81 (B) 71 (C)

Papua New Guinea

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Papua New Guinea 1st 2:1 2:2

Paraguay

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Paraguay - 4 3.5

Peru

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
4 Year Título de Licenciado / Título de [subject area] 14 13 12

Philippines

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Degree from prestigious state universities or Centres of Excellence (COE) Summa Cum Laude 4.0 / 96% / 1.0 Magna cum Laude 3.5 / 92% / 1.5 Cum Laude 3.0 / 87%/ 2.0

Poland

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Bachelor Degree (post 2003) Magister (pre- 2003) 5 4.5 / 4+ 4

Portugal

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Portugal 18 16 14

Qatar

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
GPA 4.0 scale 3.5 3.0 2.8

Romania

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Diploma de Licenta/ Diploma de Inginer 9 8 7

Russia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Russia 4.5 4.0 3.5

Rwanda

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
4 year bachelor (Hons) degree (480 credits) 1st, 16/20 (80%) 2:1,14/20 (70%) 2:2, 12/20 (60%)

Saudi Arabia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
GPA 4.0 scale 3.5 3.0 2.8
GPA 5.0 scale 4.5 3.75 3.5

Senegal

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Maitrise, Diplome d'Etude Approfondies,Diplome d'Etude Superieures or Diplome d'Etude Superieures Specialisees 16/20 or Tres Bien 14/20 or Bien 12/20 or Assez Bien

Serbia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Diplomirani/ Bachelor's degree 9 8 7

Sierra Leone

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Classification - 2:1 2:2
Percentage grading - 60-69% 50-59%
Letter grading - B+ B

Singapore

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Classification First Upper second Lower second
GPA 4.0 scale 3.7 3.0 2.7
GPA 5.0 scale 4.5 3.5 3.0

Slovakia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Slovakia 1.5 or B 2.0 or C 2.5 or C/high D

Slovenia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Slovenia 9.5 8.5 7

South Africa

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Classification 1st 2:1 2:2
Percentage scale 75-100% 70-74% 60-69%

South Korea

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
GPA out of 4.5 4.0 / A 3.5 / B 3.0 / C+
GPA out of 4.3 4.0 / A 3.0 / B 2.7 / C+

Spain

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Licenciado / Título de Ingeniero / Título de Arquitecto 8.5 7 6.5
UCM grading 3.0 2.0 1.5

Sri Lanka

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Sri Lanka 70% 60% 55%

Sudan

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Sudan (North and South) 1st or 70% or B+ 2:1 or 66% Mid 2:2 or 60% or B

Sweden

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Sweden - Overall grade of VG with a minimum of 90 credits at VG Overall grade of G with a minimum of 90 credits at G

Switzerland

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Switzerland 6 5 4

Syria

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
State universities 4 years of study 80% 70% 60%
Private universities 4 years of study 90% 80% 70%

Taiwan

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Category 1 (4 year degree) 80% 75% 70%
Category 2 (4 year degree) 85% 80% 75%

Tajikistan

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Tajikistan - 4.5 4

Tanzania

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Tanzania 1st 2:1 2:2

Thailand

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
GPA 4.0 scale 3.5 3.2 2.8

Trinidad and Tobago

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
For degrees studied at The University of West Indies or degrees accredited by ACTT 1st or B+ or 70% 2:1 or B or 65% 2:2 or B- or 60%

Tunisia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Licence, Maîtrise, Diplôme National d'Ingénieu 15 (tres bien) 14 (bien) 11 (assez bien)

Turkey

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Lisans Diplomasi or a Műhendis Diplomasi 3.5 3 2.5

Turkmenistan

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Turkmenistan - 4.5 4

Uganda

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Uganda 1st or 4.4 2:1 or 3.8 2:2 or 3.0

Ukraine

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Dyplom Magistra or a Bachelors degree (11 / 5) 11 or 5 9 or 4.5 8 or 4

United Arab Emirates

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
GPA 4.0 scale 3.5 3.0 2.6

United States of America

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
GPA 4.0 scale 3.5 3.2 2.8

Uruguay

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Licenciado (4 year) 10 9 8

Uzbekistan

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Bakalavr Diplomi / Diplomi (Specialist Diploma) 90% or GPA 4.5 80% or GPA 4.0 70% or GPA 3.0

Venezuela

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Licenciado/Professional title. (4 year) 18/20 or 8/9 16/20 or 7/9 14/20 or 6/9

Vietnam

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Vietnam 8.0 7.0 6.0

Zambia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Master's A or 4.0 or 80% B+, 3.5 or 70% B or 3.0 or 60%

Zimbabwe

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
3/4 year degree 1st or 75% 2:1 or 65% 2:2 or 60%

English language requirements

Applicants must meet the minimum English Language requirements. Further details are available on the International website.

Fees and funding

UK / EU fee

Full-time degree per annum
£9,300

International fee

Full-time degree per annum
£19,100

Tuition fees cover the cost of your teaching, assessment and operating University facilities such as the library, IT equipment and other support services. University fees and charges can be paid in advance and there are several methods of payment, including online payments and payment by instalment.

Find out more about master's degree funding

Our students and academics

Mariapia Lampis

Industrial Mathematical Modelling MSc graduate

I found the modules and the programme organisation excellent. My year was challenging and intense but I enjoyed studying and learning new subject.