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Mathematical modelling

Mathematics is enjoyable and creative in its own right, but can also be a powerful tool for solving real problems. This module, which includes a residential week, introduces mathematical modelling and other techniques such as data and sensitivity analysis within the framework of group-learning. You'll learn to use mathematical software and acquire presentation and group-working skills. You'll also be expected to put together a short technical report. Most of the work will be collaborative, carried out in small groups with a tutor. You should have an understanding of applied mathematics and mechanics to successfully study this module.

Modules count towards OU qualifications

OU qualifications are modular in structure; the credits from this undergraduate-level module could count towards a certificate of higher education, diploma of higher education, foundation degree or honours degree.

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Module code
Study level
2 9 5
Study method
Distance Learning
Module cost
See Module registration
Entry requirements
See Am I ready?

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What you will study

An example of a problem that can be understood better through mathematical analysis is that of the injection of medication. A mathematical model can be constructed which predicts how the concentration of the medication in the blood changes with time after an injection. This model can then be used to answer such questions as:

  • how often should a specified amount of medication be administered to be effective?
  • how much medication should be given if the period between injections is specified?
  • what happens if the medication is given intravenously?

This module will give you an introduction to, and the experience to apply, mathematical modelling to a number of real problems. A significant part of the module is the writing of a report of a mathematical model that is initiated and developed at the residential school.

Other activities at the residential school include:

  • an introduction to data modelling and analysis
  • modelling simple dynamical systems and determining to what extent a real system behaves as the model predicts
  • obtaining a physical feel for the behaviour of basic components of mechanics such as springs, friction, pulleys, masses, strings
  • sensitivity analysis to identify the parameters in a model that have most effect on the outcome of the model.

A significant feature of the module is the development of communication and group working skills. You will be working, with tutor guidance, in a small group on the presentation (it can be oral or written or both) of the results of an activity carried out at the residential school. Deciding what information to present and how to do it efficiently are important skills.

Some of your work at the residential school will be in small groups and your participation within the group will be required.

By the end of the module you will be able to:

  • acquire and demonstrate the facility and skills to undertake mathematical modelling
  • acquire and demonstrate presentation and communication skills
  • analyse real-world problems, making appropriate assumptions and simplifications, creating a mathematical model appropriate to a specific purpose, interpreting and evaluating the outcome of the model
  • communicate solutions to problems clearly and coherently to both fellow mathematicians and non-technical audiences
  • work constructively with fellow students on a common project
  • write a substantial technical report
  • select and apply the experimentation required to verify models and to understand the limitations of your models.

The residential schools will be held from mid-July to early August each year. Unfortunately, we aren't always able to offer you your first choice of date. If you have a preferred date in mind, you're more likely to get it if you register early. Each residential week will start on Saturday at 3pm and finish on the Friday at 3pm; attendance at the residential school is compulsory, you cannot pass this module if you do not attend and participate. See our Residential Schools website for more information.

You will learn

Successful study of this module should improve your skills in:

  • communicating mathematical ideas clearly
  • explaining mathematical ideas to others in both verbal and written form
  • thinking logically
  • expressing problems in mathematical language
  • working on open-ended problems
  • finding solutions to problems
  • interpreting mathematical results in real-world terms
  • analysing/interpreting data
  • using professional software in Mathcad
  • presentation before an audience
  • writing a report.

Vocational relevance

This module is particularly relevant to those who will be applying and communicating mathematics (or other technical topics) in their work.

Presentation, group working, working with and using data, and writing reports are generic skills to be gained from this module. These skills will be applicable in many non-mathematical situations.

Outside the UK

Preparatory work and the work for the first assignment can be done outside the UK. Travel to the University of Nottingham campus for the week-long residential part of the module is essential.

Teaching and assessment

Support from your tutor

Before the residential school you will have access to an electronic forum where you can discuss your preparation for the residential school and the work for the first assignment with other students and obtain help from the module team, and a tutor from whom you can expect individual advice and help. At the residential school, tutors will help you with the study material, guide you through the activities, and advise you in the preparation of your written work. You can also obtain advice and guidance from a learning adviser at the residential school. After the residential school you can contact your tutor or join in as an electronic forum for help and advice before you submit the final assessment. 

Contact our Student Registration & Enquiry Service if you want to know more about study with the Open University before you register.


The assessment details for this module can be found in the facts box above.

Please note that tutor-marked assignments (TMAs) for all undergraduate mathematics and statistics module must be submitted on paper as – due to technical reasons – we are unable to accept TMAs via our eTMA system.

The first tutor-marked assignment (TMA) is to be completed before the residential school and will be discussed during the residential school; the second TMA will be initiated and developed at the residential school and submitted to your tutor a month or so later. The end-of-module assessment (EMA) is the assessment of your satisfactory participation in the residential school activities as well as on the presentation at the end of the residential week. You will be given more detailed information when you begin the module.

Future availability

The details given here are for the module that starts in May 2014. There will be restricted entry for May 2015, when it will be available for the last time.


As a student of The Open University, you should be aware of the content of the Module Regulations and the Student Regulations which are available on our Essential documents website.

Course work includes:

2 Tutor-marked assignments (TMAs)
End-of-module assessment
Stand-alone residential school


This is an OU level 2 module and you need a good knowledge of applied mathematics and mechanics, obtained either from the first half of the discontinued OU module Mathematical methods and modelling (MST209) or from equivalent work on a predecessor module or at another university. To help you decide whether you have the necessary background, an online booklet Are you ready for MSXR209? is available.

Knowledge of the following topics is required: 

  • solving first-order differential equations
  • solving linear constant-coefficient second-order differential equations
  • partial differentiation
  • eigenvalues and eigenvectors of matrices
  • equations of motion for particles in one or two dimensions
  • modelling springs, friction and air resistance
  • solving systems of linear constant-coefficient differential equations.

If you have any doubt about the level of pre-requisite mathematical knowledge please seek advice from our Student Registration & Enquiry Service.

Preparatory work

If your experience of mathematics at this level is not recent, then you should do some preparatory work in order to help you to manipulate and to use the necessary mathematics confidently and with assurance.

If you are taking MST209 you need no special preparation. If you have taken MST209 (or MST207) in the past then you should revise the topics mentioned under Entry above. If you have had no experience of Mathematical methods and models (MST209) (now discontinued), go to the website (mentioned under Entry above) where you will find Are you ready for MSXR209?. Your regional or national centre will be able to tell you where you can see MST209 reference copies, or you can purchase them from Open University Worldwide Ltd (01908 858793).


Start End Fee
- - -

No current presentation - see Future availability

Additional Costs

Residential School fees

This module will include a residential school, when you study this the tuition fee may not include accommodation and meals, and you may be asked to pay an additional fee of up to £255. You will also be responsible for the cost of your travel to the venue. If you're on a low income you will be able to apply for help with these costs after you've registered.

Ways to pay for this module

Open University Student Budget Account

The Open University Student Budget Accounts Ltd (OUSBA) offers a convenient 'pay as you go' option to pay your OU fees, which is a secure, quick and easy way to pay. Please note that The Open University works exclusively with OUSBA and is not able to offer you credit facilities from any other provider. All credit is subject to status and proof that you can afford the repayments.

You pay the OU through OUSBA in one of the following ways:

  • Register now, pay later – OUSBA pays your module fee direct to the OU. You then repay OUSBA interest-free and in full just before your module starts. 0% APR representative. This option could give you the extra time you may need to secure the funding to repay OUSBA.
  • Pay by instalments – OUSBA calculates your annual fees and spreads them out over up to a year, enabling you to pay your fees monthly and walk away with a qualification without any further debt. APR 5.1% representative.

Read more about Open University Student Budget Accounts (OUSBA).  

Employer sponsorship

Studying with The Open University can boost your employability. OU qualifications are recognised and respected by employers for their excellence and the commitment they take to achieve one. They also value the skills that students learn and can apply in the workplace.

More than one in 10 OU students are sponsored by their employer, and over 30,000 employers have used the OU to develop staff so far. If the qualification you’ve chosen is geared towards your job or developing your career, you could approach your employer to see if they will sponsor you by paying some or all of the fees. 

  • Your employer just needs to complete a simple form to confirm how much they will be paying and we will invoice them.
  • You won’t need to get your employer to complete the form until after you’ve chosen your modules.  

Credit/debit card

You can pay part or all of your tuition fees upfront with a debit or credit card when you register for each module. 

We accept American Express, Maestro (UK only), Mastercard, Visa/Delta and Visa Electron. 

Gift vouchers

You can pay for part or all of your tuition fees with OU gift vouchers. Vouchers are currently available in the following denominations, £10, £20, £50 and £100. 

Mixed payments

We know that sometimes you may want to combine payment options. You may, for example wish to pay part of your tuition fee with a debit card and pay the remainder in instalments through an Open University Student Budget Accounts (OUSBA).

For more information about combining payment options, speak to an adviser or request a call back.

Note: Your permanent address/domicile will affect your fee status and therefore the fees you are charged and any financial support available to you. The fees and funding information provided here is based upon current details for  year 1 August 2014 to 31 July 2015.
This information was provided on 22/10/2014.

What's included

Module books, other printed materials, website, DVD, computer software; a residential week of lectures, tutorials, and group working; and online forums.

You will need

DVD player (or computer able to play DVDs); scientific calculator, preferably with graphics and with a number of memories.

You require access to the internet at least once a week during the module to download module resources and to keep up to date with module news. An optional online forum will be available so that you can meet fellow students, discuss the study material, and solicit help.

If you have a disability

Every effort will be made at the school to accommodate students with disabilities. The accommodation, both residential and teaching, will be accessible to wheelchair users. Some of the activities (e.g. involving the motion of particles) may be more challenging if your sight is severely impaired; where possible alternative sensory detection will be used. The study materials are available on audio in DAISY Digital Talking Book format.

If you feel that an assistant may be useful then you may either bring your own or ask for one to be arranged by The Open University. The assistant must have familiarity with writing mathematics.

You will need to spend some time each week using a personal computer.

You’ll have a busy and intensive week at residential school, starting on the day you arrive. There’s one free afternoon and most of the evening sessions are optional. The presentation at the end of the week can be in any form and students with disabilities will not be disadvantaged. This applies equally to participation in the group working. The practical work is carried out in small teams, and the work is shared.

After you have registered you will receive detailed information about the residential school site and the facilities available to help you with the academic programme.

If you have particular study requirements please tell us as soon as possible, as some of our support services may take several weeks to arrange. Find out more about our services for disabled students.