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Optimization

This module will interest you if you need to create mathematical models or if you use numerical software in industry, science, commerce or research. It’s concerned with the skills needed to represent real optimization problems as mathematical models, and with techniques used in numerical analysis and operational research for solving these models by computer. Explaining how and when modelling and numerical techniques can be applied, the module covers solutions of non-linear equations; systems of linear and non-linear equations and mathematical modelling; linear and integer programming; and non-linear optimization for unconstrained and constrained minimisation problems. Knowledge from OU level 2 study of calculus and matrices is assumed.

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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

Module code
M373
Credits
30
Study level
OU SCQF FHEQ
3 10 6
Study method
Distance Learning
Module cost
See Module registration
Entry requirements
See Am I ready?

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What you will study

The module is divided into three blocks of work: solutions of non-linear equations, systems of linear and non-linear equations and mathematical modelling; linear and integer programming; and non-linear optimization for unconstrained and constrained minimization problems. You will be expected to run given computer programs as part of your study, but you will not be required to write any computer programs.

In the broad area of operational research, the module will enable you to formulate a real problem in mathematical terms; to recognise whether the problem can be solved numerically; to choose a suitable method; to understand the conditions required for the method to work; to evaluate the results and to estimate their accuracy and their sensitivity to changes in the data.

Optimization is a practical subject, although it is supported by a growing body of mathematical theory. Problems that require the creation of mathematical models and their numerical solutions arise in science, technology, business and economics as well as in many other fields. Creating and solving a mathematical model usually involves the following main stages:

  • formulation of the problem in mathematical terms: this is the creation of a mathematical model
  • devising a method of obtaining a numerical solution from the mathematical model
  • making observations of the numerical quantities relevant to the solution of the problem
  • calculating the solution, usually with a computer or at least with a scientific calculator
  • interpreting the solution in relation to the real problem
  • evaluating the success or failure of the mathematical model.

Many of the problems discussed in the module arise in operational research and optimization: for example, how to get the most revenue from mining china clay when there is a choice of several mines. In this example the mathematical model consists of a set of linear inequalities defining the output from each mine, the number of mines that can be worked, the correct blend of clay and the total amount of clay mined each year. The method of solving the problem uses mixed linear and integer programming; the numerical data that need to be observed include the financial implications of opening a mine, the number of mines that can be worked with the labour force, and the quality of clay from potential mines. These data will be fed into a computer, which will combine them with the chosen method of solving the equations to produce solutions consisting of outputs from each mine in each year of operation.

This module examines all the stages but concentrates on: the first stage, creating the mathematical model; the second stage, devising a method; the fourth stage, calculating numerical solutions; and the fifth stage, interpreting the solution. Each of the three blocks of work takes about ten weeks of study:

  • Block I  – Direct and iterative methods of solving single non-linear equations, systems of linear equations and systems of non-linear equations; mathematical modelling; errors in numerical processes, convergence, ill-conditioning and induced instability.
  • Block II – Formulation and numerical solution of linear programming problems using the revised simplex method; formulation of integer programming problems and the branch and bound method of solution; sensitivity analysis.
  • Block III – Formulation and numerical solution of unconstrained and constrained non-linear optimization problems using, among others, the DFP and BFGS methods with line searches; illustrative applications.

You will learn

Successful study of this module should enhance your skills in:

  • mathematical modelling
  • operational research
  • linear programming and non-linear optimization methods
  • the use of iterative methods in problem solving
  • the use of Computer Algebra Packages for problem solving.

Professional recognition

This module may help you to gain membership of the Institute of Mathematics and its Applications (IMA). For further information, see the IMA website.

Teaching and assessment

Support from your tutor

You will have a tutor who will help you with the study material and mark and comment on your written work, and whom you can ask for advice and guidance. We may also be able to offer group tutorials or day schools that you are encouraged, but not obliged, to attend. Where your tutorials are held will depend on the distribution of students taking the module. 

Contact us if you want to know more about study with The Open University before you register.

Assessment

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 modules must be submitted on paper as – due to technical reasons – we are unable to accept TMAs via our eTMA system.

Future availability

The details given here are for the module that starts in October 2015. We expect it to be available once a year, in October.

Regulations

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:

4 Tutor-marked assignments (TMAs)
Examination
No residential school

Course satisfaction survey

See the satisfaction survey results for this course.


Entry

This is an OU level 3 module. OU level 3 modules build on study skills and subject knowledge acquired from studies at levels 1 and 2. They are intended only for students who have recent experience of higher education in a related subject, preferably with The Open University. You are expected to bring to the module some knowledge of:

  • Calculus – definition of differentiation and integration; ability to differentiate and integrate a variety of functions; Taylor’s theorem with remainder; partial derivatives; understanding of continuity and convergence
  • Matrices – ability to manipulate equations with matrices and vectors; Gaussian elimination; eigenvalues and eigenvectors; linear dependence and independence.

You could get the necessary background from our level 2 mathematics modules Pure mathematics (M208), or Mathematical methods, models and modelling (MST210) (or its predecessor MST209), or equivalent. You are more likely to successfully complete this module if you have acquired your prerequisite knowledge through passing at least one of these recommended modules.

If you have any doubt about the suitability of the module, please speak to an adviser.

Preparatory work

If you would like to do some preparatory reading, you could choose from:

  • E. W. Cheney, D. R. Kincaid (2008) Numerical Mathematics and Computing, Brooks Cole, ISBN 10: 0-495-11475-8
  • R. L. Burden, J. D. Faires (2011) Numerical Analysis, Brooks Cole, ISBN 10: 0-538-73563-5

For an introduction to linear algebra:

  • H. Anton, C. Rorres (2010) Elementary Linear Algebra: With Supplemental Applications, John Wiley & Sons, ISBN 978-0-470-56157-7

The following material from Pure mathematics (M208) would be very useful:

  • Linear Algebra Block: Unit 2 Linear Equations and Matrices; Unit 3 Vector Spaces; Unit 5 Eigenvectors.
  • Analysis Block A: Unit 2 Sequences; Unit 4 Continuity.
  • Analysis Block B: Unit 1 Limits, Unit 2 Differentiation.

Your regional or national centre will be able to tell you where you can see reference copies, or you can buy selected materials from Open University Worldwide Ltd.

Register

Start End England fee Register
03 Oct 2015 Jun 2016 £1350.00

Registration closes 10/09/15 (places subject to availability)

Register

You may need to apply for some payment or funding options earlier. Please check the Fees and Funding information or contact us for information.

This module is expected to start for the last time in October 2017.

Additional Costs

Study costs

There may be extra costs on top of the tuition fee, such as a laptop, travel to tutorials, set books and internet access.

If you're on a low income you might be eligible for help with some of these costs after you register.

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 monthly fee and number of instalments based on the cost of the module you are studying. 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 ten 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. 

Mixed payments

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

For more information about combining payment options, speak to an adviser or book a call back at a time that is convenient to you.


Please 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 valid for modules starting before 31 July 2016. Fees normally increase annually in line with inflation and the University's strategic approach to fees. 

This information was provided on 28/07/2015.

What's included

Module texts and website, including access to Maxima mathematical software which you need to download.

You will need

Scientific calculator.

We recommend you access the internet at least once a week during the module to download module resources and assignments, and to keep up to date with module news.

Computing requirements

You will need a computer with internet access to study this module as the study materials and activities are accessible via a web browser. Any other computer-based activities you will need to carry out, such as word processing, using spreadsheets, taking part in online forums, and submitting files to the university for assessment, are specified in the module materials. If any additional software is needed for these tasks it will either be provided or is freely available.

We recommend either of the following:

  • Windows desktop or laptop computer running Windows 7 or later operating system
  • Macintosh desktop or laptop computer running OS X 10.7 or later operating system.

A netbook, tablet, smartphone or Linux computer that supports one of the browsers listed below may be suitable. The screen size should be at least 1024 (H) x 768 (W) pixels. If you intend to use one of these devices please ensure you have access to a suitable desktop or laptop computer in case you are unable to carry out all the module activities on your mobile device.

We recommend a minimum 1 Mbps internet connection and any of the following browsers:

  • Internet Explorer 9 and above
  • Apple Safari 7 and above
  • Google Chrome 31 and above
  • Mozilla Firefox 31 and above.

Note: using the latest version for your browser will maximise security when accessing the internet. Using company or library computers may prevent you accessing some internet materials or installing additional software.

See our Skills for OU study website for further information about computing skills for study and educational deals for buying Microsoft Office software.

If you have a disability

You will need to spend considerable amounts of time using a personal computer.

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.