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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 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

Credits

  • Credits measure the student workload required for the successful completion of a module or qualification.
  • One credit represents about 10 hours of study over the duration of the course.
  • You are awarded credits after you have successfully completed a module.
  • For example, if you study a 60-credit module and successfully pass it, you will be awarded 60 credits.
30
Study level
3
Study method
Distance Learning
Module cost
See Module registration
Entry requirements
See Am I ready?

Student Reviews

This course naturally follows on from MST209 (or MST210 for newer students) and I would rank it near the top...
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I studied 5 OU level 3 modules and this was my favourite. A great mix of theory and applied maths,...
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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.

Vocational relevance

Mastering the material in this module will enable you to mathematically model and solve real-world problems in operational research and optimization. Such problems frequently occur in many fields including science, technology, business and economics.

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.

You can choose whether to submit your tutor-marked assignments (TMAs) on paper or online through the eTMA system. You may want to use the eTMA system for some of your assignments but submit on paper for others. This is entirely your choice.

Future availability

Optimization starts once a year – in October. This page describes the module that will start in October 2018. We expect it to start for the last time in October 2021.

Regulations

As a student of The Open University, you should be aware of the content of the academic 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 requirements

    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; ability to differentiate 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 one of our level 2 mathematics modules Pure mathematics (M208), Mathematical methods, models and modelling (MST210), Mathematical methods (MST224) or the discontinued module Mathematical methods and models (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.

    You can try our self-assessment diagnostic quiz to help you determine if you are adequately prepared for this module.

    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.

    Register

    Start End England fee Register
    06 Oct 2018 Jun 2019 £1464.00

    Registration closes 13/09/18 (places subject to availability)

    Register
    This module is expected to start for the last time in October 2021.

    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 your module has started.

    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.

    Joint loan applications

    If you feel you would be unable to obtain an OUSBA loan on your own due to credit history or affordability issues, OUSBA offers the option to apply for a joint loan application with a third party. For example, your husband, wife, partner, parent, sibling or friend. In such cases, OUSBA will be required to carry out additional affordability checks separately and/or collectively for both joint applicants who will be jointly and severally liable for loan repayments.

    As additional affordability checks are required when processing joint loan applications, unfortunately, an instant decision cannot be given. On average the processing time for a joint loan application is five working days from receipt of the required documentation.

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

    Employer sponsorship

    Studying with The Open University can boost your employability. OU courses are recognised and respected by employers for their excellence and the commitment they take to complete. 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 module 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 module.  

    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.


    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 2019. Fees normally increase annually in line with inflation and the University's strategic approach to fees. 

    This information was provided on 21/06/2018.

    What's included

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

    You will need

    Scientific calculator, but not one that is designed or adapted to offer any of the following facilities: Algebraic manipulation, differentiation or integration, language translation or can communicate with other devices or the internet. It also cannot have retrievable information stored in it such as databanks, dictionaries, mathematical formulae or text..

    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

    A computing device with a browser and broadband internet access is required for this module.  Any modern browser will be suitable for most computer activities. Functionality may be limited on mobile devices.

    Any additional software will be provided, or is generally freely available. However, some activities may have more specific requirements. For this reason, you will need to be able to install and run additional software on a device that meets the requirements below.

    A desktop or laptop computer with either:

    • Windows 7 or higher
    • macOS 10.7 or higher

    The screen of the device must have a resolution of at least 1024 pixels horizontally and 768 pixels vertically.

    To participate in our online-discussion area you will need both a microphone and speakers/headphones. 

    Our Skills for OU study website has further information including computing skills for study, computer security, acquiring a computer and Microsoft software offers for students. 

    If you have a disability

    The OU strives to make all aspects of study accessible to everyone and this Accessibility Statement outlines what studying M373 involves. You should use this information to inform your study preparations and any discussions with us about how we can meet your needs.

    To find out more about what kind of support and adjustments might be available, contact us or visit our Overcoming barriers to study if you have a disability or health condition website.