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.
Course facts | |
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About this course: | |
Course code | M373 |
Credits | 30 |
OU Level | 3 |
SCQF level | 10 |
FHEQ level | 6 |
Course work includes: | |
4 Tutor-marked assignments (TMAs) | |
Examination | |
No residential school |
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:
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:
Successful study of this module should enhance your skills in:
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.
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:
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.
If you would like to do some preparatory reading, you could choose from:
For an introduction to linear algebra:
The following material from Pure mathematics (M208) would be very useful:
Module texts and website, including access to Maxima mathematical software which you need to download.
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.
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:
The screen of the device must have a resolution of at least 1024 pixels horizontally and 768 pixels vertically.
To join in the spoken conversation in our online rooms we recommend a headset (headphones or earphones with an integrated microphone).
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.
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.
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.
The OU strives to make all aspects of study accessible to everyone. The Accessibility Statement below outlines what studying this module involves. You should use this information to inform your study preparations and any discussions with us about how we can meet your needs.
Printed materials are provided for the core module text. All of this module’s study materials are also online; this includes PDFs of any printed materials, plus some items which are only provided online. Online-only materials include video clips (with transcripts) and self-assessed quizzes. Online materials also include links to external resources, online forums and online tutorial rooms. This module uses mathematical/statistical software.
This module provides a range of learning events in the form of face-to-face and online tutorials. Online alternatives are available for face-to-face learning events. Although not compulsory, attendance at tutorials will help you consolidate your learning. If you have any concerns, please contact us as soon as possible so that we can discuss options with you.
Mathematical and scientific symbols and expressions are used throughout the module and you will be required to use such notation within assessment.
The study materials contain a considerable number of diagrams. Reading, interpreting and producing examples of these is an important part of the study of this module and is assessed. Figure descriptions are provided for all figures. If you have any concerns about this aspect of the module, please contact us for further advice.
In this module you will be working with specialist reading material which includes mathematical notation. This is delivered both online and in printed form, and also via bespoke and third party software. If you have any concerns about this aspect of the module, please contact us for further advice.
This module has Tutor-Marked Assignments (TMAs), which can be submitted online via the OU electronic TMA system or by post, and an Exam that must be taken at an exam centre. If you are concerned about any aspects of assessments, please contact us for advice on alternative assessments and support.
You will receive feedback from your tutor on your submitted Tutor-Marked Assignments (TMAs). This will help you to reflect on your TMA performance. You should refer to it to help you prepare for your next assignment. Please contact your tutor to discuss any concerns you have about this aspect of your learning.
All University modules are structured according to a set timetable and you will need time-management skills to keep your studies on track. You will be supported in developing these skills. If you are concerned about the time management required at undergraduate level, please contact us before you register on the module to find out what we can do to support you.
M373 uses the computer algebra system, Maxima. It is possible to use a command line interface for Maxima. The interactive applets have some accessibility controls, but you may need the support of a non-medical helper. Some accessibility advice is provided for the software activities in the Module Guide and the Computer Algebra Guide, but if you have any concerns, please contact us.’
Optimization starts once a year – in October. This page describes the module that will start in October 2019. We expect it to start for the last time in October 2021.
This course is expected to start for the last time in October 2021.
This module may help you to gain membership of the Institute of Mathematics and its Applications (IMA). For further information, see the IMA website.