- An undergraduate course
in
Mathematics and Statistics.
Graphs, networks and design
- On this page
| Course facts | |
|---|---|
| About this course: | |
| Course code | MT365 |
| Credits | 30 |
| OU Level | 3 |
| SCQF level | 10 |
| FHEQ level | 6 |
| Course work includes: | |
| 4 Tutor-marked assignments (TMAs) | |
| 4 Computer-marked assignments (CMAs) | |
| Examination | |
| No residential school | |
This course is about using ideas from discrete mathematics to model problems, and representing these ideas through diagrams. The word ‘graphs’ refers to diagrams consisting of points joined by lines. These points may correspond to chemical atoms, towns, electrical terminals or anything that can be connected in pairs. The lines may be chemical bonds, roads, wires or other connections. The main topics of mathematical interest are graphs and digraphs; network flows; block designs; geometry; codes; and mathematical modelling. Application areas covered include communications; structures and mechanisms; electrical networks; transport systems; social networks; and computer science. To study this course you should have a sound knowledge of relevant mathematics provided by the appropriate Level 2 study.
Modules at Level 3 assume that you are suitably prepared for study at this level. If you want to take a single module to satisfy your career development needs or pursue particular interests, you don’t need to start at Level 1 but you do need to have adequately prepared yourself for OU study in some other way. Check with our Student Registration & Enquiry Service to make sure that you are sufficiently prepared.
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What you will study
What codes are used by spacecraft in communicating with Earth? Where do you brace a framework to make it rigid? How many colours are needed for a map to ensure that neighbouring countries have different colours? How can you assign people to jobs for which they are qualified? These are some of the questions to be answered in the course. The problems range from those arising in technology, operational research and the sciences to puzzles of a recreational nature. We show the connections between problems in widely differing areas and describe methods for their solution that use the properties they have in common.
The material is presented in a down-to-earth manner, with the emphasis on solving problems and applying algorithms, rather than on abstract ideas and proofs.
The course is divided into three related areas: graphs, networks and design. The Introduction introduces two themes of the course, combinatorics and mathematical modelling, and illustrates them with examples from the three areas.
Graphs 1: Graphs and digraphs discusses graphs and digraphs in general, and describes the use of graph theory in genetics, ecology and music, and of digraphs in the social sciences. We discuss Eulerian and Hamiltonian graphs and related problems; one of these is the well-known Königsberg bridges problem.
Networks 1: Network flows is concerned with the problem of finding the maximum amount of a commodity (gas, water, passengers) that can pass between two points of a network in a given time. We give an algorithm for solving this problem, and discuss important variations that frequently arise in practice.
Design 1: Geometric design, concerned with geometric configurations, discusses two-dimensional patterns such as tiling patterns, and the construction and properties of regular and semi-regular tilings, and of polyominoes and polyhedra.
Graphs 2: Trees Trees are graphs occurring in areas such as branching processes, decision procedures and the representation of molecules. After discussing their mathematical properties we look at their applications, such as the minimum connector problem and the travelling salesman problem.
Networks 2: Optimal paths How does an engineering manager plan a complex project encompassing many activities? This application of graph theory is called ‘critical path planning’. It is one of the class of problems in which the shortest or longest paths in a graph or digraph must be found.
Design 2: Kinematic design The mechanical design of table lamps, robot manipulators, car suspension systems, space-frame structures and other artefacts depends on the interconnection of systems of rigid bodies. This unit discusses the contribution of combinatorial ideas to this area of engineering design.
Graphs 3: Planarity and colouring When can a graph be drawn in the plane without crossings? Is it possible to colour the countries of any map with just four colours so that neighbouring countries have different colours? These are two of several apparently unrelated problems considered in this unit.
Networks 3: Assignment and transportation If there are ten applicants for ten jobs and each is suitable for only a few jobs, is it possible to fill all the jobs? If a manufacturer supplies several warehouses with a product made in several factories, how can the warehouses be supplied at the least cost? These problems of the system-management type are answered in this unit.
Design 3: Design of codes Redundant information in a communication system can be used to overcome problems of imperfect reception. This section discusses the properties of certain codes that arise in practice, in particular cyclic codes and Hamming codes, and some codes used in space probes.
Graphs 4: Graphs and computing describes some important uses of graphs in computer science, such as depth-first and breadth-first search, quad trees, and the knapsack and travelling salesman problems.
Networks 4: Physical networks Graph theory provides a unifying method for studying the current through an electrical network or water flow through pipes. This unit describes the graphical representation of such networks.
Design 4: Block designs If an agricultural research station wants to test different varieties of a crop, how can a field be designed to minimise bias due to variations in the soil? The answer lies in block designs. This unit explains the concepts of balanced and resolvable designs and gives methods for constructing block designs.
Conclusion In this unit, many of the ideas and problems encountered in the course are reviewed, showing how they can be generalised and extended, and the progress made in finding solutions is discussed.
You will learn
Successful study of this course should enhance your skills in finding solutions to problems, interpreting mathematical results in real-world terms and communicating mathematical ideas clearly to both experts and non-experts.
Entry
This interfaculty course is intended for students with a variety of backgrounds. The more mathematically inclined will see how their mathematics can be used to solve problems, while those with a technological interest will learn to appreciate the use of a mathematical framework to relate different ideas.
This is a Level 3 course. Level 3 courses 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.
A suitable preparation is a background in mathematics (such as Using mathematics (MST121) and Exploring mathematics (MS221)) and 60 credits at Level 2 in mathematics, science or technology. In particular, familiarity with matrix multiplication and the matrix formulation of simultaneous equations would be an advantage, although these are reviewed in the course. Please note that you are more likely to complete this course successfully if you have acquired your prerequisite knowledge through passing these courses. Your regional or national centre will be able to tell you where you can see reference copies of the suggested courses, or you can buy selected materials from Open University Worldwide Ltd. There is also a diagnostic quiz to help you to determine whether you are adequately prepared for this course.
Don’t worry if you haven’t studied technology before. If you rely on common sense and accept certain statements of a scientific or technological nature, you should have no difficulty. Whatever your experience you should find plenty to interest you, as long as you go along with the interdisciplinary nature of the course.
If you have any doubt about the suitability of the course, please contact our Student Registration & Enquiry Service.
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.
If you have a disability
The many diagrams in the text and the computing element could be demanding if you have impaired sight or certain types of colourblindness. Written transcripts are available for the audio-visual material. Our Services for disabled students website has the latest information about availability.
To use the course software you will need to spend considerable amounts of time using a personal computer although its use is not essential. It is designed to enhance the student’s learning experience but it is possible to pass the course without using it.
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. Visit our Services for disabled students website for more information, including:
- help to determine your study requirements and how to request the support that you need
- Disabled Students' Allowances (DSAs)
- using a computer for OU study
- equipment and other support services that we offer
- examination arrangements
- how to contact us for advice and support both before you register and while you are studying.
Study materials
What's included
Course books, CDs, DVDs, software and a website.
You will need
CD player and DVD player (or computer able to play DVDs).
You require access to the internet at least once a week during the course to download course resources and assignments, submit assignments and to keep up to date with course news.
Computing requirements
You will need a computer with internet access to study this course. It includes online activities – you can access using a web browser – and some course software provided on disk.
- If you have purchased a new desktop or laptop computer running Windows since 2007 you should have no problems completing the computer-based activities.
- A netbook, tablet or other mobile computing device is not suitable for this course – check our Technical requirements section.
- If you have an Apple Mac or Linux computer – please note that you can only use it for this course by running Windows on it using Boot Camp or a similar dual-boot system.
You can also visit the Technical requirements section for further computing information including the details of the support we provide.
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 course.
Contact our Student Registration & Enquiry Service if you want to know more about study with the Open University before you register.
Assessment
The assessment details for this course can be found in the facts box above.
Please note that TMAs for all undergraduate mathematics and statistics courses must be submitted on paper as – due to technical reasons – we are unable to accept TMAs via our eTMA system.
Professional recognition
This course may help you to gain recognition from a professional body. You can view or download our Recognition leaflets 3.3 Professional Engineering Institutions, 3.4 Chartered Institution of Water and Environment Management and 3.6 Institute of Mathematics and its Applications for further information.
Future availability
The details given here are for the course that starts in October 2013. We expect it to be available once a year.
Students also studied
Students who studied this course also studied at some time:
How to register
To register a place on this course return to the top of the page and use the Click to register button.
Student Reviews
“I found this course very enjoyable. It covers a large mixed bag of subject areas. The graph parts cover graph ...”
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“If you need to do a Level 3 maths course to get your degree do this one. You don't need ...”
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Distance learning
The Open University is the world’s leading provider of flexible, high quality distance learning. Unlike other universities we are not campus based. You will study in a flexible way that works for you whether you’re at home, at work or on the move. As an OU student you’ll be supported throughout your studies – your tutor or study adviser will guide and advise you, offer detailed feedback on your assignments, and help with any study issues. Tuition might be in face-to-face groups, via online tutorials, or by phone.
For more information read Distance learning explained.
Undergraduate
| Course facts | |
|---|---|
| About this course: | |
| Course code | MT365 |
| Credits | 30 |
| OU Level | 3 |
| SCQF level | 10 |
| FHEQ level | 6 |
| Course work includes: | |
| 4 Tutor-marked assignments (TMAs) | |
| 4 Computer-marked assignments (CMAs) | |
| Examination | |
| No residential school | |
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