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Accessibility statement
Qualification dates
StartEnd
03 Oct 2026Jun 2027
This module is about combinatorics and discrete mathematics, and their applications to modelling and solving real-world problems. Applications include the famous Travelling Salesman Problem, assigning junior doctors to hospitals and storing/transmitting data resilient to errors. You’ll also see some recreational applications, e.g. how to win at simple games consistently and the mathematics of Sudoku. At the heart of all these problems is pure mathematics – in the form of graph theory, game theory, coding theory and design theory.
We present the study material in a down-to-earth manner, emphasising solving problems and applying algorithms rather than abstract ideas and proofs.
The module comprises four books:
Book A: Graphs
Unit A1: Introduction to graphs
A graph is a collection of points, or vertices, joined by lines or edges; this unit gives a general introduction to graphs. We discuss Eulerian and Hamiltonian graphs and related problems, one of which is the well-known Königsberg bridges problem.
Unit A2: Trees
Trees are graphs that occur in areas such as branching processes, decision procedures, and the representation of molecules. We discuss their mathematical properties and their applications, such as the minimum connector problem and the travelling salesman problem.
Unit A3: 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 neighbouring countries have different colours? These are two of several apparently unrelated problems considered in this unit.
Book B: Networks
Unit B1: Network flows
This unit is concerned with connectivity in graphs and digraphs. For example, what is the maximum amount of a commodity (gas, water, passengers) that can pass between two points of a network in a given time?
Unit B2: Optimal paths, packing and scheduling
How do you plan a complex engineering project encompassing many activities? This application of graph theory is called ‘critical path planning’.
Unit B3: Matchings and assignment
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? This unit considers problems where we must ‘pair off’ people or objects from two distinct groups, subject to certain constraints.
Book C: Games
Unit C1: Introduction to games
You’ll learn the basics of game theory and examine strategies for winning recreational games, such as Nim.
Unit C2: Zero-sum games
Here you’ll study games where what one player wins equals what the other loses. The main result is von Neumann’s theorem, which tells us there is always a solution to such games.
Unit C3: General games and Nash equilibria
We consider how to solve games in general using Nash equilibrium and look at applications to topics such as evolutionary biology and economics.
Book D: Designs
Unit D1: Latin squares
Sudoku is an internationally popular puzzle. A completed Sudoku is an example of a Latin square, and this unit explores the mathematics behind these arrays of symbols.
Unit D2: Error-correcting codes
When we send a message through a system where errors or interference can occur, how do we ensure that the recipient receives the same message we sent? Solving this problem is the topic of coding theory.
Unit D3: Block designs
If an agricultural research station wants to test different crop varieties, how should they arrange the crops to minimise bias due to variations (for example, in the soil and sunlight)? The answer lies in the study of block designs.
The full content list is on the Open mathematics and statistics website.
There are no formal entry requirements to study this module.
However, you’ll need appropriate knowledge of mathematics. You’d normally prepare by having passed:
Or their engineering equivalents, plus OU level 2 study.
Are you ready for MST368?
You should be confident and fluent with the concepts covered in the diagnostic quiz and follow the advice.
The key topics to revise include:
You’ll get help and support from an assigned tutor throughout your module.
They’ll help by:
Online tutorials run throughout the module. While they’re not compulsory, we strongly encourage you to participate. Where possible, we’ll make recordings available.
Course work includes:
For this module, we may use an assessment verification process to meet the requirements of relevant accrediting, professional, statutory or regulatory bodies. As part of this process, you may be asked to attend a short post-assessment video discussion, lasting around 15 minutes. During the discussion, you’ll need to show a photo ID and talk through your answers to a small number of questions with a tutor or a member of the module team. The discussion is not graded and is only used to confirm that you completed the assessment yourself.
We regularly review the assessments in our modules, so we may update the examination method used for this module to an in-person exam or a remotely invigilated (proctored) exam. When we are making such a change, we will make it clear on this page. If we need to make a change after you have registered, we will notify you as soon as possible. If you have additional requirements, we will support you to complete your assessments.
You’ll have access to a module website, which includes:
Additionally, the website includes:
We also provide physical:
The OU strives to make all aspects of study accessible to everyone, and this Accessibility Statement outlines what studying MST368 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 Disability support website.
Graphs, games and designs (MST368) starts once a year – in October.
It will next start in October 2026.
We expect it to start for the last time in October 2030.
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