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.
This module has been awarded a quality mark by the Royal Statistical Society, providing reassurance that the teaching, learning and assessment within this module is of high quality and meets the needs of students and employers.
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:
We’re using a new examination verification process for this module. We may ask you to attend a 15-minute post-exam video discussion, where you’ll present a photo ID and discuss your answers to a small number of questions with a tutor or member of the module team. The discussion isn’t graded; it’s only to verify that you completed the exam yourself.
You’ll have access to a module website, which includes:
Additionally, the website includes:
We also provide physical:
You can study this module on its own or use the credits you gain towards an Open University qualification.
MST368 is an option module in our:
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.
As a student of The Open University, you should be aware of the content of the academic regulations, which are available on our Student Policies and Regulations website.
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There may be extra costs on top of the tuition fee, such as set books, a computer and internet access.
If your income is not more than £25,000 or you receive a qualifying benefit, you might be eligible for help with some of these costs after your module has started.
There may be extra costs on top of the tuition fee, such as set books, a computer and internet access.
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Read more about Open University Student Budget Accounts (OUSBA).
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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).
We know that sometimes you may want to combine payment options. For example, you may get support from your employer to pay part of your tuition fee and pay the remainder by credit or debit card.
For more information about combining payment options, contact 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 fee information provided here is valid for modules starting before 31 July 2026. Fees typically increase annually. For further information about the University's fee policy, visit our Fee Rules.
