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Planarity

Many topological graphs have edges that cross. The aim is to re-draw the graph in such a way that none of the edges cross. The task informs students they are required to design a printed circuit board and since the wires are not insulated they must not cross.

Planarity: presentation - an...

Minimum Spanning Tree

The aim of a minimum spanning tree is to connect every vertex of the network using the edges having the least possible total weight. The task requires students to analyse information about a town centre and suggest which roads should be pedestrianized. [

Minimum spanning tree: presentation...

Matchings

A matching is a set of edges on a bipartite graph in which no two edges share a common vertex. A bipartite graph consists of two sets of vertices X and Y. The edges only join vertices in X to vertices in Y. A matching in a bipartite graph is the pairing of some or all of the vertices in X with some or all of the...

Flows

The network flow problem involves finding the optimum route through a flow network; a directed graph where each arc has a capacity and each arc receives a flow. Typical examples include: evacuation plans and delivery services. The problem involves students analysing the plan of a school canteen and deciding whether...

Dijkstra's Algorithm

Dijkstra's algorithm finds the shortest path for a given problem. Dijkstra's algorithm can be used to find the shortest route between two cities. This algorithm is so powerful that it not only finds the shortest path from a chosen source to a given destination, it also finds all of the shortest paths from the...

Curved Fold

This resource, from the Royal Institution, provides students with the opportunity to explore the formation of a parabola through a paper folding activity. Students follow a set of simple instructions which describe how to fold a piece of A4 paper and are asked to describe what shape is produced. The activity is...

Bin Packing

The purpose of bin packing is to pack a collection of objects into containers called bins. The bins are all the same size and the objects to be packed are different sizes. The aim is to pack the objects into the bins using the fewest possible bins. In this example students are asked to save computer files onto a CD...

Air Miles

This More Maths Grads resource, from the Maths Careers website, investigates the maths used in transport and is based on the travelling salesman problem.

Students are given a table containing information on the cost of air travel between nine different cities and asked to plan a route that visits each...

What is structural engineering? Structural engineering for beginners

This presentation provides a great introduction to the work of structural engineers. Created by the The Institution of Structural Engineers, it provides an overview of the types of activities undertaken by structural engineers, examples of the impact that they make on society and provides an overview of the types...

Fusion 360 - Using static stress simulation to optimise a shape

This Powerpoint presentation provides instructions for creating a static stress simulation on a simple shape. Using the results of the simulation, you can then run a shape optimisation study to create the optimum dimensions for the shape within the given loads and movement. This is a great activity for those who...

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