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3.6 FSMQ Decision Mathematics (9997)
Decision Mathematics (9997)
|What you need to learn||Throughout your work you need to develop a critical and questioning approach to your own use of decision mathematics diagrams and techniques and also learn how these can be used to draw conclusions and summarise findings.
You will carry out work that involves you in:
selecting appropriate data to use
drawing appropriate network(s)
carrying out an analysis using an algorithmic approach
drawing conclusions and summarising findings.
The key ideas that you will meet and some specific techniques that you need to be able to use are set out below.
|Using networks to model real world situations|| |
You should be able to represent a situation so that some of the relationships are clarified by the use of appropriate networks.
In drawing networks you should consider and understand:
terminology such as vertices, edges, edge weights, paths and cycles
directed and undirected edges and graphs
be able to store graphs as matrices e.g. adjacency/distance matrices
understand the degree of a vertex and be aware of odd and even vertices
|Trees and spanning trees||You should understand that a tree is a connected graph with no cycles and that every connected graph contains at least one tree connecting all the vertices of the original graph.|
|Shortest Paths||In developing ideas about shortest paths you will need to appreciate that problems of finding paths of minimum time and cost can both be considered to be shortest path problems|
|Route Inspection Problem||In developing ideas about route inspection you will need to appreciate the connection with the classical problem of finding an Eulerian trail.|
|Travelling Salesperson Problem||In developing ideas about the Travelling Salesperson Problem you will need to appreciate the connection with the classical problem of finding a Hamiltonian cycle.|
|Critical Path Analysis||In developing ideas about Critical Path Analysis you will need to understand both how to construct and how to interpret activity networks with vertices representing activities.|
|Mathematical modelling||You should be able to apply mathematical modelling to situation relating to the topics covered in this module. You will need to interpret results in contexts.|
|Using calculators and computers||The use of a standard scientific calculator is sufficient for this unit.
However, software for the construction of networks or for the carrying out of algorithms is available commercially.