# GRAPHS AND NETWORKS - 2017/8

Module code: MAT3043

Module provider

Mathematics

Module Leader

SKELDON A Prof (Maths)

Number of Credits

15

ECTS Credits

7.5

Framework

FHEQ Level 6

JACs code

G150

Module cap (Maximum number of students)

N/A

Module Availability

Semester 2

Overall student workload

Independent Study Hours: 117

Lecture Hours: 33

Assessment pattern

Assessment type | Unit of assessment | Weighting |
---|---|---|

School-timetabled exam/test | IN-SEMESTER TEST (50 MINS) | 20 |

Examination | EXAMINATION | 80 |

Alternative Assessment

N/A

Prerequisites / Co-requisites

None

Module overview

Graph theory is an aesthetically appealing branch of pure mathematics with strong links to other areas of mathematics (combinatorics, algebra, topology, probability, optimisation and numerics) and well developed applications to a wide range of other disciplines (including operations research, chemistry, systems biology, statistical mechanics and quantum field theory). This module provides an introduction to graph theory. There is an emphasis on theorems and proofs.

Module aims

This module aims to provide an introduction to graph theory, motivated and illustrated by applications to the life, physical and social sciences and to business.

Learning outcomes

Attributes Developed | ||
---|---|---|

1 | Demonstrate understanding of the language and proof techniques used in elementary graph theory | KC |

2 | Apply methods from combinatorics, linear algebra and topology to graphs | KCT |

3 | Apply graph theoretical methods and techniques to network optimisation problems; | CT |

4 | Demonstrate an elementary knowledge of a range of applications of graph theory to the life, physical and social sciences and to business. | CPT |

Attributes Developed

**C** - Cognitive/analytical

**K** - Subject knowledge

**T** - Transferable skills

**P** - Professional/Practical skills

Module content

Indicative content includes:

The language of graph theory;

Elementary results on paths, cycles, trees, cut-sets, Hamiltonian and Eulerian graphs;

Examples from enumerative theory, including Cayley’s theorem on trees;

Graphs embedded in surfaces; the genus of a graph;

Spectral methods: the adjacency and Laplacian matrices;

Graph polynomials, colourings and Ising / Potts models;

Network route and flow optimisation problems;

Applications to Markov chains and decision processes;

Introduction to flux balance and related methods in systems biology;

Examples and properties of small world and scale free networks.

Methods of Teaching / Learning

The learning and teaching strategy is designed to:

Equip students with the knowledge, practical experience and confidence to apply the techniques of Graph Theory to abstract and practical problems.

The learning and teaching methods include:

3 hours of lectures and tutorials per week for 11 weeks. Learning takes place through lectures, tutorials, exercises, coursework, tests and background reading.

Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate:

That they have learned the basic material in the field, and are able to apply it to examples and problems.

Thus, the summative assessment for this module consists of:

In-semester test. Constitutes 20% of the final mark.

Final Examination, 2 hours, end of Semester. Constitutes 80% of final mark.

Formative assessment and feedback

Students will receive verbal feedback in tutorials. There will also be unassessed coursework on which students will receive written feedback

Reading list

Reading list for GRAPHS AND NETWORKS : http://aspire.surrey.ac.uk/modules/mat3043

Programmes this module appears in

Programme | Semester | Classification | Qualifying conditions |
---|---|---|---|

Mathematics and Physics MPhys | 2 | Optional | A weighted aggregate mark of 40% is required to pass the module |

Economics and Mathematics BSc (Hons) | 2 | Optional | A weighted aggregate mark of 40% is required to pass the module |

Financial Mathematics BSc (Hons) | 2 | Optional | A weighted aggregate mark of 40% is required to pass the module |

Mathematics with Music BSc (Hons) | 2 | Optional | A weighted aggregate mark of 40% is required to pass the module |

Mathematics with Statistics BSc (Hons) | 2 | Optional | A weighted aggregate mark of 40% is required to pass the module |

Mathematics BSc (Hons) | 2 | Optional | A weighted aggregate mark of 40% is required to pass the module |

Mathematics MMath | 2 | Optional | A weighted aggregate mark of 40% is required to pass the module |

Mathematics and Physics BSc (Hons) | 2 | Optional | A weighted aggregate mark of 40% is required to pass the module |

Mathematics MSc | 2 | Optional | A weighted aggregate mark of 40% is required to pass the module |

Mathematics and Physics MMath | 2 | Optional | A weighted aggregate mark of 40% is required to pass the module |

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2017/8 academic year.