Unit name | Probability 2 |
---|---|

Unit code | MATH20008 |

Credit points | 20 |

Level of study | I/5 |

Teaching block(s) |
Teaching Block 2 (weeks 13 - 24) |

Unit director | Professor. Holroyd |

Open unit status | Not open |

Pre-requisites |
MATH11005 Linear Algebra and Geometry, MATH10011 Analysis and MATH10013 Probability and Statistics |

Co-requisites |
None |

School/department | School of Mathematics |

Faculty | Faculty of Science |

**Unit Aims**

To survey basic models of applied probability and standard methods of analysis of such models.

**Unit Description**

A wide range of phenomena from areas as diverse as physics, economics and biology can be described by simple probabilistic models. Often, phenomena from different areas share a common mathematical structure. In this course a variety of mathematical structures of wide applicability will be described and analysed. The emphasis will be on developing the tools which are useful to anyone modelling applications, rather than the applications themselves.

Students should have a good knowledge of first year probability and of basic material from first year analysis. As the course builds on Probability 1 it will also deepen students' understanding of the basis of probability theory.

**Relation to Other Units**

This unit develops the probability theory encountered in the first year. It is a prerequisite for the Level H/6 units Introduction to Queuing Networks, Further Topics in Probability 3, Bayesian Modeling and Financial Mathematics, and is relevant to other Level H/6 probabilistic units.

At the end of the course the student should should:

- have gained a deeper understanding of and a more sophisticated approach to probability theory than that acquired in the first year

- have learnt standard tools for analysing the properties of a range of model structures within applied probability

Transferable Skills:

- construction of probabilistic models

- the translation of practical problems into mathematics

- the ability to integrate a range of mathematical techniques in approaching a problem.

The unit will be taught through a combination of

- synchronous online and, if subsequently possible, face-to-face lectures
- asynchronous online materials, including narrated presentations and worked examples
- guided asynchronous independent activities such as problem sheets and/or other exercises
- synchronous weekly group problem/example classes, workshops and/or tutorials
- synchronous weekly group tutorials
- synchronous weekly office hours

90% Timed, open-book examination 10% Coursework

Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.

If you fail this unit and are required to resit, reassessment is by a written examination in the August/September Resit and Supplementary exam period.

**Recommended**

- Geoffrey Grimmett and David Stirzaker,
*Probability and Random Processes,*OUP, 2001 - Howard M. Taylor, and Samuel Karlin,
*An Introduction to Stochastic Modelling (3rd Ed.),*Academic Press, 1998