What you will study
This module in probability and its applications emphasises probability modelling and developing the properties of the models. A considerable amount of mathematics is sometimes required for this development, but we do not always give formal proofs, particularly if the proof does not illuminate the probabilistic ideas.
The module consists of six books.
The first one, which is introductory, revises and develops ideas about probability and introduces some techniques that will be used frequently in the module.
The second book develops models for events occurring in time, including the Poisson process and several extensions of it, and patterns in space, including models for random scatter and clustering of objects.
The third book develops models for processes in which events can occur only at discrete time points, such as a Bernoulli process. This includes practical situations such as the ruin of a gambler and the extinction of a family surname.
In the fourth book, probability models are developed for situations in which events can occur at any time. Examples include queues, the spread of epidemics, and the change in the size of a population due to births and deaths.
In the fifth book, models are developed for various situations, including genetics, the renewal of components, and the change in stock market prices.
Computer simulations are used to illustrate some of the phenomena studied, and associated activities are included in a separate book.
You will learn
Successful study of this module should enhance your skills in understanding mathematical arguments, expressing problems in mathematical language, finding solutions to problems and interpreting mathematical results in real-world terms.
This module may help you to gain membership of the Institute of Mathematics and its Applications (IMA). For further information, see the IMA website.