MTH4241 · Random processes in the sciences and engineering

Overview

This unit introduces the methods of stochastic processes and statistics used in the analysis of biological data, physics, economics and engineering. At the completion of the unit you will understand the application of classical techniques, such as Poisson processes, Markov chains, hidden Markov chains, random walks, martingale theory, birth and death processes, and branching processes in the analysis of DNA sequences, population genetics, dynamics of populations, telecommunications and economic analysis.

Areas of study: Applied mathematics Financial and insurance mathematics Mathematical statistics Mathematics Pure mathematics

Offerings

Assessment

The Handbook lists an examination for this unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

The Handbook lists no prerequisite, corequisite or prohibition for this unit.

Learning outcomes

1. Critically analyse and synthesise the concept of random variables varying with time
2. Perform analysis of Markov chains in both discrete and continuous time.
3. Demonstrate an in-depth understanding of key processes in probability, including the Poisson process, birth process, birth and death process, branching processes, random walks, and martingales
4. Apply probability processes to complex and practical situations, including queues, epidemics, servicing machines, networks, financial markets, and insurance risk, showcasing the ability to solve real-world problems with advanced probabilistic methods

Workload

Three 1-hour seminars; One 2-hour applied class (in weeks 2-12) and 7 hours of independent study per week.

Student experience, not official rules. Nothing here changes what the Handbook says.