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 … For more content click the Read More button below.

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.

Offerings

S1-01-CLAYTON-ON-CAMPUS

Rules

Enrolment Rule

Contacts

Chief Examiner(s)

Professor Kais Hamza

Unit Coordinator(s)

Professor Kais Hamza

Notes

This Level 4 unit and its Level 3 counterpart MTH3241 share the same core content and learning activities such as seminars and applied classes. However, studies at Level 4 are distinguished from those at Level 3 by a deeper understanding of mathematical theories and their applications, higher levels of critical thinking, and greater autonomy in learning.

Learning outcomes

On successful completion of this unit, you should be able to:

Critically analyse and synthesise the concept of random variables varying with time

Perform analysis of Markov chains in both discrete and continuous time.

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

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

Teaching approach

Active learning

Assessment

1 - Continuous assessment

2 - Final assessment - Exam (3 hours and 10 minutes)

Scheduled and non-scheduled teaching activities

Applied sessions

Seminars

Workload requirements

Workload

Learning resources

Required resources

Dimitri P. Bertsekas and John N. Tsitsiklis, Introduction to Probability, Athena Scientific, 2002.

Gregory F. Lawler, Introduction to Stochastic processes, Second Edition, Chapman and Hall, 2006.

Henry C. Tuckwell, Elementary Applications of Probability Theory, Chapman and Hall, 1988.

Howard M. Taylor and Samuel Karlin, An Introduction to Stochastic Modeling, Academic Press, 1984.

Peter Guttorp, Stochastic Modeling of Scientific Data, Chapman & Hall, 1995.

Sheldon M. Ross, Introduction to Probability Models, Academic Press, 2007.

Other unit costs

Costs are indicative and subject to change.Miscellaneous items required (unit course reader, printing, stationery) - $120

Availability in areas of study

Applied mathematics
Financial and insurance mathematics
Mathematical statistics
Mathematics
Pure mathematics