MTH4241 Random processes in the sciences and engineering
Faculty of Science
MTH4241 Random processes in the sciences and engineering is a level 4, 6-credit-point, undergraduate and postgraduate unit from the Faculty of Science, offered in 2027 in Semester 1 at Clayton. It has no prerequisites and unlocks 2 units.
- Credit points
- 6
- Offered in 2027
- Semester 1
- Clayton
- Assessment
- Exam 50%
- and 1 other task
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Requisites
Before MTH4241
No prerequisites or corequisites besides the enrolment rules below.
After MTH4241
2 units list MTH4241 as a prerequisite or corequisite.
Enrolment rules
You must be enrolled in the Graduate Certificate in Mathematics or the Master of Mathematics
Prohibition: MTH3241
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.
Offerings in 2027
| Teaching period | Campus | Mode |
|---|---|---|
| First semester | Clayton | On campus |
Assessment
- Continuous assessmentDemonstration50%
- Final assessment - Exam (3 hours and 10 minutes)Examination50%
Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.
Learning outcomes
When you finish this unit, you should be able to:
- 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 and teaching
- Applied sessions22 hours
- Seminars36 hours
- Teaching approachActive learning
Three 1-hour seminars;
One 2-hour applied class (in weeks 2-12) and
7 hours of independent study per week.
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.
Contacts
- Chief Examiners
- Professor Kais Hamza
- Unit Coordinators
- Professor Kais Hamza
Common questions
What are the prerequisites for MTH4241?
MTH4241 has no prerequisites, but enrolment rules apply.
What can I take after MTH4241?
MTH4241 is a prerequisite or corequisite for 2 units, including MTH5220 and MTH5230.
When is MTH4241 offered?
In 2027, MTH4241 runs in Semester 1 at Clayton.
Does MTH4241 have an exam?
Yes. The exam is worth 50% of the final mark, alongside 1 other task.