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MA50257: Methods for stochastic systems

[Page last updated: 03 August 2022]

Academic Year: 2022/23
Owning Department/School: Department of Mathematical Sciences
Credits: 6 [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Masters UG & PG (FHEQ level 7)
Semester 1
Assessment Summary: CW 50%, EX 50%
Assessment Detail:
  • Coursework (CW 50%)
  • Examination (EX 50%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Learning Outcomes: After successfully completing this unit students will be able to
1. list and describe a number of real-world systems which are most appropriately described in terms of stochastic models;
2. formulate and analyse stochastic models using appropriate mathematical techniques;
3. efficiently simulate stochastic models using a computer;
4. describe in mathematical terms the connections and differences between a range of stochastic methods, and between stochastic and deterministic modelling;
5. Analyse stochastic methodologies and associated analytical techniques.

Aims: The aim of this unit is to introduce stochastic processes from the point of view of modelling real world systems. The mathematical methods learned in this course are useful in many application areas: mathematical biology, statistical physics, financial mathematics, etc. This course introduces a broad range of techniques that we might use when representing real-world processes. The unit should be an accessible introduction to stochastic modelling for students who might otherwise avoid the subject for fear that they do not have a sufficient background in probability. The emphasis of this course will be on understanding of stochastic processes through their computational modelling, rather than on rigorous theory and analysis of published stochastic methodologies and their analysis.

Skills: Numeracy T/F/A
Problem Solving T/F/A
Programming T/A
Academic reading T/F/A
Writing reports T/F/A

Content: Stochastic modelling of chemical reactions; well-stirred systems, Gillespie algorithm, chemical master equation, analysis of simple systems, deterministic vs. stochastic modelling, systems with multiple favourable states, stochastic resonance, stochastic focusing.
Stochastic differential equations: numerical methods, Fokker-Planck equation, first exit time, backward Kolmogorov equation, chemical Fokker-Planck equation.

Programme availability:

MA50257 is Optional on the following programmes:

Department of Mathematical Sciences


  • This unit catalogue is applicable for the 2022/23 academic year only. Students continuing their studies into 2023/24 and beyond should not assume that this unit will be available in future years in the format displayed here for 2022/23.
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