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MA30257: Methods for stochastic systems

Follow this link for further information on academic years Academic Year: 2017/8
Further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Further information on credits Credits: 6      [equivalent to 12 CATS credits]
Further information on notional study hours Notional Study Hours: 120
Further information on unit levels Level: Honours (FHEQ level 6)
Further information on teaching periods Period:
Semester 1
Further information on unit assessment Assessment Summary: CW 25%, EX 75%
Further information on unit assessment Assessment Detail:
  • Coursework (CW 25%)
  • Examination (EX 75%)
Further information on supplementary assessment Supplementary Assessment:
Further information on requisites Requisites: Before taking this unit you must take MA20220, MA20221, & MA20225 - Some familiarity with coding in Matlab will be required. This course may be taken without one or more of these pre-requisites at the lecturer's discretion. Please consult the lecturer.
Further information on descriptions Description: Aims:
The aim of this unit is to introduce stochastic process 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.

Learning Outcomes:
After successfully completing this unit student 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.

Skills:
Numeracy T/F/A
Problem Solving T/F/A
Programming T/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.
Further information on programme availabilityProgramme availability:

MA30257 is Optional on the following programmes:

Department of Mathematical Sciences
  • TSMA-AFM08 : MSc Modern Applications of Mathematics
  • TSMA-AWM14 : MSc Modern Applications of Mathematics
  • USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 3)
  • USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
  • USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
  • USMA-AFB13 : BSc(Hons) Mathematics (Year 3)
  • USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
  • USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
  • USMA-AFM14 : MMath(Hons) Mathematics (Year 3)
  • USMA-AFM14 : MMath(Hons) Mathematics (Year 4)
  • USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
  • USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
  • USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)
  • USMA-AFB01 : BSc(Hons) Mathematics and Statistics (Year 3)
  • USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 4)
  • USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 4)
  • USMA-AFB05 : BSc(Hons) Statistics (Year 3)
  • USMA-AAB06 : BSc(Hons) Statistics with Study year abroad (Year 4)
  • USMA-AKB06 : BSc(Hons) Statistics with Year long work placement (Year 4)

Notes: