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Programme & Unit Catalogues

## MA30257: Methods for stochastic systems

Academic Year: 2017/8
Owning Department/School: Department of Mathematical Sciences
Credits: 6      [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Honours (FHEQ level 6)
Period:
Semester 1
Assessment Summary: CW 25%, EX 75%
Assessment Detail:
• Coursework (CW 25%)
• Examination (EX 75%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
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.
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.
Programme 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: This unit catalogue is applicable for the 2017/18 academic year only. Students continuing their studies into 2018/19 and beyond should not assume that this unit will be available in future years in the format displayed here for 2017/18. Programmes and units are subject to change in accordance with normal University procedures. Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules. Undergraduates: Find out more about these and other important University terms and conditions here. Postgraduates: Find out more about these and other important University terms and conditions here.