MA30257: Methods for stochastic systems
[Page last updated: 23 October 2023]
Academic Year:  2023/24 
Owning Department/School:  Department of Mathematical Sciences 
Credits:  6 [equivalent to 12 CATS credits] 
Notional Study Hours:  120 
Level:  Honours (FHEQ level 6) 
Period: 

Assessment Summary:  CW 25%, EX 75% 
Assessment Detail: 

Supplementary Assessment: 

Requisites:  Before taking this module 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 prerequisites at the lecturer's discretion. Please consult the lecturer. 
Learning Outcomes: 
After successfully completing this unit student will be able to
1. list and describe a number of realworld 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. 
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 realworld 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. 
Skills:  Numeracy T/F/A
Problem Solving T/F/A Programming T/A 
Content:  Stochastic modelling of chemical reactions; wellstirred 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, FokkerPlanck equation, first exit time, backward Kolmogorov equation, chemical FokkerPlanck equation. 
Course availability: 
MA30257 is Optional on the following courses:Department of Mathematical Sciences

Notes:
