Monte Carlo Simulations (L7) (865G1)

15 credits, Level 7 (Masters)

Spring teaching

An introduction to an important simulation technique for probabilistic and deterministic problems with applications to all sciences including computer science, finance, economics, engineering, mathematics and physics. 

The initial part of the module is about computer simulated randomness and begins with pseudo random generators and simulating one dimensional random variables. From the moment that we can simulate one random variable we can simulate a whole discrete process, such as Markov chains and use the simulations to extract statistical results of their equilibria. We will also explore applications in Physics via the Ising model and to Statistics via the goodness of fit tests.

The module is a mixture of coding with probability theory and we will be using R software for the simulations. 

Some questions we will explore: 

• How far from truly random are pseudo-random number generators and why does it matter? 
• After we see the data resulted from a simulation, how confident are we that the theoretical model will give the same data? Are there ways to raise our confidence so we can use simulations for predictions? 
• Can we simulate complicated realistic models with everyday usage, such as financial markets? 

Contact hours and workload

This module is approximately 150 hours of work. This breaks down into about 33 hours of contact time and about 117 hours of independent study. The University may make minor variations to the contact hours for operational reasons, including timetabling requirements.

We regularly review our modules to incorporate student feedback, staff expertise, as well as the latest research and teaching methodology. We’re planning to run these modules in the academic year 2022/23. However, there may be changes to these modules in response to feedback, staff availability, student demand or updates to our curriculum. We’ll make sure to let you know of any material changes to modules at the earliest opportunity.