Introductory description

N/A

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

Review of important concepts from Probability
Discrete-time Markov chains
Continuous-time Markov chains
Stochastic models of interacting processes (including population dynamics, epidemics)
Basic network definitions and statistics
The Erdos-Renyi random graph and connection to percolation
Heterogeneous network models
Random processes on networks

Learning outcomes

By the end of the module, students should be able to:

• Recall and apply standard network statistics such as degree distribution and clustering coefficient.
• Understand the probabilistic and combinatorial foundations of random processes and network theory, respectively.
• Work with standard stochastic models of population dynamics and epidemiology, such as branching and contact processes
• Mathematical modelling: Building a quantitative probabilistic model from a phenomenological description
• Work with popular random graph models such as Erdos-Renyi, Configuration Model and Preferential Attachment.
• Understand and implement simple algorithms to simulate random processes and networks

Indicative reading list

Handbook of Stochastic Methods, CW Gardiner, Springer 2004.
Networks: An Introduction, MEJ Newman, OUP 2010.
Probability and Random Processes (3rd ed.), G Grimmett and D Stirzakek, OUP 2001.
Random Graph Dynamics, R Durrett, CUP 2007.

View reading list on Talis Aspire

Subject specific skills

See learning outcomes.

Transferable skills

Students will acquire key reasoning and problem solving skills which will empower them to address new problems with confidence.