Lecturer: Stefan Grosskinsky (Mathematics and Complexity)

Module Aims:
This is one of 4 core modules for the new MSc in Mathematics of Systems. The main aims are to provide a broad background in theory and applications of complex networks and random processes, and related practical and computational skills to use these techniques in applied mathematical research and modelling. Students will become familiar with basic network theoretic definitions, commonly used network statistics, probabilistic foundations of random processes, some commonly studied Markov processes/chains, and the links between these topics through random graph theory.

Link to Module Resources

Syllabus:
1. Introduction to Probability
2. Discrete-time Markov chains
3. Continuous-time Markov chains
4. Stochastic models of interacting processes (including population dynamics, epidemics)
5. Introduction to entropy maximization and phase transitions
6. Basic network definitions and statistics
7. The Erdos-Renyi random graph and connection to percolation
8. Heterogeneous network models
9. Bipartite and maximum-entropy network models
10. Random processes on networks

Illustrative Bibliography:
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.
Probability on Graphs, G. Grimmett, CUP 2010.

Teaching: (see main calendar for timetable)
per week: 2 x 2 hours of lectures, 2 x 2 hours of classwork
duration: 5 weeks

Assessment: (for deadlines see Module Resources page)
Written homework assignments (50%), Class test and oral examination (50%)