Prof Andrew Lewis-Pye

This course is available on the MSc in Applicable Mathematics. This course is available with permission as an outside option to students on other programmes where regulations permit.

Mathematical maturity and an ability to write mathematical proofs. Linear algebra (diagonalisation, eigenvalues and eigenvectors), some graph theory and some basic game theory would be useful, but necessary knowledge from these areas will be revised during the course. 

Globalisation and the growth of the internet have meant not only an increasing need to understand the way in which social and communication networks form and operate, but also an unprecedented amount of data available to aid in this analysis. The last decade has seen a coming together of multiple scientific disciplines in an effort to understand how these highly connected systems function. The aim of this course will be to give an introduction to the study of networks, requiring as little background knowledge as possible. The course will begin with an analysis of some of the fundamental properties normally observed in real world networks, such as the small world property, high degrees of clustering and power law degree distributions. After reviewing required notions from game theory, we shall then apply these techniques to an analysis of the spread of behavioural change on networks, together with cascading effects and epidemic models. The final part of the course will be concerned with specific applications to the world wide web and page ranking.

This course is delivered through a combination of classes and lectures totalling a minimum of 30 hours across Michaelmas Term. 

Written answers to set problems will be expected on a weekly basis.

(1) D. Easley, J. Kleinberg. Networks, crowds and markets, Cambridge University Press, 2010. 

(2) M. Newman. Networks: An Introduction, Oxford University Press, 2010.

(3) The Rise of the Network Society, The Information Age: Economy, Society and Culture, 2010 edition, Manuel Castells.

Exam (80%, duration: 2 hours) in the summer exam period.
Presentation (20%).

20% of the final grade will be determined by groupwork, in which groups of around four or five students are each allocted a research paper by the lecturer. The students then have to meet (virtually or in person) in order to discuss and understand the paper, before giving a group presentation on the subject matter at the beginning of Lent Term.