Mathematical Models of Social Behaviour


Course start Wednesday November 8th 2017, 14:15-16:00 Room 64119, Ångström lab. 

Course will be every Wednesday 14:15-16:00 from then on until I have nothing interesting left to say.

To attend the course just come to first lecture. Lectures at same time weekly, plus labs for discussing and developing projects.

Requirements: PhD student in mathematical area. Masters students in mathematics, computer science and scientific computing are welcome to register by contacting Olga Kaj (

This course looks at the ways in which mathematics is increasingly used to model social behaviour of humans. A series of lectures will look at how models have been applied by social media sites to classify our behavior, in modelling the spread of ideas, explaining in-group thinking, social networks, segregation and social development. A focus here will be on meaningful analysis that can be used to inform the public and policy makers.
Course content

1.   Algorithmic bias. Proving the impossibility of constructing algorithms that have both predictive parity and give equal false positive rates for two different groups.

2.   Classification. How Facebook and other social networks uses Singular Value Decomposition to classify our personalities.

3.   Language processing. Unsupervised learning of the structure of language. Progress and problems.

4.   Positive feedback and spread of ideas. Ordinary and partial differential equations for modelling social epidemics, voting behaviour and fads.

5.   Preferential attachment. Stochastic models of how things and people become popular. Power laws. Problems with citation metrics.

6.   Models of ‘filter bubbles’ and Twitter.

7.   Segregation and social change. The Shelling model. Phase transitions. Modelling social uprisings.
The Micro-macro link.

8.   Democracy and development. Modelling change in developmental indicators.

9.   Deep learning.  Bayesian methods and machine learning.

10. How does ‘Artificial Intelligence’ work.

The course will also contain some background on obtaining and storing social data, and ethical issues about data.

In addition to the lectures, which will be an overview of the subject, the student will be (working in a pair with another student) expected to obtain a data set (with help of the course instructor), implement a model, establish an empirical connection between the model and the data, and present the results in the form of both a report and a blog article. Depending on the length of the project the course can be taken as either 5hp or 10hp.