MA433      Half Unit
Mathematics of Networks

This information is for the 2021/22 session.

Teacher responsible

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. 

Course content

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. This year, some or all of this teaching will be delivered through a combination of virtual classes and lectures delivered as online videos.

Formative coursework

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

Indicative reading

(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.

Course selection videos

Some departments have produced short videos to introduce their courses. Please refer to the course selection videos index page for further information.

Important information in response to COVID-19

Please note that during 2021/22 academic year some variation to teaching and learning activities may be required to respond to changes in public health advice and/or to account for the differing needs of students in attendance on campus and those who might be studying online. For example, this may involve changes to the mode of teaching delivery and/or the format or weighting of assessments. Changes will only be made if required and students will be notified about any changes to teaching or assessment plans at the earliest opportunity.

Key facts

Department: Mathematics

Total students 2020/21: 12

Average class size 2020/21: 6

Controlled access 2020/21: No

Value: Half Unit

Guidelines for interpreting course guide information

Personal development skills

  • Leadership
  • Self-management
  • Team working
  • Problem solving
  • Communication
  • Application of numeracy skills
  • Specialist skills