Introductory description

To introduce mathematical and computational approaches in network science for the study of complex systems. Network science has applications in a wide range of real-world problems. The module will contribute to training MMath, MSc and PhD students in skills which are asked for in many areas of research, business, industry and government.

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.

Topics from:

Network science
Selfish routing
Interacting particle systems
Reduction of dynamical systems
Dynamics of networks of oscillators
Large deviation theory
Representation and inference of many-variable probabilities
Analogues for many-body quantum systems
Aggregation methods
Data assimilation
Biophysical modelling
Fluid dynamic models

Learning outcomes

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

• Have a sound knowledge of and appreciation for some of the tools, concepts, models, and computations used in the study of networks
• Read and understand current research papers in the field
• Gain some experience with communicating scientific research
• Gain some experience working with real-world data

Indicative reading list

1. M. E. J. Newman, Networks: An Introduction, Oxford University Press, 2010
2. A. Barrat et al, Dynamical Processes on Complex Networks, Cambridge University Press, 2008
3. Various papers and review articles to be specified by the instructor.

Interdisciplinary

The module overlaps with several disciplines other than mathematics, such as computer science and statistics. The applications (which students may pursue in more depth in their essays) may also intersect with further discplines, such as Sociology, Economics, and Biology.

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. They will also gain some experience with manipulating real-world data and communicating research findings.