# MA6M4 Topics in Complexity Science

**Lecturer:** Marya Bazzi

**Term(s):** Term 2

**Commitment:** 30 lectures

**Assessment:** Essay Draft 5%, Essay 80% and Presentation 15%

**Formal registration prerequisites: **None

**Assumed knowledge: **The module MA398 Matrix Analysis and Algorithms provides some methodological foundations in linear algebra and matrix algorithms as well as hands-on experience in programming that would be relevant for the module. The particular concepts from MA398 that will be important are vector and matrix norms, singular value decomposition, eigenvalue decomposition, and algorithmic computational cost.

**Useful background:** Some notions from ST202 Stochastic Processes such as Markov processes and Markov chains, basic concepts in graph theory as covered in MA241 Combinatorics, and algorithms in MA252 Combinatorial Optimisation for tackling NP-hard problems would be helpful but are not required.

**Content:** This course aims to provide an introduction to network science, which can be used to study complex systems of interacting entities. Networks are interesting both mathematically and computationally, and they are pervasive in sociology, biology, economics, physics, information science, and many more fields. Networks have grown in importance over the last few decades and most of the topics to be considered are active modern research areas. Possible topics in complexity include:

- 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

**Aims:** 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

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 disciplines, such as Sociology, Economics, and Biology.

**Books: **

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.