Postgraduate Lectures - Course PY5016: Complex Systems

Lecturer: Dr. Stefan Hutzler

Rationale:
Complex Systems is a module taken by postgraduate physics students. It deals with the mathematical description of emergence of properties out of a system of interacting parts and includes applications of physics to problems in finance and sociology. The modulus provides an overview of this field which has recently become very popular but it is only marginally covered in undergraduate syllabi.

Module Aims:
This module will equip postgraduates with key concepts for dealing with complexity and thus enable them to review and examine research literature in this field. The ideas and techniques developed and discussed in this module will benefit students working in a variety of research areas.

Module Learning Outcomes:
On successful completion of this module, students will be able to:
1)  identify a number of novel applications of physics to problems outside the traditional physics domains.
2) employ novel tools for data analysis that have recently been developed in statistical physics.
3) apply analytical and numerical calculations to problems in complexity

Teaching and Learning Methods, including contact hours:  
Frontal Teaching: 9 hrs
Individual Reading: 27 hrs
Assignments: 2 home assignments

Syllabus:

• Examples of Complex Systems
• Mathematical Preliminaries
• Power Laws
• Agent Models
• Networks
• Econophysics and Sociophysics

Assessment:
2 home assignments

Evaluation of the module:
Student feedback will be gathered at the end of the last lecture. This will be thoroughly assessed and will be an important source when reviewing  the module.

Indicative Reading and Resources:

G. Caldarelli, Scale-Free Networks: Complex Webs in Nature and Technology, Oxford University Press, 2007

B. M. Roehmer, Driving Forces in Physical, Biological and Socio-economic Phenomena: A Network Science Investigation of Social Bonds and Interactions, Cambridge University Press 2007

R.N. Mantegna, H.E. Stanley, An Introduction to Econophysics: Correlations and Complexity in Finance, Cambridge University Press 1999.

P. Erdi, Complexity Explained, Springer 2007.

G. Nicolis and C. Nicolis, Foundations of Complex Systems: nonlinear dynamics, statistical physics, information and prediction, World Scientific Publishing, 2007.