Complexity Science
The Warwick Master's Course

This book presents introductions to the essential mathematical aspects of complexity science, suitable for advanced undergraduate/masters-level students and researchers.

Robin Ball (Edited by), Vassili Kolokoltsov (Edited by), Robert S. MacKay (Edited by)

9781107640566, Cambridge University Press

Paperback / softback, published 21 November 2013

454 pages, 40 b/w illus.
22.8 x 15.2 x 2.4 cm, 0.66 kg

Complexity science is the study of systems with many interdependent components. Such systems - and the self-organization and emergent phenomena they manifest - lie at the heart of many challenges of global importance. This book is a coherent introduction to the mathematical methods used to understand complexity, with plenty of examples and real-world applications. It starts with the crucial concepts of self-organization and emergence, then tackles complexity in dynamical systems using differential equations and chaos theory. Several classes of models of interacting particle systems are studied with techniques from stochastic analysis, followed by a treatment of the statistical mechanics of complex systems. Further topics include numerical analysis of PDEs, and applications of stochastic methods in economics and finance. The book concludes with introductions to space-time phases and selfish routing. The exposition is suitable for researchers, practitioners and students in complexity science and related fields at advanced undergraduate level and above.

Preface
1. Self-organization and emergence Mario Nicodemi, Anas Ahmad Rana, Chris Oates, Yu-Xi Chau and Leigh Robinson
2. Complexity and chaos in dynamical systems Yulia Timofeeva
3. Interacting stochastic processes Stefan Grosskinsky
4. Statistical mechanics of complex systems Ellak Somfai
5. Numerical simulation of continuous systems Colm Connaughton
6. Stochastic methods in economics and finance Vassili Kolokoltsov
7. Space-time phases Robert S. MacKay
8. Selfish routing Robert S. MacKay.

Subject Areas: Stochastics [PBWL], Mathematical modelling [PBWH], Numerical analysis [PBKS], Complex analysis, complex variables [PBKD]