Complexity Science

The Warwick Master's Course

Robin Ball (University of Warwick), Vassili Kolokoltsov (University of Warwick), Robert S. MacKay (University of Warwick)

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English

Cambridge University Press
21 November 2013

Complex analysis, complex variables; Numerical analysis; Mathematical modelling; Stochastics

Series: London Mathematical Society Lecture Note Series

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.

Edited by: Robin Ball (University of Warwick), Vassili Kolokoltsov (University of Warwick), Robert S. MacKay (University of Warwick)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 408
Dimensions: Height: 228mm, Width: 152mm, Spine: 24mm
Weight: 660g
ISBN: 9781107640566
ISBN 10: 1107640563
Series: London Mathematical Society Lecture Note Series
Pages: 454
Publication Date: 21 November 2013
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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.

Robin Ball is a Professor of Physics at the University of Warwick. Vassili Kolokoltsov is a Professor in the Department of Statistics at the University of Warwick. Robert MacKay is a Professor of Mathematics at the University of Warwick, where he is also the Director of Mathematical Interdisciplinary Research. He is a Fellow of the Royal Society.