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.

About the Authors

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.

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