Complexity Science

Ecosystems, the human brain, ant colonies, and economic networks are all complex systems displaying collective behaviour, or emergence, beyond the sum of their parts. Complexity science is the systematic investigation of these emergent phenomena, and stretches across disciplines, from physics and mathematics, to biological and social sciences. This introductory textbook provides detailed coverage of this rapidly growing field, accommodating readers from a variety of backgrounds, and with varying levels of mathematical skill. Part I presents the underlying principles of complexity science, to ensure students have a solid understanding of the conceptual framework. The second part introduces the key mathematical tools central to complexity science, gradually developing the mathematical formalism, with more advanced material provided in boxes. A broad range of end of chapter problems and extended projects offer opportunities for homework assignments and student research projects, with solutions available to instructors online. Key terms are highlighted in bold and listed in a glossary for easy reference, while annotated reading lists offer the option for extended reading and research.

• New concepts and methodologies are introduced alongside examples from a range of complex systems, to demonstrate the relevance and cross-disciplinary nature of complexity science
• Two-part structure supports a range of teaching, including shorter, more conceptual courses, to extended courses offering full mathematical treatment of complexity science
• A broad range of homework problems and extended projects offer readers the chance to reinforce their understanding of key topics, and develop a critical approach to describing and modelling real complex systems