Complexity Science
The Study of Emergence

This introductory textbook provides detailed coverage of the rapidly growing field of complexity science, for a broad audience of readers.

Henrik Jeldtoft Jensen (Author)

9781108834766, Cambridge University Press

Hardback, published 17 November 2022

458 pages
26 x 18.2 x 2.5 cm, 1.12 kg

'This is a very structured and well-done textbook on complex systems. I am teaching LLMs and NLP for complex systems and it will provide a lot of help with foundations of complexity science that I can use as examples and problems in my classes on LLMs.' Anamaria Berea, George Mason University

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.

Part I. Conceptual Foundation of Complexity Science: 1. The Science of Emergence
2. Conceptual Framework of Emergence
3. Specific Types of Emergent Behaviour
4. The Value of Prototypical Models of Emergence
Part II. Mathematical Tools of Complexity Science: 5. Branching Processes
6. Statistical Mechanics
7. Synchronisation
8. Network Theory
9. Information Theory and Entropy
10. Stochastic Dynamics and Equations for the Probabilities
11. Agent-Based Modelling
12. Intermittency
13. Tipping Points, Transitions and Forecasting
14. Concluding Comments and a Look to the Future.

Subject Areas: Algorithms & data structures [UMB], Statistical physics [PHS], Mathematical modelling [PBWH], Information theory [GPF]