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The P versus NP problem is the most important open problem in computer science, if not all of mathematics. Simply stated, it asks whether every problem whose solution can be quickly checked by computer can also be quickly solved by computer. This book provides a nontechnical introduction to P versus NP, its rich history, and its algorithmic implications for everything we do with computers and beyond. The book traces the history and development of P versus NP, giving examples from a variety of disciplines, including economics, physics, and biology. It explores problems that capture the full difficulty of the P versus NP dilemma, from discovering the shortest route through all the rides at Disney World to finding large groups of friends on Facebook. The book explores what we truly can and cannot achieve computationally, describing the benefits and unexpected challenges of this compelling problem.

This book provides a short, hands-on introduction to the science of complexity using simple computational models of natural complex systems—with models and exercises drawn from physics, chemistry, geology, and biology. By working through the models and engaging in additional computational explorations suggested at the end of each chapter, readers very quickly develop an understanding of how complex structures and behaviors can emerge in natural phenomena as diverse as avalanches, forest fires, earthquakes, chemical reactions, animal flocks, and epidemic diseases. This book provides the necessary topical background, complete source codes in Python, and detailed explanations for all computational models. Ideal for undergraduates, beginning graduate students, and researchers in the physical and natural sciences, this unique handbook requires no advanced mathematical knowledge or programming skills and is suitable for self-learners with a working knowledge of precalculus and high-school physics. The book enables readers to identify and quantify common underlying structural and dynamical patterns shared by the various systems and phenomena it examines, so that they can form their own answers to the questions of what natural complexity is and how it arises.