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I redesigned a course around the reasoning tools, which are more general and useful than topics. This organization, which I have used at MIT and Olin College of Engineering, is re- flected in this book—which teaches you one tool per chapter, each selected to help you build insight and master complexity.

There are the two broad ways to master complexity: organize the complexity or discard it. Organizing complexity, the subject of Part I, is taught through two tools: divide-and-conquer reasoning (Chapter 1) and making abstractions (Chapter 2).

Discarding complexity (Parts II and III) illustrates that “the art of being wise is the art of knowing what to overlook” (William James [24, p. 369]). In Part II, complexity is discarded without losing information. This part teaches three reasoning tools: symmetry and conservation (Chapter 3), proportional reasoning (Chapter 4), and dimensional analysis (Chapter 5). In Part III, complexity is discarded while losing information. This part teaches our final tools: lumping (Chapter 6), probabilistic reasoning (Chapter 7), easy cases (Chapter 8), and spring models (Chapter 9).

Using these tools, we will explore the natural and human-made worlds. We will estimate the flight range of birds and planes, the strength of chemical bonds, and the angle that the Sun deflects starlight; understand the physics of pianos, xylophones, and speakers; and explain why skies are blue and sunsets are red. Our tools weave these and many other examples into a tapestry of meaning spanning science and engineering.

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