Historically, the social sciences have been fragmented in two ways. First, as the plural in the name suggests, the study of human behavior embraces many different foci, including (among others) economics, political science, communication, anthropology, and management. Second, in recent decades, the social sciences have drawn on an increasing array of mathematical and conceptual tools, including graph theory, game theory, and nonlinear dynamics.

This breadth of material poses a formidable challenge to new students and their professors. On one hand, a curriculum composed of specialized courses in each contributing discipline risks atomizing the student’s view of the field, pitting (for example) social network analysts against game theorists, and defers engagement with the underlying social questions that motivate many students in the first place. On the other hand, introductory survey courses too often present the foundational disciplines at an informal level, leaving the student with a sense that the field lacks rigor and encouraging a “cookbook” approach that applies the tools in a rote manner without understanding their inner logic.

This text offers an integrated, but not superficial, introduction to these new mathematical concepts and their application across a range of social problems. Each section provides rigorous proofs of key results and rich references to the literature, while remaining accessible to the undergraduate with only a high school mathematics background. References among the sections show how the concepts from different underlying sources contribute to a truly interdisciplinary approach to important social questions. As someone with a background in the conventional disciplines, I found the first few sections confusing. Is this a mathematics book? A book about social networks? A book about economics? As each section built on those before, I realized that the authors are challenging the isolated status of those conventional disciplines. The shared use of new mathematical tools in a number of social disciplines is drawing those disciplines together into a new synthesis, which this book seeks to capture.

After an introductory chapter, the book is organized into seven parts, each a mini-text on a specific tool or application area.

Part 1 introduces basic concepts in graph theory and social networks. The notion of networks is a unifying thread throughout the book (though it would be overly constraining to describe the book as a “network book” along the lines of recent offerings by Newman [1] and Jackson [2]).

Networks are interesting not only for their structure, but for the processes that they support. Part 2 provides an introduction to game theory as a formal system that can usefully describe interactions among parties whose relations are captured in a graph.

Part 3 introduces markets, casting them in terms of the graph- and game-theoretic concepts in the first two sections. The result is a novel perspective that will yield new insights even for those with a classical economics background.

Part 4 explores the World Wide Web as an example of an information network. After developing formal models of search, it brings the previous parts to bear in a discussion of sponsored search.

Part 5 discusses network dynamics at the population level, using models that presume decision-makers have a fairly global picture of the network’s structure, while Part 6 focuses on dynamics that result from local observations and actions by network nodes. Both sections consider both dynamics on networks and dynamical changes in the structure of the network itself.

Part 7 draws on the rich array of themes in the previous six sections to analyze three kinds of systems encountered in the real world: commercial markets (more detailed and realistic than the idealized mechanisms in Part 3), voting, and property rights.

The book is an ideal text for introductory classes. It also holds great promise for people with a strong background in another field who wish to understand some of the key questions addressed by the social sciences. Each chapter but the first has exercises, and many chapters have optional material that provides additional details on concepts introduced in the chapter. The abundance and accessibility of proofs of central concepts will be particularly helpful in helping students to understand the inner logic and limitations of standard results. A bibliography of over 400 entries extends through 2009, and includes pointers to many classic papers, as well as newer work.