I just read "A Quantitative Tour of the Social Sciences," edited by Andrew Gelman and Jeronimo Cortina. I highly recommend the book for anyone who does quantitative research, including part-time quantitative analysts and ambitious undergraduates. The aim of the book is to expose the reader to the similarities and differences in quantitative thinking across five core social science disciplines: history (a welcome but oft neglected member of the social sciences), economics, sociology, political science, and psychology. The editors are unabashedly in favor of methodological pluralism, and present as diverse set of views as possible. What is notable about this volume is that for each discipline the authors have included exercises ranging from conceptual questions to hands-on data analyses. From my perspective, especially illuminating chapters include Andrew Gelman's thoroughly informative discussion of the application of game theory to trench warfare (in part because he discusses the criticisms of his paper as it went through peer review) and Jeronimo Cortina's overview of the potential outcomes model of causality (which, while familiar to more advanced readers, is presented with enviable clarity).
The chapters capture most of the differences among the disciplines in quantitative thinking. However, a few differences in mathematical modeling may be missed. In particular, likely reflecting an enduring interest in social context and interconnections among individuals, sociologists tend to use multilevel models and social network methods more frequently than other social scientists. As well, economists are much more likely to focus on trying to interpret observational data causally through the use of instrumental variables and, to a lesser extent, regression discontinuity design. Notwithstanding, overall this book is a welcome addition to the bookshelf of any scholar who does quantitative work.
