This book illustrates the use of probability ideas and techniques in the social sciences. Recent curriculum reports* have emphasized the importance of applications for the undergraduate mathematics curriculum. The present work includes seven expository articles intended to acquaint readers with a variety of widely used probabilistic models within social science and to bring out some basic features of mathematical modeling.
I do not imply in offering this volume that social science models are more ideal for illustrating applications of probability than other subjects. A similar set of articles using examples from biology and medicine, from the physical sciences and engineering, from business and law, could (and should) also be prepared. What is important is less the subject matter of the applications than the spur to teachers and· students to spend more time in their probability courses (and in other mathematics courses, too) discussing applications. Developing in their students the art of modeling, that is, of constructing a useful mathematical model of some real-world phenomenon, should be a higher priority than it now is for departments of mathematics. Although a very difficult task for teachers, we must not shy away on that account. Of course, reading about applications and modeling is quite different from the activity of mathematical modeling itself. Bringing illustrative examples of the sort presented in this volume into the classroom is one way of easing into the more challenging task.
Applications in demography, linguistics, management science, political science, psychology, and sociology are included in our seven chapters. Although the boundary lines between different social sciences are fuzzy and economists are likely to be interested in many of these applications, no unit on economics itself is included. There is already a vast literature on mathematical economics, and probabilistic models still appear to be less important than deterministic optimization techniques in economic theory.

Download File Size:4.7 MB

---