Our society faces difficult problems, for instance, fairly allocating scarce resources, making good societal decisions about energy use and pollution, reasonably disseminating urban and social services, and understanding and eliminating social inequalities. These problems involve in an important way issues in the social sciences. Increasingly, mathematics is being used, at least in small ways, to tackle these problems, and also to develop the necessary underlying principles of such fields as sociology, psychology, and political science.

This volume is the first in the section, Mathematics and the Social Sciences. The section is expected to present mathematical treatments of social scientific problems as well as theories and mathematical tools, techniques, and questions motivated by problems of the social sciences. It is anticipated that this classification will concern itself with such fundamental topics as learning theory, perception, signal detection, scaling and measurement, social networks, social mobility theory, voting behavior, social choice, and utility theory. At the same time, the section will concern itself with applications to problems of society, and deal with such problems as environment, transportation, urban affairs, and energy, from a societal point of view.

The problems of the social sciences in general, and the problems facing society in particular, are extremely complex. We should not expect too much of mathematics when it comes to solving these problems. On the other hand, mathematics, as the language of science, has a very important role to play.