Mathematical Models in the Social Sciences

Mathematical Models in the Social Sciences

Mathematical Models in the Social Sciences

Mathematical Models in the Social Sciences

Excerpt

This book is based on notes developed for a one semester junior mathematics course at Dartmouth College. The course is a natural counterpart of the usual "Mathematical Methods of Physics" course, with techniques and applications selected from the social sciences. Since the course is frequently elected by social science majors, the prerequisites have been kept at a minimum.

It should be emphasized that this book is designed for a mathematics course, not for a course in the social sciences. The subject matter to be taught is mathematical; the problems in the social sciences are introduced only to provide motivation for learning certain techniques. In this sense, the analogy to the courses in "Mathematical Methods of Physics" is complete.

Chapter I is designed to give background information on the nature of mathematical models, and to serve as a methodological guide for the remaining chapters. It is hoped that the student will read this chapter first, and that he will return to it periodically as he progresses through the rest of the volume.

The remaining chapters are independent of each other. The instructor may select any subset of the models for his course. Our experience indicates that a semester course can conveniently cover five or six models. Each chapter will formulate one or more problems both from the point of view of the social scientist and of the mathematician. The major part of the chapter is devoted to teaching the student the necessary mathematical techniques, and in applying them to the stated problems. Finally the results are interpreted.

The prerequisites for the course at Dartmouth consist of a year of calculus and a course in finite mathematics. The student should be acquainted with the basic techniques of differentiating and integrating functions of one variable, and should know how to solve a very simple differential equation. In addition some elementary knowledge of probability theory and of matrix methods is assumed.

In some cases it was convenient to make use of techniques which go beyond these prerequisites; these are treated in the appendices. In each . . .

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