Math for the Biological and Social Scientist
ONE of the most notable of recent developments on the Dartmouth educational scene has been the rise in enrollment in mathematics courses. Although no man is required by the College to take math, almost every student has at least one semester of the subject before graduation. There are many reasons for this interest but one of the outstanding has been the progress made in the application of modern mathematics to new fields, especially to the biological and social sciences. So important has been this development that the Social Science Research Council recently appointed a committee under the chairmanship of Professor William G. Madow of the University of Illinois to explore the kinds of mathematical training most needed by the social scientist. The Dartmouth Mathematics Department, working independently of the committee, pioneered a course last spring to meet the specific needs of the modern student of these disciplines. Calling the course "Math 6, An Introduction to Finite Mathematics," the department intended to give it on a small scale as an experiment. Quite unexpectedly 170 students elected it.
A prerequisite for the new course is Mathematics 3, an introduction to the basic ideas of analytic geometry and the differential and integral calculus. Dartmouth is fortunate that its entering freshmen have sufficiently good preparation to allow putting them directly into this course. More than 500 men, almost all of them freshmen, elected Math 3 this year. Just as this course introduces the student to three classical branches, the second semester's new course introduces him to three modern branches of mathematics: mathematical logic, probability theory, and matrix algebra.
While by necessity the course can cover only the most fundamental ideas, the student learns a fair amount of skill and develops a feeling for the way mathematics can be applied in a variety of fields. In the field of genetics, for example, the student learns how, by applying probability theory and matrices, the mathematician can predict some characteristics of the offspring of a given male and female even to the tenth generation. In the field of government a mathematical model has been proposed which gives a numerical measure of the power one individual has in a given legislative or voting assembly. By the application of mathematical logic to this model it is found that in the Security Council of the United Nations, for example, any one of the five big nations theoretically has a voting power of .197, whereas any one of the small nations has a power of .002.
Another recent development, called linear programming, has been of great value in the field of economics. In a typical problem the mathematician will know the number of factories a company owns and how much each can produce. He will also know the number and location of the cities to which the company ships its goods. He will be able to tell the company which factory should ship to which city and thereby minimize transportation costs. Large sums of money are reported to have been saved by such companies as Heinz and Honeywell by bringing in the mathematicians.
It is interesting to note that when the report of the Madow committee was published last June they recommended that colleges and graduate schools offer the social scientists the kind of training which was already being given in Dartmouth's experimental Math 6. The medical schools also support the work of this course with enthusiasm.
Even on the basis of one semester's experience it is clear that this course will become a permanent feature of mathematics training at Dartmouth, and the Department is now designing a follow-up to Math 6 which will be offered when the present freshmen are juniors or seniors.
