MATHEMATICS A

To several hundred undergraduates the program of Mathematics A is of immediate importance, for the distribution requirement has resulted in a heavy enrollment year after year. The aim of the course may be considered two-fold: first, to present an exposition of the language of mathematics and the methods of mathematical technique; second, to discipline the student's mind in the art of exact thinking by requiring of it activities of a highly analytic and synthetic nature. Thus an attempt is made to lead a large number of men through a valuable cultural experience which will, at the same time, serve for a few of them as technical training on which to base a more intensive study of mathematics.

The present method of performing this difficult maneuver, although in many ways a remarkably successful compromise, is still open to criticism on several fronts; the most conspicuous of these weakness now consists in the extraordinary length of the program of instruction. The syllabus of the material covered consists of a list of topics in the fields of analytic geometry, trigonometry, and differential and integral calculus, embracing a great mass of fundamental mathematical learning, and including many radically different concepts. Moreover, in the customary presentation the work leaps with disconcerting rapidity from analytic geometry to calculus, with a fairly long digression on trigonometry interpolated during the second half year, and the timeliness of the changes is by no means apparent. Perhaps in a less thorough attack upon the subject, this shifting of ground would not be confusing, but Mathematics A is nothing if not through. By a grimly regular series of daily exercises the student is brought into contact with every idea and every method in the large repertory of the course; he is rsponsible for each such item of the examination, and he knows very well in that connection that the grading of his papers is both swift and sure, for an answer is either right or wrong.

At the end of the year a well organized course should leave the student impression which clearly distinguishes the highlands from the lowlands of the terrain which has been traversed; he should perceive intuitively a brief coherent outline of the entire work. Yet Mathematics A, to cover the prescribed ground, must proceed at a pace which renders all but the most brilliant men incapable of obtaining a thorough grasp of the topics as they rush by, and the diverse nature of the subjects which are treated does not help to clarify the final picture. If the course intended merely to present a series of glimpses of the extraordinary panorama of mathematical thought obtained from a somewhat removed point of vantage, perhaps the confusion could be avoided. The perspective,however, which the student must at present take is of very different nature he is placed over a hole in the floor of an express train and calmly told to count the ties.