Dartmouth's Intellectual Life
The Department of Mathematics
Lest the non-scientific minded reader pass this article bywithout reading it, the editor wishes to announce, that he,a non-mathematical minded person read it through withthe greatest degree of interest and found it fascinating.The approaches to all scientific subjects have changed somuch in twenty-five years that Dartmouth men of an earlierperiod who have visions of mathematics as a mere processof memory and grubbing will wish that they attended college in these days' of relativity. A short time ago the editorwent to see an illustrated lecture on a subject dealing largelywith mathematics and from that time has had a fond placein his heart for calculations and mathematical speculations. The offering of popudar courses in mathematicswas not possible years ago; it is possible today and it isdone.
MATHEMATICS has been described as being at once a science, a metaphysics, and a fine art (Spengler). A consideration of its foundations connects it with philosophy, the central body of its superstructure finds its way to an ever increasing extent into the sciences both pure and applied, much of its research partakes of the work of the artist. In a college, as distinguished from either a technical or a graduate school, the work of the department of mathematics should be planned with reference to its general cultural values; i.e., it should, in so far as this is possible, do justice to all three of its aspects mentioned above. It must at the same time, however, give adequate technical training to meet the requirements of other departments, notably those of astronomy, physics, and chemistry. Fortunately, these somewhat conflicting aims are to some extent reconciled by the fact that the cultural values referred to cannot be properly realized without a certain amount at least of technical facility on the part of the student.
At Dartmouth every freshman is required to take a year course in either Latin or Mathematics. About seventy-five percent choose the latter (some, of course, take both). In the course for freshmen we attempt to give them a technical grounding in trigonometry and analytic geometry sufficient for later courses in other departments; but we confine this technical training to the requisite minimum in order to be able to emphasize as well the general cultural values referred to. Among the latter are to be mentioned primarily the establishment of a standard of precise and accurate thought* and the development of insight into the way in which mathematics has entered into the evolution of our present civilization. The latter could not have arisen without the infinitesimal calculus. Therefore we have made a
*Is not one of the fundamental purposes of education the establishment of standards in the various forms of intellectual activity? place, small though it be, for an introduction to the ideas and methods of the calculus in this freshman course, realizing that most of the students will elect no more mathematics. The department is still actively experimenting with various plans for improving this course.
We offer in the sophomore year a year-course in the calculus (Course 11, 12) which is largely technical in character and is required for all majors in mathematics and physics, is alternative with a course in physics for the major in chemistry, and is recommended as a desirable preparation for work in other departments including the Tuck School. This work in the calculus is continued in a junior course (13, 14) and in a senior course (51, 52), thus providing a continuous program extending through the last three years of the college in what is known as mathematical analysis. It is a part of the requirement for all students majoring in mathematics. As indicating the increasing desirability in other departments of mathematical preparation beyond that contained in the freshman course, it may be added that we are offering this year, at the request of the department of chemistry, a one-semester course designed primarily for juniors majoring in that department.
A POPULAR INFORMATIVE COURSE
There is a considerable amount of curiosity on the part of many people to know "what advanced mathematics is all about." To satisfy this entirely worthy interest the department has for some years been offering one "survey" course, the so-called synoptic course (32). Frankly superficial in character, it attempts to make clear what the mathematician means by such strange things as four-dimensional space, non-euclidean geometry, the theory of numbers, analysis situs. It also takes up some of the applications of mathematics that have general interest such as the mathematical theory of music, chronology, the making of maps. The topics change somewhat from year to year according to the interests of the instructor and of the class. It has proven itself a popular and we believe not unprofitable course, even though Professor Silverman, when he gives it, is wont to begin his first lecture with the words: "This is the most useless course in college."
The department offers one course without any prerequisites whatever, except that a student taking it must have at least junior standing. This is the course on the Foundations of Mathematics (54). Little if any knowledge of mathematics beyond that of high school algebra and geometry is presupposed; but a certain amount of intellectual maturity, of power of abstract thinking, is necessary. In this course the logical foundations of mathematics are considered, the fundamental concepts, such as point, line, number, etc. are analyzed, the nature of axioms, postulates, etc. discussed. It is a course of interest primarily to students majoring in mathematics or in philosophy, and to others with a liking for abstract thought.
Another group of courses is offered primarily for students of economics and those interested in a business career. These courses (21, 22, 23, 24, 28) cover the mathematics of finance, insurance, and statistics.
COURSES FOE MAJOR STUDY
The remaining courses in the department are intended primarily for students majoring in mathematics or physics. They give a comprehensive view of more advanced domains of the subject. Several are of the type ordinarily taken by graduate students during their first year of graduate work. They include courses on higher algebra (19, 20), projective geometry (38), modern analytic geometry (57), the theory of functions (55, 56), the differential equations of physics (59), vector analysis (33), differential geometry (63), etc. A description of the work of the department would be incomplete without at least a reference to the manifold extra-curricular activities of its members. They are engaged in research; during the past three years 28 papers were read by members of the department at meetings of the American Mathematical Society. They have been active in the administration of our national mathematical organizations; two have been vicepresidents of the Society; one has been vice-president and is now president of the Mathematical Association of America. Some members of the department have been and are active in the important work of the College Entrance Examination Board. One is a member of the Dartmouth College Athletic Council and associate municipal judge of Hanover; another is Dean of Freshmen and Director of Admissions, a third is now devoting most of his time to the personnel work of the College. The work of Professor Haskins as chairman of the faculty committee on the library deserves special mention. The remarkable ability and devotion he has shown in the planning and building of the Baker Library is known and appreciated by his colleagues in Hanover. It should be known and appreciated also by the alumni.
