NAVAL MATHEMATICS
Few Alumni Have Covered Ground of V-12 Course
A BASIC CANDIDATE in the V-12 Program comes to Dartmouth for four terms. During these four terms he will take: Term I: M1: Algebra, Plane and Spherical Trigonometry (5 hours a week) II : M2 : Plane and Solid Analytic Geometry (5 hours a week) III : M5 : The Calculus M8 : Navigation (in all 8 hours a week) IV : M6 : The Calculus (cont.) M9 : Navigation Ai : Analytical Mechanics (in all 8 hours a week)
This sounds like a lot of mathematics; and it is. It sounds like an accelerated, a hurried program; and it is. It even sounds as if this program would cram mathematics into a student a little faster than he could absorb it. It does.
Less than five per cent of Dartmouth alumni have, in times past, mastered mathematics to an extent comparable to this program. No country hais ever attempted to teach so much mathematics to so many people in so short a time. The pendulum has swung very, very far to one side.
The Navy courses in mathematics are organized into sections containing from 20 to 40 students each. There are, for example, 22 sections of Mi. The Director makes out a detailed program for the term; he provides a common final examination; in between the start and the finish the instructor of a section is entirely on his own. Most of the sections of the first two terms are taught by our Associates in Mathematics. The regular members of the Department divide their time between the courses of the civilian college, and the Navy courses of the third and fourth term.
The instruction is largely by the lecture method; although it is a very informal lecture frequently interrupted by questions and discursions. A new and challenging type of problem is formulated; a method of attack is found; sample problems are solved; and the pupil is told to go and do likewise. "Home-work" is, unfortunately, not as prominent a part of the course as it is in the civilian courses. The time of the trainee is limited, the physical strength of the instructor is not adequate to the reading of daily papers in all his sections, and there are very few competent undergraduates to assist us. Mathematics is a cumulative subject, and we use frequent tests to tie 'together the facts and methods of the course.
A trainee comes to us in July, say, and he may be and usually is, almost entirely innocent of mathematical knowledge; but the next March, only eight months later, he is scheduled to begin the calculus. A good deal of work has to be done in those eight months. We try very hard not to let the course seem hurried or crammed. When we can, we make the work point up to things that really appeal to our students: the determination of distance and course in great circle sailing, or the trajectory of a projectile. But for most pupils the internal workings of mathematics simply do not have the same fascination as the internal mechanism of a machine gun; it is a long pull for an alert, active youngster who wants to get out and shoot Japs; and it takes finesse and jockeying to ensure smooth, continuous progress.
Despite the fact that you have to climb fifty-two steps to get there, I think that one of the pleasantest places in Hanover these days is the headquarters of the Mathematics Department, situated on the third floor of Dartmouth Hall. We try to keep business and paper work down to a minimum. We try to maintain an unhurried, unworried atmosphere. Throughout the day the regular members of the Department and the Associates can and do stop, and talk. There is a lot of discussion of music, a good deal of post mortem about last night's contract, but a surprising amount of conversation is based on: "What is the best way of presenting the next assignment in trigonometry?" It is stimulating, invigorating conversation. At first, the "regulars" were on the giving end, and the Associates on the receiving end; but that is no longer true. History, and Psychology, and Sociology, and Philosophy have now had two terms of teaching experience, and they have something to say. I like the way they tell us how bad the text-books are; how misleading and ambiguous some of the explanations are; how poorly worded the problems are. I like their novel approach to problems that we have wrestled with for years. It is very good for all of us.
The Navy program of mathematics is a pretty good one for the present circumstances; remembering that it must be taught in widely varying institutions by instructors of widely varying standards. It is no criticism of this program to say that it is not one I should like to see adopted in normal times by a college of liberal arts. It is of necessity too hurried, too crammed with too many things. It asks too much of many students; but not nearly enough of the best students. In practise there is a tremendous difference between five times a week, and the more customary three times a week. There is a tremendous difference in a program which eliminates all holidays.
I think it is important for the post-war college that the mathematicians and their associates do see these things, and that they are talking about them, now. We are genuinely ambitious to do better in the future than we ever have before. But during this emergency, we have developed this one mental attitude: we can take any responsibility that we are asked to assume, and we can take it in stride, and laugh about it as we do the job.
V-12 MATHEMATICS STAFF, including both regulars and associate teachers from other departments, pose on the Dartmouth Hall steps. Front row, left to right, Profs. Philip E. Wheelwright (Philosophy), Bancroft H. Brown (V-12 director), Robin Robinson '24, Edwin M. Bailor (Psychology). Second row—Robert E. Riegel (History), Fred W. Perkins, Robert H. Denison (Zoology), Warren E. Montsie 'l5 (French), Charles J. Lyon (Botany), Louis L. Silverman, Robert K. Carr '29 (Political Science) . Back row—W. Cutting Johnson '33 (Clark School), Chester H. Forsyth, Charles E. Wilder, John R. Williams '2O (History), Merle C. Cowden (German), and Louis C. Mathewson. The entire staff was not present.
DIRECTOR OF V-12 MATHEMATICS
This is the second of a series oF brief articles describing the content and workings of the large basic courses in the Navy V-ia Program. A similar description of history is scheduled for an early issue.
