Tutorial Work in Mathematics at the University of Buffalo

Abstract

Since 1931 the senior division of the College of Arts and Sciences at the University of Buffalo has been under the so-called Tutorial System whereby each student, having been accepted by a department as a majoring student, is given opportunity to pursue independent work in that particular subject. The object of this paper is to describe the tutorial system as it functions in the fepartment of Mathematics in the hope that someof its features may prove useful to departments of mathematics in other colleges even though they do not have the complete system. Our philosophy with regard to majors in mathematics is consistent with the general philosophy of the tutorial system that each student should be given the opportunity for individual study and research. Although this can be done in some departments without a great deal of background we have felt that students in mathematics at the beginning of their junior year do not have an adequate background to begin individual projects. The average student at this time lacks a certain matuirity in mathematics necessary for such projects. Our program of tutorial work in the junior year is devised to provide background material and develop a degree of mathematical maturity. The students are divided into small groups of three or four each. These groups meet once a week throughout the year with an instructor to study and discuss the history and foulndations of mathematics and also the various branches of mathematics No text book is used and we try to avoid definite assignments. General topics are suggested by the tutor for discussion. The students then use the library to gather material to bring back the following week. Certain references are recommended but the students are urged to use additional books and periodicals for supplementary material. Topics chosen outside the history of mathematics include mathematical logic, the number system, types of geometries, fundamental concepts of the calculus. Much of the success of these discussion groups depends on the tutor. He must encourage the students to use the library intelligently. He must also encourage them to do some independent thinking. He must remain in the background during the discussion periods, but still guide the discussion so that it is fruitful and distributed throughout tie group. It is an assignment which can be done in a mediocre way more easily than it can be done well if the tutor is not convinced