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Introduction

Supervision is the word used in Cambridge¹ to describe small-scale teaching. In mathematics, the typical supervision consists of a supervisor -- normally a college or university lecturer, a research worker in one of the university departments (not always the mathematics departments), or a research student -- going over mathematical problems with a pair of students. Sometimes, if there is a shortage of supervisors, there may be more students in the group, and sometimes there may be just one student but colleges (who have to foot the bill) do not like this because it is expensive.

Supervisions are arranged by colleges, acting individually or in groups, and the responsibility for providing supervisions lies with the Director of Studies in mathematics in each college. The general aims of a supervision are to explain and amplify the material given in the lectures and to prepare students for the Tripos Examinations.

Most colleges expect their students to receive four supervisions for a lecture course of 24 lectures and three supervisions for a 16-lecture course, plus (probably) a revision supervision near the examinations. There are also a few 12-lecture courses (two supervisions) and one 8-lecture course (one supervision).

There is no one correct way of supervising and there is no one set of arrangements which is common to all colleges and to all lecture courses. You should bear this in mind when reading the information and advice given below.