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Teaching and Examining


Lecturer Guidelines

The Faculty publishes a Guide for Lecturers for those lecturing in the Faculty of Mathematics. It is intended to help lecturers, particularly those new to Cambridge, to give good lectures. The Guide complements the material below that outlines of the responsibilities of those giving lectures in the Faculty.

Lecturing: Responsibilities

For each course, it is the lecturer's responsibility:

  • to lecture the material in the course and recommend reading;

  • to provide examples sheets for use in supervisions;

  • to assist examiners in producing a fair examination;

  • to assist in monitoring the course.

The Lecture Course

Lecturers provide students with an account of all the material in the schedules at an appropriate level. They also recommend suitable books.

The students' notes and any handouts given out by the lecturer should provide students with a firm basis for their work on the examples sheets and for the examination.

Lecturers may change the order of topics in the schedules provided there are no repercussions for other courses. If they do so supervisors should be informed in good time.

When giving a course for the first time, lecturers often find it useful to study the lecture notes of a previous lecturer; it is perfectly acceptable to use these as a basis for their own notes. After giving a course for the last time, lecturers should be prepared to lend their lecture notes, handouts and examples sheets to their successor. Particular efforts are naturally needed in the case of a new course.

Examples Sheets

Examples sheets provide essential support for teaching in supervisions. They test and augment the understanding provided by the lecturer. Students' answers to questions commonly form the basis for a supervision. The normal conventions, recommended by the Faculty Board, for examples sheets are as follows:

  • The number of example sheets per course should be 4 for a 24 lecture course, 3 for a 16 lecture course and 2 for a 12 lecture course. Each sheet is handed out in sufficient time for students to work on it before the relevant supervision. In particular students should be able to tackle all of the first sheet after six lectures of the course.

  • Examples sheets are structured so that they are suitable for all students. In particular there should be some elementary questions on each sheet so that less confident students can reassure themselves that they have learnt something.

  • The content and length of each examples sheet should be suitable for discussion (with a typical pair of students) in an hour-long supervision. There is no prescribed number of questions, but most examples sheets have around 10–12 questions when the questions are of typical length and difficulty. Having too many questions needlessly adds to the overall student workload.

  • Lecturers solicit comments from supervisors and students on questions on their examples sheets by means of an (eg e-mail) address on each sheet. Lecturers respond in all cases of difficulty. All students and supervisors should be made aware of any errors found on the sheets.

  • A number of supervisors, for example those who are supervising a course for the first time, welcome advice on the essential points that a particular question is designed to test. Rather than field several queries on the same questions, lecturers often find it sensible to write out or sketch solutions. These can be lodged in the Departmental Librarians' offices. (As with examination questions, it is often a great benefit to write out a solutions, or see a written solution, to a problem to check that it is of appropriate length and level.)

  • Lecturers must be vigilant in checking that any change made to their courses is reflected in the examples sheets. New courses call for particular care in the setting of examples sheets. There may not be a sufficient body of past Tripos questions to serve as a guide in preparation for the examinations. It may be appropriate for the lecturer to provide a collection of suitable Tripos questions for revision purposes.

The Examinations

Lecturers have the duty to check that the proposed examination questions are: correct; of an appropriate length and difficulty; cover the material in the course adequately; and use the same notation and conventions as the lecturer.


Lecturers should co-operate with colleagues and the Teaching Committee in monitoring the effectiveness of the teaching provided by the Faculty, for example by peer review of lecturing. In addition, they should encourage feedback from the students. Every lecturer should give out questionnaires, for return to the Faculty Office, (usually) in the penultimate lecture, and should allow the students 5 minutes during the lecture to complete them.