# Undergraduate Mathematics: Course Information

## Overview

The undergraduate mathematics course, the Mathematical Tripos, lasts three or four years.

Students take Parts IA, IB and II of the Mathematical Tripos in consecutive years. They are then eligible to graduate with the BA Honours degree. They may, with the agreement of their college, continue to Part III of the Mathematical Tripos, after which they are eligible for the BA and M.Maths degrees. In order to stay on for the fourth year, students have to have achieved a first class in the third year or have demonstrated strong evidence of first class potential. For details of the fourth year, see Master of Mathematics / Master of Advanced Study in Mathematics,

Three years after becoming eligible for the BA degree, and with no further study, students are eligible for the MA degree.

In the first year (only), there are two options: Pure and Applied Mathematics; and Mathematics with Physics. In the second year and, especially, the third year there is a wide choice of lecture courses, but no opportunity to substitute courses from other Faculties. There is no coursework or continuous assessment, except for the Computational Projects courses (see below).

You can read more about the course in the documentation section below and in the sections on lectures, examinations, and supervisions.

## Documentation

The following documents are available on-line:

- Guide to the Mathematical Tripos
- Detailed information about the course.
- Mathematics with Physics
- Information about the first year option with 25% physics.
- Courses in Part IA of the Mathematical Tripos
- Informal descriptions of first year courses.
- Courses in Part IB of the Mathematical Tripos
- Informal descriptions of second year courses.
- Courses in Part II of the Mathematical Tripos
- Informal descriptions of third year courses.
- Schedules for the Mathematical Tripos
- Formal descriptions and syllabuses for all the courses available in the Tripos.

## Lectures

For each course, the Faculty Board agrees a syllabus and a number of lectures. The purpose of lectures is to cover all the material in the syllabus in a concise and consistent way. Unlike many universities courses (in the U.S. particularly), there is generally no `book of the course' that covers the right material at the right level.

Lectures are provided by the Faculty (not the colleges) and take place in central lecture theatres for Parts IA and IB, and in the CMS for Part II (the third year). Each lecture lasts about 50 minutes. All lectures take place in week day and Saturday (but not Sunday) mornings.

In the first year, there are two lectures a day (i.e. 12 a week), for 20 weeks, and students should attend all lectures. In the second and third years, the lecturing load is roughly the same, but because there is a choice of lectures the timetables of individual students may differ.

There is no standard way of lecturing: some lecturers write exclusively on blackboards; some use overhead projectors or powerpoint displays; some give out printed notes. The method used by individual lecturers depends on their style and also on the sort of material that they are covering.

## Supervisions

Supervision is the name given to small-group teaching sessions (tutorials elsewhere). Normally for mathematics there are two students and one supervisor. The supervisor may be a professor, lecturer, researcher, graduate student or any other suitably qualifier mathematician.

Supervisions are arranged by colleges for their own students, and many will take place in the rooms of fellows of the college (who are often lecturers as well). One solution is given for, roughly, every 6 lectures, so students have on average two supervisions a week.

The purpose of the supervision is to ensure that students have understood the material in the lectures. Normally, the students work through an example sheet given out by the lecturer during the week preceding the solution and hand in their work the day before the supervision. The supervisor marks the work, which then forms the basis for much of the discussion in the supervision.

## Computational Projects (CATAM)

The CATAM Computational Projects courses provide an education in solving mathematical problems using a computing environment. The emphasis is on developing mathematical skills rather than programming abilities.

There is a Computational Projects course in each of Part IB and part II. They count, for examination purposes, roughly the same as a 16-lecture course and are assessed by means of notebooks and programmes submitted before the examinations in the summer. The courses are not compulsory, but nearly all students take them since it is the only way of obtaining marks outside of the examination room.

## Examinations

Each year's work is examined by means of four three-hour papers taken at the end of May. For part IB and II, each paper of the four papers is cross-sectional, meaning that there are questions relating to each course on each of the papers. Students can decide for themselves the number of courses they wish to revise for examinations; some students revise a wide range of courses and others prefer to revise a small number very thoroughly.

Students are classed (first class, upper second class, lower second class, third class) in each part of the Tripos, but no attempt is made to give an overall class. For Part II, the traditional name of Wrangler is given to anyone in the first class. This derives from the ancient form of the examination, which was not written but took the form of a dispute or 'wrangle'. The practice of ranking all the candidates, the top candidate being the Senior Wrangler, was abandoned in 1909.

Past Tripos examination papers are available on line.

At the end of the 19th century and the start of the 20th century a **wooden spoon** was presented to the student at the bottom of the examination class list of the Mathematical Tripos. Examinations were tough in those days. In one year, there were 36 hours of examinations. The Senior Wrangler scored 16,368 out of a possible 33,541, and the man who got the wooden spoon scored a princely 247. Fortunately, the heroic era of the Tripos is long gone.

## The Archimedeans

The University mathematics society The Archimedeans and the Student Rep pages provide an invaluable source of information of all kinds, including official and unofficial lecture notes.