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Undergraduate Mathematics



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 may, with the agreement of the Faculty, continue to Part III of the Mathematical Tripos in their fourth year, after which they are eligible for both BA Honours and MMath 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 that they are more likely than not to achieve a first-class equivalent mark in the fourth year. For details of the fourth year, see Master of Mathematics / Master of Advanced Study in Mathematics.

About 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.


The following documents are available on-line:

Guide to Courses in Part IA
Informal descriptions of first year courses.
Guide to Courses in Part IB
Informal descriptions of second year courses.
Guide to Courses in Part II
Informal descriptions of third year courses.
Schedules and Form of Examinations for the Mathematical Tripos
Formal descriptions and syllabuses for all the courses available in the first three years of the Tripos.
Transferable Skills
You may think that the only skills that you acquire on a mathematics course are mathematical, but that is far from being the case. Generic skills, such as problem solving, are valued by a wide-range of employers.
Guide to the Mathematical Tripos
Information about the course, intended primarily for prospective applicants.
Mathematics with Physics
Information about the first year option with 25% physics, intended primarily for prospective applicants.


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.


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.


Examination papers
The examinations in the first three years consist of four three-hour papers taken at the end of May and the beginning of June. In the first year, two topics are examined on each paper, while in the second and third years each paper is cross-sectional, meaning that instead of each lecture course having a dedicated examination paper, each examination paper has questions on multiple lecture courses. The flexibility that this allows is regarded as one of the strengths of the Tripos: you choose how many courses you wish to revise for the examination and therefore can work at your own pace. Some students revise a wide range of courses and others prefer to revise a small number very thoroughly. The examinations in the fourth year are modular, but you have some flexibility in the number of exams taken. Past Tripos examination papers are available online:

Students are classed (first class, upper-second class, lower-second class, third class) in each part of the Tripos. In addition, from 2023 onwards, students graduating with a BA at Cambridge will be awarded an overall class for their degree. In the Mathematical Tripos, the overall class for the BA degree will be the class awarded in Part II.

Historical curiosities
  • For Part II, the traditional name of Wrangler is still 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 publishing the ranking of all candidates, the top candidate being the Senior Wrangler, who enjoyed celebrity status, was abandoned in 1909.
  • For a period until 1909 it was traditional to present a wooden spoon to the student at the bottom of the examination class list of the Mathematical Tripos (a spoon from 1906 is illustrated below). 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 candidate who received the wooden spoon scored a princely 247. Fortunately, the examination format is rather different these days.
A wooden spoon

Additional Resources

The pages of the University mathematics society, The Archimedeans, and those of the Student Representatives, provide useful sources of information of all kinds, including official and unofficial lecture notes.