General information

Admissions: Part III admissions decisions for continuing Part II students are made by the Faculty Board by a process outlined at the bottom of this page. The effect of this process is as follows. Permission is automatic if you obtain a First in Part II Mathematics. If you do not obtain a First in Part II Mathematics you may ask your College to apply on your behalf for permission to continue. The committee set up to make decisions will consider your past examination performance, the recommendation from your College, your own letter and any other relevant material to decide if you 'are more likely than not to get at least a Merit in Part III of the Mathematical Tripos'.
Note that your degree aim will be BA+MMath. Specifically, you must NOT graduate at the end of Part II. If a student graduates with a BA after three years study, they cease to be eligible for the MMath. Applications to the Student Loans Company should be for 'Maths 4 Years' with UCAS code G100, Campus B, qualification MMath.

Dates: Part III begins on the first week of Michaelmas Full Term, with registration and an induction meeting.

Terms: Part III is timetabled within undergraduate terms but vacations are important for consolidating understanding of lecture material and for writing essay (see later). Many students stay in Cambridge for part of the vacations to use library facilities.

Location: All Part III activities take place at CMS, where there is a large room for the exclusive use of Part III students (with books, computers, coffeemaking facilities etc). The Betty and Gordon Moore science library is onsite.

Help and advice: You will have more direct contact with the Departments in Part III than in Part II, and you will be allocated a subject contact in the Departments with whom you will be required to meet from time to time. But your College Director of Studies and College Tutor will play broadly the same role as when you were undergraduates. In Part III there are relatively few undergraduatestyle supervisions. It is therefore essential that if you experience difficulties and drop behind you consult one of your academic advisors promptly.

The course: The course structure is as follows. Lecture courses are either 16 lectures (2 units) or 24 lectures (3 units). Each course has an examination paper, taken in June. You are allowed to submit up to 19 units of examination credit. 3 units of this may be an extended essay written some time between the end of Michaelmas Term and the deadline for submission, which is early in Easter Term. (If you submit an essay then you are limited to 16 units of written examination.) The essay is not compulsory, but the great majority of Part III students choose to write essays; the work is generally an enjoyable change and a valuable training for research. Most students take more lecture courses than are required for the examination and then decide later which they will choose for the examination. (This choice is made early in Easter Term.)

Choosing courses: A list of the courses expected to be available in the next academic year will be distributed. Further changes to this list will be avoided if possible, but may be essential. Course descriptions are available on the web. These are the descriptions of the current year's courses, which will be updated by midJuly. In October each Part III student will receive a booklet containing finalised course descriptions.
There is no requirement that students must restrict their choice of courses to those given by one Department. Most students take courses from one or two subject areas, but some take a wide variety. Courses may be selected freely from those available, within the constraints of the lecture timetable (which is arranged carefully to avoid clashes between related courses). The examination timetable corresponds to the lecture timetable, i.e. courses that are lectured at the same time are examined at the same time. It is not therefore possible for students to sit examination papers in two courses that were lectured at the same time.

Conclusion: Part III is hard work. It is extremely important to keep up with the lectures, and this requires a lot of time outside of the lectures themselves. But you will learn a lot of interesting mathematics!
Statement by the Faculty Board
approved on 6th May 2021
Under University Regulations, Cambridge students who wish to take Part III of the Mathematical Tripos must have the permission of the Faculty Board of Mathematics. The Faculty Board has appointed a Permissions Committee to make decisions on its behalf, and has issued guidelines to that Committee.
The Faculty aims to allow those students to progress who are more likely than not to get at least a Merit in Part III of the Mathematical Tripos. This is the criterion for permission to progress from Part II to Part III.
The Faculty has decided that those obtaining a First in Part II of the Mathematical Tripos should automatically be allowed to progress to Part III. Students who are not granted permission automatically (including candidates from other Triposes even if they have a first) and who wish to proceed to Part III, should ask their College to apply to the Faculty's Permissions Committee on their behalf. Each application should consist of
 a letter from the student,
 a letter from the College written by a mathematician who knows the student,
 the student's full set of Part II supervision reports.
Students who wish mitigating circumstances of a medical nature (including mental health) to be considered by the Permissions Committee should in addition ask their College to apply for an "Allowance to Progress" to the Exam Access and Mitigation Committee (EAMC). The EAMC cannot put a student in standing for Part III, but will offer the Faculty's Permissions Committee an opinion on whether there are mitigating circumstances that warrant special consideration.
Notes on the application procedure (and appeals procedure), including advice on the form of the student letter and the College letter, are given below.
The Faculty Board has instructed the Permissions Committee that decisions are to be made on a casebycase basis and that, though the Committee may consider past experience, it is not to be bound by precedent. The Faculty Board has recommended that
 students in the top 40% in Part II of the Mathematical Tripos whose applications are supported by the college should normally be allowed to progress to Part III;
 students obtaining a first in NST physics and whose applications are supported by the College should normally be allowed to progress to Part III.
Applications should reach the Secretary of the Faculty Board of Mathematics by noon on Thursday 8th July 2021. The Permissions committee start their considerations soon after this deadline, so any delay is extremely inconvenient. If this deadline is missed (e.g. because of a late change of mind), and a good case can be made, applications can exceptionally be considered after this date. Applicants awaiting a decision by the EAMC will only be dealt with by the Permissions Committee once the EAMC decision is known. At the discretion of the Chair, decisions on all such applications may be taken by two or more members of the Permissions Committee, not both of the same College as the applicant, acting in consultation.
Students and Colleges are reminded that, if a student graduates with a BA after three years study, they cease to be eligible for the MMath. A student who is unsuccessful in their application for permission to take Part III can graduate at a later congregation or in absentia.
Notes on Progression from Part II to Part III of the Mathematical Tripos
Deadlines. The College is responsible for ensuring that applications reach the Secretary of the Faculty Board of Mathematics by noon on 8th July 2021. Note that if this deadline missed, and a good case can be made, late applications will, exceptionally, be considered.
Destination. The application should be addressed to:
The Permissions Committee
Secretary of the Faculty Board of Mathematics
c/o Undergraduate Office
Centre for Mathematical Sciences
Wilberforce Road
Cambridge CB3 0WA
and emailed to undergradoffice@maths.cam.ac.uk with the subject line "Permissions 2021:", followed by the CRSid of the student on whose behalf the application is submitted. Please retain a copy for your records.
Format. All documents should be submitted in Portable Document Format (PDF). Typed letters are much preferred to handwritten notes.
Student Letter. Students are more likely to be admitted if their letter makes it clear how doing Part III will fit into their future plans, what type of courses they wish to do and why they think they will do well in them. It is important that students discuss their plans with someone in the College.
College Letter. The Faculty aims to allow those students to progress who are more likely than not to get at least a merit in Part III of the Mathematical Tripos. This is the criterion for permission to progress from Part II to Part III.
The College letter should be an academic assessment written by the Director of Studies, or another mathematician who knows the student. Remembering that Part III is a very demanding course, intended to stretch the most able students, this academic judgement should be reasoned and supported by firm evidence, e.g. by reference to
 past performance,
 supervision reports,
 comments sought for the purpose of the letter from supervisors in the student's chosen field of study.
The primary aim of the College letter is to provide evidence to help the Permissions Committee's deliberations. It should also contain a recommendation, indicating whether the College supports the application and if so, how strongly. The letter should address the question as to whether the applicant's Tripos record does provide a representative picture of the student's mathematical abilities.
The primary evidence is the detailed Tripos record of the student. Additional evidence should be provided if it is thought that the Tripos record does not provide a representative picture of the student's mathematical abilities and there are reasons to believe that the student will be more, or less, suited to Part III. For example, the first three years of the Tripos do not necessarily allow students with specific abilities in a particular area to show their potential in the same way as they might in Part III. Conversely, performance in earlier parts of the Tripos may be highlighted for those candidates whose performance in Part II fell below expectations. In all cases, a full set of Part II supervision reports is expected to be included with the application.
In case of illness or disability the Senior Tutor should additionally make an application for an "Allowance to Progress" to the Exam Access and Mitigation Committee (EAMC). This application can only be made after exam results have been published, and should be accompanied by a letter from a medical practitioner. Medical evidence should not be sent to the Faculty. The EAMC cannot put a student in standing for Part III, but will offer the Faculty's Permissions Committee an opinion on whether there are mitigating circumstances that warrant special consideration.
Applicants awaiting a decision by the EAMC will only be dealt with by the Permissions Committee once the EAMC's decision is known. A full list of the EAMC's meeting dates is available at https://www.studentregistry.admin.cam.ac.uk/aboutus/EAMC. Applications are due by the Thursday preceding the week of the meeting, though Colleges may impose earlier internal deadlines. Applicants are encouraged to meet the relevant deadlines for the EAMC meeting on 9 July 2021 if possible so that applications may be processed by the Permissions Committee as soon as possible thereafter
Candidates from other Triposes. Applications from candidates from other Triposes, e.g. NST, must demonstrate ability in an area of mathematics comparable with candidates from the Mathematical Tripos. The application should highlight the mathematical experience of the applicant and the match with the type of Part III courses they wish to do. The application should include rankings in each of the three years of the Tripos, with details about performance in individual subjects. For NST Physics applicants, it should normally include evidence from Part II supervision reports in mathematical subjects and the results of TP1 and TP2.
Examination Appeals. If a student appeals against the result of their Part II examination the application for progression to Part III will not be decided until the result of that appeal is known.
Who tells Whom. The Chair of the Permissions Committee will communicate the decision to the Senior Tutor of the College who should pass it on to the student and the Director of Studies.
Appeals. If a candidate wishes to appeal against the decision of the Permissions Committee the "Procedure for the Review of Decisions of University Bodies", listed in Chapter II, Section 26 of the Statutes and Ordinances. It will help us speed up the process if you simultaneously send a copy of the appeal to the Undergraduate Office (email: undergradoffice@maths.cam.ac.uk).