These are some of the questions we are often asked. You should also consult the FAQ provided by the Cambridge Admissions Office for general admissions questions, not necessarily specifically related to Mathematics. Click on each question below to see the answer.

## Admissions

## How do I apply?

The process of applying to study at Cambridge is the same for all subjects, and comprehensive information is available from the Cambridge Admissions Office. You should consult their information on applying to Cambridge, and their Q&A page about the application process.

## How important is the personal statement?

Your personal statement is just one of many other components that we use to build a picture of your aptitude and potential for Mathematics and the Cambridge undergraduate course. We look for evidence of the qualities you need in all the sources of information we have, and we use them together, taking individual context into account. If you have had the opportunity for activities that show your interest in, and commitment to, mathematics, it is good to mention these in your personal statement: for example maths books or YouTube lectures that you've read or watched and enjoyed, or if you've helped younger students in your school in mathematics. However, you should not worry if you don't have any extra activities to mention: we are aware that many candidates may not have the opportunity or financial resources for buying books or for other enrichment activities.

Usually, you would use your personal statement to mention any extra-curricular activities you have done. However, as far as we're concerned, you don't need to worry about any activities which are not related to mathematics. Because we have many other maths specific ways to asses your potential (such as the interview and STEP), your personal statement is a much smaller component of our assessment than it is for other Universities. However, you shouldn't forget that what you write in your statement may be very important for your other University choices.

## What is My Cambridge Application (previously the SAQ)?

Once you’ve submitted your UCAS application, you will be contacted by email and asked to complete an additional questionnaire called 'My Cambridge Application (previously the Supplementary Application Questionnaire, or SAQ). You should use it for supplying additional information that isn't on the UCAS form, but can be useful to us when we assess your application. You should use the My Cambridge Application form to tell us, especially:

- What maths topics you have covered in the maths (and the physics) syllabus of the qualifications you are taking - this will help interviewers ask appropriate questions;
- Any other maths-specific information not in the UCAS form, e.g. whether you have access to any help/formal teaching in preparing for STEP.

There is a guide to completing your My Cambridge Application form on the Cambridge Admissions website – though you will also be guided through it as you fill it out.

## What is Adjustment? Does Cambridge participate in UCAS Adjustment?

UCAS Adjustment allows students who have met all the conditions of their conditional-firm offer, and exceeded at least one, the opportunity to be considered by other universities without jeopardising their place.

Cambridge does participate in UCAS Adjustment. If you have been interviewed in Cambridge, but weren't made an offer, then you sit STEP 2 and 3 anyway, and get grades 1 and 1, you may be eligible for a place through Adjustment. You can find out more about the process and eligibility on the Cambridge Admissions Adjustment page

## We sometimes hear that work experience will make the application stronger. Is this true?

Work experience may be useful for your own personal development - but none is required for the mathematics course.

## Will the fact that I'm reapplying this year affect my application?

Repeat applications are unlikely to be successful unless there is some substantial new evidence, such as the STEP offer having been met, or exceptional circumstances that were not apparent at the time of the previous decision.

## I am taking a gap year. Will that be a disadvantage?

Most Colleges have a preference for immediate entry. This is because in mathematics there is a particular danger of going ‘off the boil’, and this has to be balanced against the extra maturity gained from a gap year. Some Colleges are more encouraging than others about taking a gap year, and you can check all Colleges' declared attitude to a gap year in the table on p. 14 of the Guide to Admissions. You should also check directly with the College where you wish to apply. If you do take a gap year, then you should plan to keep up your mathematics in some way if possible, and you should certainly get back into good practice (for example, by working through past STEP papers) before you start the course.

## Is there any help available to international students to work through the application process?

There is clear and comprehensive information for international students about how to apply provided by the Cambridge Admissions Office. Colleges' admissions offices can also be helpful.

## I've already started a degree at another University. Can I apply to study Mathematics at Cambridge?

The University of Cambridge will not allow credit transfer for undergraduate study elsewhere in the UK or abroad (except through the established arrangements for Affiliated Students who have completed a full undergraduate degree). In exceptional circumstances, applicants who are at another university and who want to begin the first year Mathematics in Cambridge may be considered, but these applications would need to be accompanied by a strong letter of recommendation from the current course leader or other academic tutor, outlining their support of the application. Colleges do not normally accept students for the three-year undergraduate course if they have already taken up a place to study at another UK university. In particular, students who are already studying Mathematics elsewhere are unlikely to be considered.

## What would be your advice for someone thinking of doing a Maths degree?

Do as much maths as possible! And this could be using books (school books or perhaps one or two from the Faculty Reading List), using online videos (the Mathologer, Numberphile, and 3Blue1Brown are great ones), solving maths puzzles from any source (e.g. the many books by Martin Gardner, or the online 'Cut-the-knot' site), and also doing maths competitions if you have the opportunity.

## Qualifications

## Why do you give conditional offers based on STEP?

We have around 250 places available each year. Given the very large number of students who achieve top grades in A-levels (in 2020 about 6,200 achieved A* in Further Mathematics), it becomes very difficult to distinguish between high performing candidates, so we need some other measure.

Why STEP?

- STEP is a far better predictor of success in the Mathematical Tripos than A-levels. One reason for this is that the questions are less standard and less structured, which helps to distinguish between ability (or potential) and good teaching.
- Preparing for STEP is very good preparation for University mathematics, and will help you in the transition from school to University.
- The STEP marks and the scripts themselves are available for College staff to look at. This means that it is possible to make allowances for a near miss and to make judgements on the actual work rather than on just the marks or grades.
- STEP is the same examination for all applicants (whatever qualifications they may have studied for), so it is a fairer way of assessing applicants, and it ensures that everyone who starts our course in October has the necessary technical skills to undertake our course.
- Using STEP allows us to make offers to many more candidates who show mathematical potential at interview, but do not have quite enough mathematical knowledge and skills because of educational disadvantage. We can then provide sustained support to motivate the students and help them prepare for the exams and for mathematics at university level. So STEP is a powerful tool for increasing opportunities whatever your educational background.

Free help to prepare for STEP (at any time, before and after interviews or even in Year 12/the year before you apply) is available from maths.org/step. Another very useful resource that many of our students have used is the (free to download) book by Stephen Siklos Advanced Problems in Mathematics.

## My school does not offer any help in preparing for STEP. Will I be disadvantaged?

No. You should mention in your application that you don't have any help from your school (there is a specific question about this), and you should use the free help available online. In particular, use the (free) STEP Support Programme and the (free to download) book by Stephen Siklos Advanced Problems in Mathematics as early as possible. If you are invited for interview and you are made an offer, and your school does not offer help preparing for STEP, the Faculty and Colleges provide free additional support with preparing for STEP. Priority is given to students from UK maintained schools, and you will be contacted after you have received an offer.

## I’m thinking of taking STEP in year 12, will my results be accepted?

Many Colleges will consider applications from students who have already taken STEP, but there is no guarantee that they won’t ask you to sit a STEP paper again, and they may even ask for a higher grade as part of their offer. Since admissions decisions are made by Colleges rather than the Faculty, you should contact the College to which you wish to apply. The Cambridge Admissions Office pages have a full list of Colleges. In practice, unless your mathematical preparation and understanding is already very advanced, it may be better for you to concentrate on preparing for your A levels (or equivalent), alongside starting to practice for STEP without rushing, aiming to deepen your understanding and familiarity with STEP questions.

## Will I be able to sit STEP in my school? What if I live abroad?

You can normally take STEP exams at your school – check with your Exams Officer. If your school is not already registered as a STEP test centre, they can apply to become a test centre – even if you are the only person taking a test - and schools do not pay any fees for becoming a test centre. This is usually possible also if you live abroad. OCR has a useful STEP FAQ with full answers to this and many other questions about STEP.

## What should I do if one of my school exams clashes with a STEP exam?

If STEP clashes with one of your other exams, then you should contact the exam officer at your school. It might be possible to change the start time or date.

## What is the 'flexible offer'?

Depending on individual circumstances, some Colleges^{1} may make an A level applicant an offer that will be met if they achieve EITHER A*A*A with at least a grade 1 in STEP 2 and 3, OR A*A*A* with at least a grade 1 in just one of the two STEP papers taken. This is a ‘Widening Participation’ offer and is used especially for applicants from groups that have had to overcome significant educational disruption and/or socio-economic disadvantage, and who do not have access from their school to specific support to prepare for STEP. Whether they use the 'flexible offer' or not, all Colleges encourage applications from well-qualified students from groups that are currently under-represented and/or disadvantaged, and are prepared to be flexible. You can find more information about how the University uses contextual data here.

1. Downing, Emmanuel, Fitzwilliam, Girton, Jesus, King's, Lucy Cavendish, Newnham, Robinson, Sidney Sussex, St. John's, Trinity Hall.

## Is Further Mathematics A-level essential? What if my school doesn't offer Further Mathematics A-level?

In order to keep up with the pace of the first year course, it is essential that A-level students are fluent with the content of the Further Mathematics A-level syllabus before arriving at Cambridge. If this is not offered at your school then there is help available from the AMSP (Advanced Mathematics Support Programme). You can get free help for studying independently to prepare for A-level Further Maths at https://amsp.org.uk/students/a-level-further/resources, and see also https://amsp.org.uk/students/a-level/resources for A-level Maths. Your school can also get help from the AMSP to provide Further Mathematics to their students: they should contact the AMSP Area Coordinator, and if your school is in one of the AMSP Priority Areas there is additional support available. You should also contact the College that you wish to apply to for further help and guidance.

## My school offers the full Mathematics A-level in Year 12, then Further Mathematics in Year 13. Will my A* in Maths A level in Year 12 count towards my offer? Will I need to take a fourth A level in Year 13?

A* in Mathematics in Y12 will be normally counted as part of the offer. Many Colleges will accept A* in Maths in Y12 followed by A*A in two more subjects, one of which must be Further Mathematics, in Y13. If you are not taking three A levels in Year 13, you will need to show evidence of being able to cope with the equivalent amount of workload, but this could mean taking two STEP papers alongside two A levels in Y13.

## Is Physics at A-level (or the equivalent) essential?

No. Even though there is a significant component of theoretical physics (applied mathematics) in our course, Physics A-level is not needed. None of our theoretical physics lectures assumes knowledge of physics and the material is treated from a very mathematical point of view (so there is no need to worry if you did not like school physics). In any case, we offer a non-examinable mechanics course aimed at first-year students who have not had the opportunity to study much mechanics.

## Does the third A-level subject have to be a science?

Taking a third A-Level which is not a science should not affect your application as long as you have the maths-related requirements. You should check with the College you wish to apply to, though: some Colleges do prefer the third A-level to be a science, for others it can be any other solid academic subject (e.g. French, or Latin, or History, or Economics, ...). Subjects like General Studies or Critical Thinking, though, will never be part of a conditional offer for Mathematics.

## I am taking the IB, which has no mechanics in the mathematics course. Is this a big disadvantage?

No. But it is useful to take HL physics; the IB physics course is much more mathematical than its A-level counterpart, and it provides a good preparation for our course.

## I am taking the IB, and my school only offers the Mathematics Higher Level 'Applications and Interpretations'. What should I do?

We ask students taking the IB to choose the Mathematics HL 'Analysis and Approaches' course, because the content of HL 'Applications and Interpretation' does not provide sufficient preparation for our course. If your school does not offer you this choice, then you will need evidence of some additional mathematical preparation (e.g. A-level Further Mathematics, or some other qualification). You should contact the College that you wish to apply to directly for further advice and guidance.

## I am an international student and the pre-University qualifications in my country are very different from A-levels. Will I need to take A-levels?

Every year we accept many students who have taken a wide variety of qualifications from all over the world (e.g. the German Abitur, the International IB, AP tests, and many others). You can check typical minimum entry requirements for a full list of international qualifications, and you should also ask the College where you wish to apply.

## Should I take four A-levels?

Applicants are normally expected to have three A-levels only, and Colleges are very well aware that students may not have any choice in the number of A-levels they can take. Many of our applicants do take four A-levels, but you will not be disadvantaged if you have three A-levels. As a rule of thumb, if most students in your school take four A-levels, then you would probably be expected to take four A-levels, unless you have a compelling explanation of the reason that you are taking three. If most students at your school take three A-levels, then you would not be expected to take four A levels.

## If I take four A-levels, will my offer be based on all four A-levels?

Offers are normally based on three A-levels only (the College will tell you which), and STEP papers. If you have already completed A-level Mathematics in Year 12, though, and are taking three A-levels in Year 13, a College may make an offer based on your three A-levels in Year 13.

## I am taking a gap year. Would this mean that my entry requirements will be higher?

No. Your entry requirements will be the same as if you had planned to start the course immediately. You will normally be asked to take all your exams, including STEP, before your gap year.

**The Interview and Assessment**

## What will the interview be like?

In a mathematics interview you will be asked to solve some mathematical problems. That's all: maths, followed by some more maths. All we are interested in is your ability to tackle mathematical problems. There are no trick questions. The main purpose of the interview is to see how you think about a mathematical problem. An interview will typically last for about 20 to 40 minutes (you will be told in advance).

## What should I wear at interview?

Interviews are conducted in an informal atmosphere. You should just wear what you're comfortable in. We're only interested in your mathematical potential!

## If I apply for the Mathematics course at Cambridge, how likely am I to be invited to interview ?

All Colleges like to interview all realistic applicants. In the past few years, well over 80% of applicants have been invited to interview every year.

## What do you look for in a candidate?

You can find your answer to this in the statement agreed by all Colleges on 'What qualities we look for'.

## What constitutes mathematical potential?

There are many qualities that are indicative of mathematical potential, for example: the ability to make connections between different mathematical ideas, the ability to think logically, the flexibility to understand new concepts quickly and use them to solve challenging problems, the mathematical curiosity to see standard problems from different angles and to explore possible generalisations, or different applications. In an interview, if you are able to solve a problem straight away, this tells us that you're good at solving that particular problem (and perhaps that you have seen it before). On the other hand, if you get stuck, then we will give you hints and we'll have the opportunity to see if you can use them, think logically, apply concepts that you haven't seen before. That's why we will always ask some questions where you will get stuck somewhere, which really helps us judge your mathematical potential (and don't worry: we won't let you be stuck and waste your time, but we will guide you and give you hints!).

## Will the interview questions be all on pure maths?

In a typical interview there will be mostly questions about topics like numbers, sequences, integrals, graph sketching, etc, but also sometimes probability, and some basic mechanics. If you are applying for Maths with Physics you will always be asked at least one mechanics question.

## Are there any useful resources available that you would recommend to prepare for interview?

There is some useful advice on p. 13 of the Guide to Admissions. In general, preparing for STEP is also good preparation for interview, as is trying to solve fun maths puzzles (see, e.g. the online 'Cut-the-knot' site).

## Can the interview be online or does it have to be face-to-face?

In 2023, six Colleges are holding interviews in-person for UK-based students: Gonville & Caius, King's, Pembroke, Peterhouse, Selwyn, and Trinity. Applicants for all other Colleges and applicants based overseas will have their interviews online.

## Will there be any pre-interview tests?

No, not for Mathematics (unlike other subjects), but some Colleges have written assessments at interview.

## How can I prepare for written assessments at interview?

As for interviews, preparing for STEP is also good preparation for written assessments at interview. There are also some sample questions available from Downing College and from Trinity College (Specimen written test 1, Specimen written test 2, Specimen written test 3).

**The Course**

## Is it possible to take some Economics/French/Philosophy courses (for example) as part of my degree?

No, sorry, not as part of your degree. This is a course for those wanting to take only mathematics. The exception is the Mathematics with Physics course in the first year only. The very wide choice of courses on offer from the second year onwards allows you to specialise in Mathematics and Statistics, or Pure Mathematics, or Applied Mathematics, if you wish. Many of our students choose to specialise in Theoretical Physics, which has a strong tradition in the Mathematics Faculty. In most other universities, it is possible to combine mathematics with other subjects. However, you can attend any lecture you wish in any other subject at Cambridge in your spare time.

## I am very interested in Physics. Should I apply for the Natural Sciences Course or for the Mathematics with Physics option of the Mathematical Course?

This is a decision for you to make. One consideration is that if you take the Natural Sciences Course (NST), you would be unlikely to be able to change to Mathematics at a later stage; whereas if you take the Mathematics with Physics option, you choose at the end of the first year whether to continue with Mathematics or change to Physics for the second year. If you take NST, you would have to take two lab-based subjects (Chemistry, for example) together with Physics and the NST Mathematics course which might not be to your taste; and similarly if you take Mathematics with Physics you would have to do some very pure mathematics which may not be to your taste. If you apply for Mathematics with Physics you will be judged alongside the other applicants for Mathematics, so your mathematics has to be very strong. There is more information in the Mathematics with Physics leaflet.

## Is there much choice in the Mathematical Course?

The first year is a foundational year and there is no choice. In the second year, there is a small amount of choice and some flexibility in the number of courses you take. In the third year, you choose freely about 8 courses from 36; you could specialise in one area of mathematics, but you don't have to. In the fourth year, you choose freely around 6 to 8 courses from around 80; you also have the choice of doing a mathematical essay instead of one of the courses. There is more information on the undergraduate course webpage and a summary on pp. 6-9 of the Guide to Admissions.

## What is Part III?

Part III is an optional fourth year at Masters level, leading to the MMath. It intended mainly for those who wish to go on to research, and covers a wide range of advanced mathematics and of theoretical physics. If you perform highly enough in the third year, you can stay on do do Part III and you will be joined be several other UK and international students who take it as a one-year stand-alone Masters course. There is more information on the Part III admissions webpage and a summary on p. 9 of the Guide to Admissions.

## What are the contact hours and typical workload in the Mathematics Course?

In the first year you will have two lectures every day (including Saturday), and roughly two supervisions per week. The lectures will take place in central halls (national public health restrictions permitting), for all mathematics students from all the Colleges; the supervisions will usually take place in your College (though in subsequent years they may take place in other Colleges, or in the Faculty), and you will usually be supervised with just one other student. You can see here what a typical week looks like in your first year. You will also have at least two formal meetings with your Director of Studies (a mathematician in your College who will advise you throughout your degree, and also teach you in some supervisions) at the beginning and end of each term (there are three terms in each academic year in Cambridge). Your workload should be roughly equivalent to the workload of a full time job (so about 40 hours per week, including lectures and supervisions), but this can vary depending on which courses you are taking, and what topics you find more or less demanding.

## What is a supervision like?

Supervision is the Cambridge term used to describe teaching in a small group of students (usually two). In a supervision, you will go over the work you have done on 'Example Sheets', which are sheets of questions for each course, based on the content of the lectures. The supervisor, who is normally a member of the teaching staff or a post-doctoral researcher, will mark your work (just for your own benefit, so you can understand any mistakes, or for example see better ways of answering questions: your work on example sheets will not affect your final grade), then hand it back to you and go over it during the supervision. A great strength of the supervision system is that it gives students an opportunity to discuss their individual work and particular problems, and any part of the course that you're finding difficult.

**Colleges**

## Are there any major differences between Cambridge colleges?

There are no differences in terms of your course: the Mathematics course is the same for all students, whatever their College. Some Colleges have bigger cohorts of Maths students, some smaller. The main differences between College are things like their location, their size, their buildings (old or new Colleges), different sports facilities, different College student clubs (but all students, from any College can join any of the University Student Clubs and Societies). All Colleges offer accommodation, pastoral support, academic guidance (through your Director of Studies), dining facilities, and space and opportunities for social events. The Cambridge Admissions Office pages have a useful list of Colleges.

## What is the difference between the Faculty and the Colleges?

In Cambridge, the Faculty is responsible for organising all lectures, which are attended by all students together and take place centrally in big lecture rooms (national public health restrictions permitting). Supervisions are organised by individual Colleges, or by group of Colleges together, and take place in a College (not necessarily the same College that a student belongs to) or in the Faculty, but the material used in the supervisions is the same for everybody, and the content is essentially the same in structure, but tailored to the individual students in a particular supervision. In addition, Colleges (not the Faculty) are responsible for the admission of undergraduate students. The Cambridge Admissions Office has more information about what is a College.

## How does an open application work?

Open applications are allocated to Colleges which happen, in that year, to have received fewer applications per place in that subject than the average number across all Colleges. Open applications from mature students (aged 21 or older) are allocated to one of the two mature Colleges who accept mathematicians (Hughes Hall and St Edmund's). There is more information about open offers on the University's admissions pages.