Mathematics

(including Mathematics with Physics)

Cambridge is renowned for the excellence of its Mathematics course. Equally challenging and rewarding, it offers the opportunity to study a wide range of subjects: everything from abstract logic to black holes.

Container

Overview

Flexibility: a course that suits you

Two aspects of the course that our students greatly appreciate are its flexibility and the breadth of subjects offered. The amount of choice increases each year and after Year 1 you can choose the number of options you study. Some students take as many lecture courses as they can; others take fewer and study them very thoroughly.

This structure allows you to keep your options open, giving you the opportunity to discover your strengths, extend your knowledge and develop your interests before specialising.

Our Faculty

Since Sir Isaac Newton was Lucasian Professor (1669-96), mathematics teaching and research here have been enhanced by a string of brilliant mathematicians, including six Fields Medallists and even Nobel Prize winners. Most current Faculty members are leading international authorities on their subject.

Our Faculty is also closely linked with the Isaac Newton Institute, which attracts specialists from all over the world to tackle outstanding problems in the mathematical sciences.

Course costs

Tuition fees

Information on tuition fee rates for Mathematics is available on the tuition fees page.

Additional course costs

Required: a laptop - cost if purchased new will depend on choice, but existing laptops if less than four years old are likely to be completely adequate for the course needs.

Aside from the above, there are no other compulsory additional course costs for Mathematics. Some students choose to purchase their own copy of certain texts but this is optional. Full course details are available on the Faculty of Mathematics website. If you have any queries about resources/materials, please contact the Faculty.

Changing course

About 5-10% of students change from Mathematics each year. Many of these have taken the Mathematics with Physics option in their first year, with the intention of changing to Physics (Natural Sciences).

Over the years, mathematicians have changed successfully to many other subject taught at Cambridge. However, it's not advisable to apply for Mathematics intending to transfer to a subject other than Physics.

To be able to change course, you need the agreement of your College that any change is in your educational interests, and you must have the necessary background in the subject to which you wish to change – in some cases you may be required to undertake some catch-up work or take up the new course from the start/an earlier year. If you think you may wish to change course, we encourage you to contact a College admissions office for advice. You should also consider if/how changing course may affect any financial support arrangements.

Careers

A Cambridge Mathematics degree is versatile and very marketable. The demand for our mathematicians is high in business, commerce and industry, as well as the academic world.

Around 38% of our students go on to further study¹, while others follow a wide variety of careers. Recent graduates include a metrologist, games designer, biomedical research scientist, sports statistician, journalist, cybersecurity analyst, and an AI research engineer, as well as teachers, actuaries, accountants, IT specialists, financiers and consultants.

STEP

STEP consists of two examination papers used to assess your aptitude for university study in Mathematics. It's used as part of almost all conditional offers in Mathematics (including Mathematics with Physics). The University offers a free online STEP support programme designed to help prospective applicants develop advanced problem-solving skills and prepare for the STEP exams.

¹ Based on responses to the Graduate Outcomes survey. This records the outcomes of students who completed their studies between August 2019 and July 2020. 56% of Mathematics graduates responded to the survey.

Course outline

In Year 1, you typically have 12 lectures and two supervisions each week. In the following years, the greater choice and flexibility means that the pattern of lectures and supervisions is more variable, but the average load is roughly the same.

You sit four written examination papers each year in the first three years*. In addition, there are optional computer projects in Years 2 and 3. In the fourth year, each course is examined individually, and you have the option of submitting an essay on a current research topic.

Year 1 (Part IA)

In the first year, there are two options to choose from:

Pure and Applied Mathematics, for students intending to continue with Mathematics
Mathematics with Physics, for students who may want to study Physics after the first year

You will be asked to indicate which option you wish to take as part of the application process, though it’s possible to change when you start the course. You can still continue with Mathematics in the second year if you take Mathematics with Physics.

Part IA introduces you to the fundamentals of higher mathematics, including:

the study of algebraic systems (such as groups)
analysis (a rigorous study of functions and concepts from calculus)
probability
mathematical methods (such as vector calculus)
Newtonian dynamics and special relativity

You take eight papers. Those taking Mathematics with Physics replace two Mathematics subjects with Part IA Physics from Natural Sciences, covering, for example, kinetic theory, electromagnetism, and practical work in a laboratory

Year 2 (Part IB)

In Part IB, you choose from around 15 options available. In most, the topics of the first year are studied in much greater depth, but some new topics are offered, for example:

geometry
electromagnetism, quantum mechanics and fluid dynamics
numerical analysis
applicable mathematics, which includes statistics and optimisation (a rigorous treatment of topics from decision mathematics)

There are also optional computational projects (assessed by means of reports and programs submitted before the summer examinations), using numerical or algebraic techniques to investigate mathematical problems.

Year 3 (Part II)

Year 3 gives you the opportunity to explore your mathematical interests in detail. There is a very wide choice, including papers on, for example:

cryptography
algebraic topology
number theory
cosmology
general relativity
stochastic financial models
waves
automata and formal languages
mathematical biology
the mathematics of machine learning

There are also optional computational projects.

Year 4 (Part III, optional integrated Masters)

Part III has a world-wide reputation for training the very best research mathematicians. Progression to Part III, in which around 75 to 80 options are offered, normally requires a first in Part II or a very good performance in Parts IB and II, and successful completion leads to a BA with MMath. See the Faculty website for more details.

For further information about studying Mathematics at the University of Cambridge see the Faculty of Mathematics website.

* The formal description of the undergraduate course is contained in the Schedules booklet, which is updated as necessary every year.

Entry requirements

Entry Requirements

This page details the standard entry requirements for this course. Check the document below for any variations between Colleges (some may ask for an A* in a particular subject for example):

PDF icon Mathematics entry requirements by College for 2024 entry

PDF icon Mathematics with Physics entry requirements by College for 2024 entry

(These are subject to change and will be finalised by July 2023)

Typical offers require

A Level: A*A*A + STEP
IB: 40-42 points, with 776 at Higher Level + STEP
Other qualifications: See Entrance requirements.

Subject requirements

All Colleges require: A Level/IB Higher Level Mathematics, A Level Further Mathematics (A Level students only), STEP
Some Colleges Require: A Level/IB Higher Level in a science subject; A Level/IB Higher Level Physics (for Mathematics with Physics only)

Further guidance:

STEP grades required as part of an offer vary by College but are usually at least grade 1 in two STEP papers (see individual College websites for details).
IB applicants are expected to take IB Higher Level 'Analysis and Approaches' for this course. If this option is not available at your school, please contact the College you wish to apply to for further advice and guidance.
Students applying to study Mathematics with Physics must have taken A Level Further Mathematics (including the section on Mechanics) or have taken A Level Physics in addition to Mathematics and Further Mathematics.
If A Level Further Mathematics is not available at your school, the Advanced Mathematics Support Programme may be able to help. You can also contact the College you wish to apply to for further advice and guidance.

See Entrance requirements and Choosing your post-16 subjects for additional guidance and conditions of entry.

A Levels

Depending on individual circumstances, some Colleges may make an A Level applicant an offer which will be met if they achieve either A*A*A with at least grade 1 in both of STEP papers 2 and 3 OR A*A*A* with at least grade 1 in either STEP paper 2 or 3 (both papers to be taken). See the documents above for details.

Applicants to the Mathematics course who take A Level Mathematics in Year 12, and A Level Further Mathematics and one other A Level subject in Year 13 will not usually need to take another A Level in Year 13.¹ Such students may be required to achieve A* in the two subjects taken in Year 13 (even if they achieve A* in Mathematics), and should be enhancing their subject knowledge through wider engagement beyond their A Levels. Contact a College admissions office for further advice.

¹ Students should consider potential implications this may have for their other university options.

Admission assessment

Some Colleges may require applicants for this course to take a written assessment if shortlisted for interview - please check the document above for details. You will not need to register in advance for this assessment and the Colleges will provide details directly to you.

All applicants made an offer will be required to sit STEP in June.

Please note that your performance in the assessment at interview will not be considered in isolation, but will be taken into account alongside the other elements of your application.

See Admission assessment for further information.

Submitted work

Applicants are not typically asked to submit examples of written work. Some may be asked by their College to do some reading in advance of their interview, but if this is required the College will provide full details in the letter inviting the student to interview.

Typical Mathematics entrants (A Level and IB)

For 2017, 2018 and 2019 entry, the majority of entrants from an A Level background achieved at least A*A*A* (85% of entrants). All of these successful applicants took Mathematics and Further Mathematics, 91% took Physics and 53% took Chemistry. For the same period, the majority of IB entrants achieved at least 44 points overall and/or grades 777 at Higher Level. The majority of entrants achieved grades of at least 1, 1 in STEP II and III.

This information is intended to give you a sense of the academic standard of our typical A Level entrants. We welcome applicants from a range of qualification backgrounds.

All undergraduate admissions decisions are the responsibility of the Cambridge Colleges. Please contact the relevant College admissions office if you have any queries.

Resources

Find out more about Mathematics at Cambridge

Faculty of Mathematics - Explore Mathematics in more detail on the faculty website.

Course Information - A detailed guide to the Mathematics degree.

Maths study skills - A guide to the study skills that will help you study Mathematics at Cambridge, and also give you a flavour of the teaching styles here.

Isaac Newton Institute - Isaac Newton Institute for Mathematical Sciences.

NRICH Mathematics - Free online mathematics resources designed to help students develop mathematical reasoning and problem-solving skills

Plus Magazine - An online magazine opening a door to the world of maths.

Millennium Mathematics Project - Maths education and outreach initiative.

STEP Guidance - Information about the STEP examination which applicants to study Maths at Cambridge are required to take.

STEP Support Programme - A free series of online modules designed to help potential university applicants develop their advanced problem-solving skills and prepare for the STEP exams.

Application Information - A detailed guide to applying to study Mathematics at Cambridge.

Underground Mathematics - Online mathematics resources for A Level students and teachers.

Discover Uni

Discover Uni data

Contextual information

Discover Uni allows you to compare information about individual courses at different higher education institutions. This can be a useful method of considering your options and what course may suit you best.

However, please note that superficially similar courses often have very different structures and objectives, and that the teaching, support and learning environment that best suits you can only be determined by identifying your own interests, needs, expectations and goals, and comparing them with detailed institution- and course-specific information.

We recommend that you look thoroughly at the course and University information contained on these webpages and consider coming to visit us on an Open Day, rather than relying solely on statistical comparison.

You may find the following notes helpful when considering information presented by Discover Uni.

Discover Uni relies on superficially similar courses being coded in the same way. Whilst this works on one level, it may lead to some anomalies. For example, Music courses and Music Technology courses can have exactly the same code despite being very different programmes with quite distinct educational and career outcomes.

Any course which combines several disciplines (as many courses at Cambridge do) tends to be compared nationally with courses in just one of those disciplines, and in such cases the Discover Uni comparison may not be an accurate or fair reflection of the reality of either. For example, you may find that when considering a degree which embraces a range of disciplines such as biology, physics, chemistry and geology (for instance, Natural Sciences at Cambridge), the comparison provided is with courses at other institutions that primarily focus on just one (or a smaller combination) of those subjects.You may therefore find that not all elements of the Cambridge degree are represented in the Discover Uni data.

Some contextual data linked from other surveys, such as the National Student Survey (NSS) or the Destination of Leavers in Higher Education (DLHE), may not be available or may be aggregated across several courses or several years due to small sample sizes. When using the data to inform your course choice, it is important to ensure you understand how it has been processed prior to its presentation. Discover Uni offers some explanatory information about how the contextual data is collated, and how it may be used, which you can view here: https://discoveruni.gov.uk/about-our-data/.

Discover Uni draws on national data to provide average salaries and employment/continuation data. Whilst starting salaries can be a useful measure, they do not give any sense of career trajectory or take account of the voluntary/low paid work that many graduates undertake initially in order to gain valuable experience necessary/advantageous for later career progression. Discover Uni is currently piloting use of the Longitudinal Education Outcomes (LEO) data to demonstrate possible career progression; it is important to note that this is experimental and its use may be modified as it embeds.

The above list is not exhaustive and there may be other important factors that are relevant to the choices that you are making, but we hope that this will be a useful starting point to help you delve deeper than the face value of the Discover Uni data.