Mathematics

Mathematics at the University of Cambridge offers an outstanding undergraduate degree programme designed to develop a deep understanding of the fundamental concepts and principles underlying the mathematical sciences. This course provides students with a comprehensive education in pure mathematics, applied mathematics, and mathematical physics, equipping them with analytical and problem-solving skills applicable across a wide range of scientific and technological fields. Students will explore diverse topics such as algebra, calculus, geometry, probability, and statistics, while also engaging with advanced areas including number theory, combinatorics, differential equations, mathematical logic, and computational mathematics. The teaching is delivered through a combination of lectures, supervisions, and practical sessions, encouraging critical thinking, independent research, and collaborative learning. Throughout the programme, students are supported by world-class academics who are leading experts in their fields, and access cutting-edge resources and facilities to facilitate their studies. The course structure is flexible, allowing students to tailor their studies to their interests, with options to focus more heavily on pure mathematics or pursue interdisciplinary applications in sciences, engineering, or finance. Regular assessments and exams ensure a solid understanding of core concepts, while opportunities for research projects, internships, and engaging with mathematical communities foster practical experience and professional growth. Graduates of the Mathematics programme at Cambridge are highly sought after, often proceeding to careers in academia, research, finance, technology, or education. The programme aims to produce not only competent mathematicians but also creative thinkers equipped to solve complex problems and contribute to advancements in various fields. Studying Mathematics at Cambridge is a challenging and rewarding experience that prepares students for successful careers and lifelong learning in an increasingly quantitative world.

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 irregular, but the average load is roughly the same.

You sit four written examination papers each year. In addition, there are optional computer projects in Years 2 and 3. In the fourth year, each course is examined individually.

Year 1 (Part IA)

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

• option (a) Pure and Applied Mathematics, for students intending to continue with Mathematics
• option (b) Mathematics with Physics, for students who may want to study Physics after the first year

You should state in your Supplementary Application Questionnaire (SAQ) which option you wish to take, though it’s possible to change when you start the course. You can still continue with Mathematics in the second year if you take option (b).

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

• the study of algebraic systems (such as groups)
• analysis of calculus
• probability
• mathematical methods (such as vector calculus)
• Newtonian dynamics and special relativity

You take eight subjects. Those taking Mathematics with Physics replace two Mathematics subjects with Part IA Physics from Natural Sciences, covering, for example, kinetic theory, Fourier analysis, and electromagnetism.

Year 2 (Part IB)

In Part IB, you choose from around 16 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
• applicable mathematics, which includes statistics and optimisation (a rigorous treatment of topics from decision mathematics)
• numerical analysis

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

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 more than 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. 

• All applicants to the University of Cambridge must submit an application to UCAS (the Universities and Colleges Admissions Service) by the relevant deadline.
• The Attestat o (polnom) Srednem Obshchem Obrazovanii (Certificate of Secondary Education) is not considered to be suitable preparation for a competitive application to the University of Cambridge. We strongly recommend that you undertake further study if you wish to apply for an undergraduate degree. Examples of the qualifications that would be considered suitable for admission to Cambridge are A Levels, the International Baccalaureate (IB), five or more Advanced Placement (AP) courses, or possibly the first year of an undergraduate degree at a university outside the UK. We recommend that you contact the College that you wish to apply to directly for further advice and guidance.
• IELTS – normally a minimum overall grade of 7.5, usually with 7.0 or above in each element.
• Cambridge English: Advanced – grade A or B.
• Cambridge English: Proficiency – grade A, B or C.

Assessment format

• There is no common format written assessment for Mathematics (applicants will continue to sit STEP alongside A Levels) – Colleges will assess aptitude, knowledge base and potential through short tasks at the time of interview.

You do not need to register or be registered in advance for the assessment at interview – the Colleges provide details of arrangements in the letters inviting applicants to interview.

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.

For Mathematics candidates interviewed overseas, a written Maths assessment will be administered by the overseas interviewing team which will then be made available to the Cambridge College along with the overseas interview report.

The University of Cambridge offers a diverse range of financing options for students enrolling in its Mathematics undergraduate program. International and domestic students are encouraged to explore various scholarships, grants, and funding opportunities to support their studies. For UK students, funding is often available through the UK Government's student loan system, which offers loans for tuition fees and living costs, repayable after graduation based on income levels. The Cambridge Commonwealth, European & International Trust provides scholarships specifically for international students, covering partial or full tuition fees and sometimes providing stipends for living expenses. Additionally, the Cambridge Trust offers numerous scholarships that are awarded annually based on academic excellence and potential. Certain colleges within the university also offer their own financial aid packages, including bursaries and hardship funds, to assist students facing financial difficulties. Prospective students are advised to consult the university’s official financing and funding webpage to find detailed eligibility criteria, application procedures, and deadlines. Furthermore, external organizations and government agencies may provide funding opportunities for students from specific regions or backgrounds, which can be accessed through the university's broader support services. For students with limited financial resources, the university also provides advice and guidance on part-time work opportunities during the course, subject to visa regulations for international students. Overall, Cambridge strives to ensure that financial considerations do not hinder talented students from pursuing rigorous mathematical studies, and it offers a comprehensive suite of funding options designed to meet diverse needs.

Your living expenses may be higher than for a Home student (eg if you stay in Cambridge/the UK during vacations). The minimum resources needed in Cambridge for the year (excluding tuition and College fees) are estimated to be approximately £10,080 in 2017-18 and £10,310 in 2018-19, depending on lifestyle (you should allow for increases in future years).