Pure Mathematics and Mathematical Statistics

Pure Mathematics and Mathematical Statistics at the University of Cambridge is a rigorous and comprehensive degree programme designed to equip students with a deep understanding of fundamental mathematical principles alongside advanced statistical techniques. This interdisciplinary course merges theoretical mathematics with practical data analysis, preparing graduates for a wide range of careers in academia, industry, finance, data science, and government. Throughout the programme, students explore a broad spectrum of topics, including algebra, calculus, mathematical analysis, geometry, probability theory, statistical inference, and computational methods. The curriculum emphasizes logical reasoning, problem-solving skills, and mathematical rigor, fostering an ability to approach complex problems with clarity and confidence. Students have the opportunity to engage in both individual and collaborative research projects, enhancing their analytical and communication skills. The programme also offers optional modules allowing specialization in areas such as number theory, combinatorics, mathematical logic, and advanced statistical modelling. Taught by leading experts in the field, the course combines lectures, tutorials, workshops, and computational labs to ensure a thorough understanding of both abstract mathematical concepts and their real-world applications. Cambridge’s distinguished faculty provide personalized academic support, guiding students through challenging topics and encouraging independent thinking. The degree culminates in a final dissertation or research project, offering students the chance to contribute original insights to their field of interest. Graduates from this programme are well-prepared to pursue further studies at postgraduate level or to enter roles that require high-level quantitative analysis and problem-solving skills, including data science, financial modelling, cryptography, academia, and consultant work. The programme fosters a vibrant academic community where students can participate in seminars, workshops, and mathematics outreach activities, promoting a lifelong engagement with the discipline. Joining this esteemed programme means becoming part of a tradition of mathematical excellence, innovation, and discovery at the University of Cambridge.

Structure of the PhD

Students are required to undertake a minimum of nine terms of research (i.e. three years). Students are not registered for the PhD in the first instance but are instead admitted on a probationary basis.  All students are assessed for registration towards the end of their first year of full-time study (usually June). This assessment is based on a short written report which is reviewed by two assessors. In the fifth term there might also be a further assessment of progress, for which students submit a longer piece of written work and receive an oral assessment.

Research areas

The topic of the research thesis may be chosen from the wide range of subjects studied within DPMMS. It is expected that applicants to the PhD course will investigate the research interests and expertise of our academic staff prior to making a formal application. This may be done by consulting the research pages of our website, as well as the individual profiles of our academic staff.

Additional training and opportunities

Whilst there are no mandatory taught components to the PhD degree, students may wish to undertake specific courses or further training to expand their knowledge, either for personal interest or to directly assist with their PhD research. All students are encouraged to participate and attend the wide range of lectures, seminars and events on offer within DPMMS and the Centre for Mathematical Sciences.

Many students submit a prize essay at the beginning of their fifth term. The best essays each year are of a scale and quality already adequate for a PhD dissertation, incorporating work already, or about to be, published. We intend that our students publish their work in leading journals. Our PhD students might have written several papers before they submit their dissertation, and can go on to win academic positions at leading institutions around the world.

DPMMS also promotes and encourages researcher development and transferable skills training. This can take the form of assisting with Part III catch-up lectures, attendance at skills based training sessions, or presenting work at seminars and conferences. The University also offers training via the Researcher Development Programme.

There is no requirement for PhD students to teach but there are plenty of opportunities to do so, such as offering supervisions for third year undergraduates (this involves the supervisor sitting with a pair of students for an hour, discussing their work). PhD students might help too with running examples classes for Part III students.

Apply using the Applicant Portal

The Apply Online button on the right will take you to the Applicant Portal, where you can create and submit your application, and request references.

An application is only complete when:

1. you have submitted your application via the Applicant Portal and paid the £50 application fee
2. you have uploaded the required supporting documents via the Applicant Self-Service
3. your referees have provided their references.

If you miss the deadlines specified in this section, you will not be able to submit your application.

Applications before 31 December are very strongly encouraged. Anyone wishing to apply after this date should contact DPMMS before submitting an application.

Applicants are encouraged to make informal contact with potential supervisors prior to making an application. Applicants should clearly state in the relevant field of the application form the name(s) of those member(s) of academic staff with whom they wish to work, and provide a clear indication of the areas or topics in which they intend to undertake research.

Selection Process

Applications are reviewed on a rolling basis as they are received.  The Department makes every effort to take decisions on applications at the earliest opportunity.  However, please note that it may take some time for a final decision to be made.  Applications may need to be viewed by several potential supervisors before a final decision can be reached. Once a decision has been taken on your application the result will appear on your CamSiS Self-Service page.

• Magistr (Master's Degree) at Pass level. Diploma Specialista (completed post-1991) with a minimum overall grade of good or 4/5 Bachelor's from Moscow Institute of Physics and Technology and other prestigious institutions with an overall grade of 4/5 Bologna Bachelor's from other institutions with an overall grade of 5/5, Excellent
• Diploma Specialista (completed post-1991) with a minimum overall grade of Excellent or 5/5 Bachelor's from Moscow Institute of Physics and Technology and other prestigious institutions with an overall grade of 5/5
• IELTS (Academic) 7.0
• TOEFL Internet Score 100
• £50 application fee
• First Academic Reference
• Second Academic Reference
• Transcript
• Personal Reference

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Prepare for the program requirements with English Online by the British Council.

• ✔️ Flexible study schedule
• ✔️ Experienced teachers
• ✔️ Certificate upon completion

📘 Recommended for students with an IELTS level of 6.0 or below.

Enroll in the course

The financing of the Pure Mathematics and Mathematical Statistics program at the University of Cambridge is designed to support students through a variety of funding options, including scholarships, bursaries, grants, and loans. Tuition fee funding is available from both the university and external sources, with eligibility criteria varying according to student nationality, residency status, and individual circumstances. For home students, the university offers a range of scholarships and bursaries to help cover tuition fees and living costs. These include university-funded scholarships such as the Cambridge Commonwealth, European, and International Trusts, as well as departmental scholarships specifically targeted at mathematics students.

International students can access a number of scholarships designed to promote diversity and support postgraduate study, including the Gates Cambridge Scholarships, which cover full tuition, a living allowance, and additional funding for academic costs. Undergraduates may also be eligible for government loans and grants where applicable, although funding for international students is primarily through external awards. For those requiring financial assistance, the university's Student Advice Service provides guidance on application procedures and eligibility criteria for various financial aid programs.

Students are also encouraged to explore external funding sources, including government-sponsored loans and scholarships from their home countries, as well as private foundations and charitable organizations. In addition to formal scholarships, the university offers a range of bursaries based on financial need, which do not require repayment and are designed to reduce financial barriers to studying. These bursaries can be awarded based on demonstrated need, academic merit, or a combination of both, depending on the specific fund.

Work opportunities, such as part-time roles within the university or nearby institutions, are available to help students supplement their funding. These positions are typically in administrative, research, or teaching support roles and are accessible to students in accordance with visa regulations and university policies. The university aims to ensure that financial constraints do not prevent talented students from pursuing their studies in Pure Mathematics and Mathematical Statistics by providing comprehensive financial support packages, transparent application procedures, and advice services.

The Bachelor of Arts in Pure Mathematics and Mathematical Statistics at the University of Cambridge offers students a comprehensive curriculum designed to develop a deep understanding of fundamental mathematical theories and their applications. The program is structured to provide a robust foundation in pure mathematics, covering areas such as algebra, analysis, geometry, and topology, alongside substantial coursework in mathematical statistics, probability theory, and data analysis. Students are encouraged to engage with rigorous mathematical proofs, complex problem-solving, and theoretical concepts, preparing them for advanced research or careers in academia, industry, finance, data science, and technology.

Throughout the course, students have the opportunity to learn from leading experts in the field and to participate in cutting-edge research projects. The program emphasizes both theoretical understanding and practical skills, ensuring graduates are well-equipped to analyze and interpret statistical data and to develop mathematical models relevant to real-world problems. Cambridge's tutorial-based teaching system provides personalized instruction, enabling students to deepen their understanding through regular one-on-one tutorials and group discussions.

The degree program typically spans three years for students taking a full-time route and sometimes four years for those combining it with industrial placements or specializing further in their final year. Entry requirements generally include high academic achievement in mathematics at A-level or equivalent qualifications, with a strong emphasis on mathematical coursework.

Graduates of the program gain transferable skills in logical reasoning, quantitative analysis, problem-solving, and critical thinking, which are highly valued in various sectors. The university’s vibrant mathematical community, access to advanced research facilities, and opportunities for interdisciplinary collaboration significantly enhance the learning experience. Post-graduation, many students pursue postgraduate studies, including master's and doctoral research, or enter careers in finance, technology, data analysis, academia, and public policy.

Cambridge provides an intellectually stimulating environment, with dedicated mathematics libraries, student societies like the Cambridge Students' Mathematical Society, and events such as seminars, workshops, and conferences that foster academic growth and professional networking. The program’s rigorous curriculum, combined with Cambridge’s rich academic traditions, aims to produce graduates equipped not only with excellent mathematical skills but also with the analytical mindset necessary to tackle complex global challenges.