Mathematical Analysis at the University of Cambridge offers a comprehensive and rigorous exploration of the fundamental concepts and techniques underpinning modern mathematics. Designed for students with a strong interest in pure mathematics, this programme provides a deep understanding of the principles of analysis, including sequences and series, continuity, differentiation, integration, limits, and infinite processes. Students will develop their analytical skills through a combination of lectures, problem-solving sessions, and independent research, guided by world-leading experts in the field. The curriculum emphasizes both theoretical foundations and applications, fostering a thorough grasp of how mathematical analysis underpins various scientific disciplines such as physics, engineering, and computer science. The programme also introduces advanced topics like measure theory, functional analysis, and differential equations, preparing students for research or continued study in mathematics or related fields. Students benefit from the university’s rich academic environment, accessing cutting-edge resources and collaborating with renowned faculty members. The course structure includes core modules designed to build a solid base in analysis, complemented by optional modules allowing students to tailor their studies according to their interests and career goals. Throughout the programme, emphasis is placed on developing precise mathematical thinking, problem-solving abilities, and rigorous proof techniques. Graduates of the Mathematical Analysis programme are well-equipped for careers in academia, research institutions, or industries where quantitative and analytical skills are highly valued. The university’s focus on fostering an intellectually stimulating environment ensures that students are challenged and inspired to push the boundaries of their mathematical knowledge. Whether pursuing further study or entering the workforce, students will emerge from the programme with a strong foundation in analysis and the ability to apply mathematical concepts to complex real-world problems.

During their first year students will undertake:

• CCA teamwork projects in various areas of analysis.  These are often associated with Part III (MMath/MASt) courses in areas of analysis, going beyond the course content through supervised team projects.  These are known as CCA Core Courses.
• Two supplimentary courses chosen from the extensive menu of Part III (MMath/MASt) and graduate courses offered by the Faculty.
• An initial research project with their prospective supervisor.  This should amount to the equivalent of about three month's solid work (spread through the year, taking into account other components of the course).
• An external research project is undertaken in Lent term.  The project is selected from a range of projects offered by partner organisations, either in industry or in another University department.  A list of available projects will be made available in Michaelmas term.  This should amount to the equivalent of about one month's solid work.

Placements

Depending on the nature of the research dissertation, visits to work in other leading international research centres, or placements in industry, are encouraged during the final year of the PhD. CCA industry partners include BP, EADS, L3-TRL Technology, MathWorks, Microsoft, Schlumberger, Ultra Electronics, Waymont Consulting.

Feedback

Students can expect to receive an online feedback report each term.

Assessment

Thesis

Assessment for the PhD is by submission of a dissertation and oral examination. There is no standard format for the dissertation in Mathematics (i.e. no prescribed word limit).  Candidates should discuss the format appropriate to their topic with their supervisor.

Other

The structured elements of the first year are assessed as follows:

• CCA Core Courses are assessed by submission of a report and presentation by students to the first year cohort.
• The two supplimentary Part III courses are assessed by oral examination.
• The initial research project is assessed by written report and oral presentation.
• The external research project is assessed by written report and oral presentation.

At the end of the first year (June) students will also undergo a review meeting with the CCA Co-Directors.  The Co-Directors will consider reports from supervisors/co-ordinators of first year structured elements, together with a short factual statement on training and research activities undertaken since admission (to be prepared by the student).

In the second year students will undergo a further review of progress in June with a Co-Director and their supervisor.  An updated statement on training activities, completed research papers, and work in progress will be considered as part of this review.

• 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

The University of Cambridge offers a comprehensive range of financing options for students enrolled in the Mathematical Analysis program. These opportunities are designed to support students financially throughout their studies and to help reduce the burden of tuition fees and living costs. Undergraduate students can apply for government-backed loans, such as those provided through the Student Loans Company in the UK, which cover tuition fees and provide maintenance loans to assist with living expenses. Additionally, the university offers a variety of bursaries and scholarships based on academic merit, financial need, or specific criteria such as nationality or background. These awards can significantly offset the cost of tuition and living costs, making the program more accessible to a diverse range of students.

International students are encouraged to seek external funding sources, including government scholarships from their home countries, private foundations, and international organizations that support students pursuing mathematics studies abroad. Cambridge’s own funding database provides detailed information on numerous scholarships available to international applicants, including the Gates Cambridge Scholarship, which covers full fees and provides a maintenance stipend for students showing exceptional academic potential and leadership qualities. Furthermore, some colleges within Cambridge offer their own financial aid packages, grants, and work-study opportunities to help students fund their educational journey.

Many students also participate in part-time work or internships during their studies to manage living expenses. The university’s Career Service assists students in finding suitable employment opportunities both on and off-campus, which can complement academic pursuits and provide valuable professional experience. Additionally, the university encourages prospective students to explore external grants, sponsorships, and fellowships offered by research councils or industry partners, particularly for those interested in advanced research projects or postgraduate studies beyond the bachelor’s level.

Cambridge’s commitment to accessible education means that transparent information about costs and funding options is widely available. The financial support system aims to ensure that all talented students, regardless of their financial background, have the opportunity to study Mathematical Analysis at one of the world’s leading universities. Prospective students are advised to consult the university’s official financial aid pages and contact relevant departments early in the application process to maximize their chances of receiving appropriate funding support. The university continues to seek additional funding sources and develops new financial aid initiatives to further enhance the accessibility and affordability of its programs.

Mathematical Analysis at the University of Cambridge is a rigorous and comprehensive program designed to develop a deep understanding of the fundamental principles underpinning modern mathematics. The course covers a broad range of topics, including real analysis, complex analysis, and functional analysis, providing students with a solid foundation in the logical structure of mathematical thought. The program emphasizes both theoretical understanding and practical application, preparing students for careers in academia, research, or industry where analytical skills are essential. Students engage with challenging coursework, participate in seminars and tutorials, and have opportunities for original research under the guidance of leading experts in the field. The curriculum is designed to foster critical thinking, problem-solving abilities, and a mastery of mathematical language and reasoning. The program often includes lectures from renowned mathematicians, collaborative projects, and access to extensive resources at the university’s libraries and research centers. Graduates of the Mathematical Analysis program at Cambridge typically go on to pursue doctoral studies, work in scientific and technological industries, or contribute to mathematical research and education. The program is renowned for its high academic standards, supportive learning environment, and the vibrant intellectual community at the University of Cambridge, attracting talented students from around the world who are eager to explore the depths of mathematical analysis.