Partial Differential Equations

Field of Study: Mathematics
Programme Title: Partial Differential Equations (PDEs)
Degree Level: MSc (Master of Science)
Duration: 1 year (Full-time)
Location: University of Oxford, Department of Mathematics

Description:
The MSc in Partial Differential Equations at the University of Oxford offers a comprehensive and rigorous study of the theory, methods, and applications of partial differential equations. This programme is designed for students with a strong background in mathematics who wish to deepen their understanding of this fundamental area, which plays a crucial role in applied mathematics, physics, engineering, finance, and other scientific disciplines. Throughout the programme, students will engage with advanced mathematical techniques used to analyze and solve PDEs, including analytical methods, numerical approaches, and qualitative theory. They will explore classical equations such as Laplace, Helmholtz, wave, heat, and Schrödinger equations, as well as modern developments in nonlinear PDEs, inverse problems, and mathematical modeling.

The curriculum combines core lectures, seminars, and independent research, encouraging students to develop a solid theoretical foundation alongside practical problem-solving skills. Key topics include existence and uniqueness theorems, regularity theory, stability analysis, and spectral theory. In addition to coursework, students undertake a research project that allows them to investigate a specific area of partial differential equations in depth, often in collaboration with leading experts in the field.

The programme is highly interdisciplinary, providing insights into how PDEs are used to model phenomena across various scientific fields. Students will benefit from the university’s rich academic environment, access to world-class faculty, and state-of-the-art research facilities. Graduates of this MSc program are well-prepared for doctoral research or careers in academia, industry, or government agencies where advanced mathematical expertise in PDEs is required. The programme's rigorous academic structure and emphasis on independent research make it an excellent choice for students aiming to contribute to the development of cutting-edge mathematical science.

This MSc in Partial Differential Equations exemplifies Oxford’s commitment to excellence in mathematical education, fostering critical thinking, analytical skills, and a deep understanding of complex mathematical systems.

The role of PDEs within mathematics, especially nonlinear analysis, geometry, topology, stochastic analysis, numerical analysis, and applied mathematics, and in other sciences (such as physics, chemistry, life sciences, climate modelling/prediction, materials science, engineering, and finance) is fundamental; it is at the heart of many scientific advances and is becoming increasingly significant.

At the same time, the demands of applications have led to important developments in the analysis of PDEs, which have in turn proved valuable for applications.

A sizeable yearly cohort has allowed the CDT to create new training mechanisms, so that you will learn theory, analysis, and applications of PDEs in a variety of fields in a coherent manner with a natural progression, by-passing a traditionally separate 'pure' or 'applied' approach to learning.

You will undertake a four-year programme with the first year consisting of a set of intensive courses focusing on the analysis and applications of PDEs. The first year also includes two ten-week mini-projects allowing you to broaden your knowledge and find a field suitable for you to develop your main research topic for years two to four. 

There will be annual reviews of your progress, drawing on indicators such as attendance, assessment of your mini-projects, and course results at the end of your first year, followed by the submission of a written report, in support of your transfer from Probationary Research Student status to DPhil status at the end of your second year, and a Confirmation of Status interview at the end of your third year, to ascertain progression towards the submission of your DPhil thesis.

Applicants are normally expected to be predicted or have achieved a first-class undergraduate degree with honours (or equivalent international qualifications), as a minimum, in mathematics or a related numerate discipline. 

For applicants with a degree from the USA, the minimum GPA sought is 3.6 out of 4.0.

A previous master's degree is not required, though the requirement for a first-class undergraduate degree with honours can be alternatively demonstrated by strong performance in a master's degree.

Highly motivated and mathematically capable students with a degree in other subjects are also encouraged to apply.

If you hold non-UK qualifications and wish to check how your qualifications match these requirements, you can contact the National Recognition Information Centre for the United Kingdom (UK NARIC).

No Graduate Record Examination (GRE) or GMAT scores are sought.

• Official transcript(s)
• CV/résumé
• Statement of purpose/personal statement:One to two pages
• References/letters of recommendation:Three overall, generally academic

ENGLISH LANGUAGE REQUIREMENTS

Standard level

Financial aspects of the Partial Differential Equations program at the University of Oxford are structured to support both domestic and international students through a variety of funding options. Undergraduate students pursuing this program can benefit from numerous scholarships, bursaries, and financial aid packages provided by the university and external organizations. The university offers merit-based scholarships for outstanding applicants, which significantly reduce tuition fees and provide living expense support. For postgraduate students, funding opportunities include taught course scholarships, research grants, and departmental awards, all aimed at alleviating financial burdens and encouraging academic excellence.

International students are encouraged to apply for specific scholarships designed for non-UK residents, which may cover full or partial tuition fees, as well as living costs. Examples include the Oxford International Scholarships and various college-specific bursaries. Additionally, many students supplement their funding through external sources such as government-sponsored loans, research grants, or sponsorships from their home country. The university also facilitates access to work opportunities, including graduate teaching assistantships and research positions, which enable students to earn while they learn, further helping to manage costs.

Students are advised to carefully review the university’s financial aid portal and departmental websites for the latest funding opportunities, application deadlines, and eligibility criteria. The university’s student services also provide personalized advice on financing studies, budgeting, and planning for living expenses. For international students, additional support is available to navigate visa requirements and application processes for scholarships and funding. Overall, the university aims to ensure that financial constraints do not hinder capable students from pursuing advanced studies in Partial Differential Equations, fostering an inclusive academic environment.

The Partial Differential Equations (PDE) program at the University of Oxford offers an in-depth study of the fundamental equations governing various physical phenomena. This program is designed for students with a strong background in mathematics, particularly those interested in advanced topics in analysis, applied mathematics, and mathematical physics. The course covers a broad range of topics including the theory of linear and nonlinear PDEs, methods of classical and modern solution techniques, and their applications to real-world problems in science and engineering. Students explore the mathematical structure of PDEs, stability analysis, existence and uniqueness theorems, and numerical methods for approximating solutions. The curriculum emphasizes both theoretical understanding and practical skills, preparing students for research or careers in academia, industry, or government laboratories.

The program typically involves lectures, seminars, and research projects, allowing students to engage deeply with current research topics. Faculty members at Oxford renowned for their expertise in PDEs and related areas supervise student projects, encouraging original research and critical thinking. The program also offers opportunities to collaborate across disciplines, reflecting the cross-cutting nature of PDEs in fields such as physics, finance, biology, and engineering. Students may have access to advanced computational resources and software tools used for the simulation and analysis of PDEs. For prospective students, a strong foundation in calculus, linear algebra, and differential equations is recommended, and prior exposure to mathematical analysis or numerical methods can be advantageous. Upon completion, graduates will have gained comprehensive knowledge and skills in the theory, application, and computation of partial differential equations, positioning them well for further academic research or professional roles that require advanced mathematical expertise.