This course is offered by the Faculty of Mathematics as a full-time period of research and introduces students to research skills and specialist knowledge. Its main aims are: to give students with relevant experience at first-degree level the opportunity to carry out focused research in the discipline under supervision; and to give students the opportunity to acquire or develop skills and expertise relevant to their research interests. It involves minimal formal teaching: students are integrated into the research culture of the Department of Pure Mathematics & Mathematical Statistics (DPMMS), or the Department of Applied Mathematics and Theoretical Physics (DAMTP), as appropriate. They may attend the Departments’ programmes of research seminars and other graduate courses, but most research training is overseen by their research supervisor, and, where appropriate, within a research group. Opportunities to develop research and transferable skills also exist through attendance at training sessions organised at Department, School or University level as part of the wider postgraduate programme, and informally through mentoring by fellow students and members of staff. By the end of the programme, students will have: acquired a comprehensive understanding of techniques, and a thorough knowledge of the literature, applicable to their own research; demonstrated originality in the application of knowledge, together with a practical understanding of how research and enquiry are used to create and interpret knowledge in their field; shown abilities in the critical evaluation of current research and research techniques and methodologies; demonstrated some self-direction and originality in tackling and solving problems, and acted autonomously in the planning and implementation of research.