This course is a four-year PhD in Mathematics, in an area of Analysis or its Applications. The scope includes Partial Differential Equations, Geometric Analysis, Probability, Computational Analysis, High-Dimensional or Non-Parametric Statistics and Mathematics of Information.

The CCA PhD follows EPSRC's cohort-based training model. A unique first year programme offers wide-ranging training in Analysis, emphasising teamwork and offering opportunities to work on two research projects, one supervised in the Faculty of Mathematics, the other by a user of mathematics in another department of the University or in industry.

## Prerequisites

The prerequisites for the CCA PhD course are:

- a four-year undergraduate degree in mathematics or a mathematics-related subject; or a three-year undergraduate degree plus a Masters degree in mathematics or a mathematics-related subject
- prior experience studying analysis is an advantage
- candidates should be able to demonstrate evidence of academic excellence.

## Course Structure

Mathematical analysis provides the conceptual framework and methodology for a large part of current mathematical research and innovation. It underpins the majority of novel applications of mathematics in science, engineering and industry. Problems originating in science, engineering and industry are typically formulated in mathematical terms using analysis, while new mathematical ideas, techniques and algorithms usually make their impact in application areas through the means of analysis. Training at Cambridge Centre for Analysis (CCA) emphasises the whole range of modern techniques, their interconnections and applications.

The CCA PhD is a four-year course leading to a single PhD thesis. Students are expected to submit the thesis for examination at the end of the fourth year; an additional writing-up year is not expected. The main distinctive feature of training at CCA is the structured programme running over the first nine months when, besides beginning work on an initial research project, students work in teams to learn a broad spectrum of modern analysis, undertake an external project supervised by a user of mathematics in science or industry, and participate in a range of seminars, including an industrial workshop. Our students find this method of learning stimulating and enjoyable and the joint activity leads to an inclusive and well-integrated cohort.

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, each of which leads to a report and presentation by students to the first year cohort. Current courses:
- Two courses chosen from the extensive menu of Part III and graduate courses. These are assessed by oral examination.
- An initial research project with their prospective supervisor and an external project. These are assessed by written report and oral presentation.

Students beginning the CCA PhD all have a prospective supervisor from the Faculty of Mathematics, who directs the initial research project, which forms part of the first year programme. Often students will progress to work with the same supervisor for the PhD but the possibility remains open to switch to a new area in the course of the first year, or to work on a PhD project jointly supervised in another department of the University or in industry.

Throughout their time at CCA students are also encouraged to take part in other CCA activities, such as the graduate analysis seminar series, public engagement and other transferable skills courses, designed to equip students with a range of competencies, knowledge and experience necessary to thrive as a mathematical analyst.