Cambridge Mathematics of Information (CMI) offers a four-year PhD programme, with a structured first year. Research areas in CMI range widely across the field of `data science’ including statistics and probability; applied, pure and computational analysis; and the theory and modelling of complex, dynamical and physical systems. Training, especially in the first year, emphasises not only individual study but also teamwork, communication and engagement with users of mathematics. Students are based at the Centre for Mathematical Sciences, which houses the Department of Pure Mathematics and Mathematical Statistics, Department of Applied Mathematics and Theoretical Physics, Statistical Laboratory, Isaac Newton Institute and Betty and Gordon Moore Library.

This cutting-edge training centre in the Mathematics of Information will produce a new generation of leaders in the theory and practice of modern data science, with an emphasis on the mathematical underpinnings of this new scientific field. As the relevant skill sets are multi-faceted in nature, ranging from computational, algorithmic to analytical and statistical expertise, they are best acquired in an interdisciplinary, cohort-based education system that exposes all students simultaneously to the many interlaced aspects of mathematics in data science, with a strong emphasis on industrial collaboration. Subject areas of key importance are identified: large scale optimisation and variational methods, high-dimensional and non-parametric statistics, functional data analysis, Bayesian inference, mathematical inverse problems, partial differential equations, quantum information theory and computing, operations research and statistical learning theory, probability & random matrix theory, ergodic- & computational complexity theory.

The CMI 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 CMI 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 the following:

A core module which will train all students, independently of their research specialism, in the use of a variety of methods of modern data science, including the construction and analysis of statistical algorithms for high dimensional problems, applied numerical & image analysis, inverse problems, mathematical foundations of modern signal processing (Fourier & Wavelet methods, compressed sensing), mathematical modelling (fluid dynamics, mathematical biology, biomedical physics), and areas of scientific computing

A further module is chosen from one of three scientific pillars of the PhD training programme:

• high-dimensional statistics and computational analysis,
• modelling of complex, dynamical and physical systems and
• probability theory and pure analysis.

These clusters will consist of group-based project research work that accompanies selected advanced lecture courses offered by the highly successful `Part III’ Master’s course within the mathematics Faculty 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.

Two further taught courses chosen from the extensive menu of Part III and postgraduate courses. These are assessed by an oral examination.

An initial research project with their prospective supervisor and an external project. These are assessed by written report and oral presentation.

All students undergo a review at the end of their first year, and again at the end of their second year.

Students beginning the CMI 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 CMI students are also encouraged to take part in other PhD training activities, such as the postgraduate analysis seminar series, public engagement and transferable skills courses, designed to equip students with a range of skills, competencies, knowledge and experience necessary to thrive as a modern mathematical data scientist.

Open Days

The University of Cambridge Postgraduate Virtual Open Day usually takes place at the beginning of November. It’s a great opportunity to ask questions to admissions staff and academics, explore the Colleges virtually, and to find out more about courses, the application process and funding opportunities. Visit the Postgraduate Open Day page for more details.

Details of activities hosted by the Faculty of Mathematics can be found on the Faculty website.

Departments

This course is advertised in the following departments: