Course summary

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.