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PhD in Mathematics of Information


The Cambridge Mathematics of Information (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 chosen from one of three scientific pillars of the PhD training programme:

a) high-dimensional statistics and computational analysis,

b) modelling of complex, dynamical and physical systems and

c) 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 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 activities, such as the graduate 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.