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Summer Research Programmes


Successful projects are fuelled by a good match between the mathematicians' expectations and the project requirements. The project description should highlight the main purpose of the project and what key skills might be required (e.g. coding/data science). When presenting your project to students in the seminar series, you should not try to cram in too much background information but focus on what the mathematician will actually do day to day as well as how supervision will work.  Consider the best way to get the mathematician up to speed in their research field at the start of the project and plan for some flexibility in the project which allows for adaptations depending on the skills, ingenuity and interests of the mathematician. A realistic project plan is important - if things go well the outcomes will then exceed the expectations of both parties.

Project choice

We are learning that the greatest gains to both host and student occur when the project is a good match between the mathematician’s expectations and the project’s requirements. This is a knotty problem for prospective hosts, who may not have much experience with mathematicians, particularly since there is considerable variation in the expectations and desires of students. A few general principles do apply.

Mathematicians usually want to use their ingenuity and their skills. While spending a brief period early on sharing in the bench work to get the feel of it is probably worthwhile, this experience probably does not exercise either their skills or their ingenuity. If it is all they do, they may feel they have not made any significant contribution that a student in the field could not have made.

There will be students who want the experience of seeing the standard mathematical technology in operation. They will be well content to take a data set, apply standard technology and packages and admire the results. They will apply the technology intelligently and expedite publication of the work. This type of project is important experience for them: reassurance that there are employment opportunities outside of the obviously mathematical. It will not challenge their ingenuity. For such projects a host probably does not want a student suggesting that a totally different approach. The student again gets the satisfaction of a job completed, but again, the satisfaction of making a game changing contribution is not there.

There will also be students who are eager to challenge their ingenuity with real problems. These students will thrive on pitting their wits against problems that a host may have only vague ideas how to approach. It may be difficult to describe such problems clearly. One example which worked well, was of the form “we have heard about some new methods of data analysis…., here are some data sets, do the methods offer any improvement over standard methods?” In such projects, there is a higher risk of ending the project with a disappointing result (welcome to the world of real research), but the possibility of the thrill of actually using one’s mathematical wit to make an enduring contribution to something really useful is such that many mathematicians will happily take the gamble.


Thought needs to be given in advance as to the most efficient method of getting a mathematician up to speed in those aspects of the host’s field which are necessary. The obvious perhaps is worth stating: What a mathematician finds difficult is not what a researcher trained in the field might find difficult.

At the beginning of their projects, CMP students generally need to "get up to speed" in a new field in a short period. We've found that one of the best ways to make this work is to have a “Project Partner” (often a graduate student or postdoc) the CMP student can talk to an a regular basis (ideally daily) for the first few weeks of the project. Many of our most successful projects have involved such project partners, and their availability will be viewed as a positive when we review bursary applications.

Beginning with the most simplistic description, whether wikipedia articles or on-line courses from less ambitious universities is generally more efficient than reference to standard texts or course notes from Cambridge. The most efficient method by far is to tell the student what basic ideas are covered in a selection of suitable reading, give the student a chance to read through, and be available at her or his elbow to clarify any sticky points as she/he reads through. We do encourage host supervisors to designate a host partner for the project, exactly someone who can sit at the next desk and fill that role.

Working habits

Mathematical problems generally yield more readily to pulsed efforts: try hard for a short period to solve a problem or read an article, then drop it, do something else, then come back to it. As a result, we get used to working patterns which to the lab-based scientific community may seem frankly lazy. (We do get lazy at times, particularly when a problem is proving intractable; we drop it early and delay the return.) As a result, people get into habits of working late at night or early in the morning often in the comfort of their own rooms. Do make it clear at the interview what the lab’s working practice is. Students will get a lot merely from being in the environment, particularly if the environment includes group breaks for coffee, tea and lunch. The casual conversation about the weekend’s delights and disasters will facilitate asking the deeper questions which might lead to seriously good ideas.

In-person vs. remote working

In person projects are preferred, however, hosts and students may agree on one of three options to carry out projects: (i) on-site / in-person, (ii) a combination of in-person and remote (hybrid), (iii) remote projects.  This allows for maximum flexibility. 

Planning for a remote project

In addition to the logistical considerations relating to the student not being physically present with the host, the ideal situation will limit the possibility of intellectual isolation.  Our concern is that students are more likely to feel isolated due to the remote format. Strategies that have worked to prevent this in analogous contexts are having weekly virtual coffee breaks, inviting to the student to research presentations that may be related to their work, and organising regular meetings between the student and the host or members of the host’s group.  We envision that this may be especially important in the early phase of the project, when the student is getting up to speed with the background material.