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Faculty of Mathematics

 

Project partners:

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 someone (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.

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 their 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.

I personally would encourage prospective hosts to take that gamble as well if their project is at an early stage where a potentially radical rethink might be welcome.

Preparation:

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.

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 intractible; 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.