I spent Thursday, Friday and Saturday of last week at the University of Warwick, at the Young Researchers in Mathematics conference. This is the third year that this conference has taken place; the original initiative was taken by Cambridge students, and the meeting was held there on its first two outings. Now it has gone national; next year it will be in Bristol. There were no Queen Mary students at this year’s meeting; I will do my best to ensure that this is not the case next year!

It was a great conference, with a real buzz. There were about 200 young researchers (mostly PhD students) in a wide range of areas; of the talks, the largest groups were statistics/probability, mathematical physics, and combinatorics. The contributed talks were 40 minutes; this gave speakers the luxury of explaining the background to their work, and almost all that I heard took advantage of this. The passion and excitement they obviously felt about their subject were quite unlike what you get at a normal conference.

I had been invited to give a talk, so I spoke about *Synchronization*, including some speculations about the probability that a random automaton with two transitions is synchronizing (as in my last posting on the symmetric group). But I thought that an important part of earning my expenses was to be available to talk to anyone who wanted to come and have a chat; and indeed, I did quite a bit of talking, on sum-free sets, generating groups by transversals of subgroups, etc., as well as about how to find a post-doc position, the philosophy of mathematics, and other such important matters, to various people. I recommended books ranging from Steven Finch’s *Mathematical Constants* to Robert M. Pirsig’s *Zen and the Art of Motorcycle Maintenance*.

I also went to many of the contributed talks, some in group theory and combinatorics, others ranging more widely (differential geometry and mathematical physics, among other things). The standard of the talks was very high indeed, and I learned a lot, from the basic idea behind parametrized complexity, to applications of species to statistical mechanics, to the use of octonions in the search for an 8-dimensional solution to the Yang–Mills equation, to the story of non-periodic tilings.

The conference poster, programme, etc., featured some eye-catching artwork. Inside the front cover were the logos of the sponsors. Among them was MSOR (the Mathematics, Statistics and OR Network of the Higher Education Academy). As I reported last year, MSOR is a victim of the cuts; their funding ends in July this year, though they have applied for transitional funding until December. But they had a table at the meeting, being worked by Peter Rowlett, and he gave me a copy of the current issue of their newsletter, *MSOR Connections*.

Apart from an article by Vivien Easson (who has the office next to mine) on the MoreMathsGrads scheme (an initiative for widening participation), it contained an iteresting and provocative analysis of the National Student Survey data by Paul Hewson, a statistician at Plymouth. I’d like to say a bit about this.

Hewson approached the task in a somewhat more intelligent fashion than the processing of our internal student questionnaires which I reported recently. The NSS questionnaire contains a number of statements on which the students are invited to respond on a five-point scale “Strongly disagree | Disagree | Neither agree nor disagree | Agree | Strongly agree”. These were aggregated into a binary variable taking the value 0 for the first three responses and 1 for the last two (slightly questionable, I would have thought, but the rationale is that the last two questions indicate some agreement with the statement).

These responses were modelled as Bernoulli random variables (i.e. tosses of a biassed coin) where the parameter (the probability of getting 1) depends on three explanatory variables: individual student characteristics (age, gender, tariff, residence), institution, and subject, and the coefficients estimated by Bayesian methods. He remarks that individual characteristics have a big effect: for example, females are more likely to complete the questionnaire than males. He says, “This is an interesting topic which deserves closer attention.” (Our department is in trouble for low response rate: should we gender-bias our admissions?)

The main thrust of the article is the subject comparisons. Degree courses have been aggregated into 19 areas, of which one is “Mathematical sciences”.

Unsurprisingly, on Question 22, “Overall, I am satisfied with the quality of the course”, mathematical sciences is slap bang in the middle. But other questions throw up more interesting results. On Question 6, “Assessment arrangements and marking have been fair”, mathematical sciences come out clearly on top. Well, either your answer is right or it is wrong, and there is not much to argue about, yes? On Question 19, “The course has helped me present myself with confidence”, mathematical sciences is bottom by a very wide margin. I suppose that in most subjects, students can form opinions and learn to expound them; in mathematics, this possibility hardly exists.

But the one I found most depressing was Question 21, “As a result of the course, I feel confident in tackling unfamiliar problems”. Now I think most mathematicians believe that problem-solving is the key transferable skill which our students learn. But the student responses put us about two-thirds of the way down the list.

Of course, this is only a survey, and has massive methodological problems, as Hewson points out. But as he says, “The least that can be said about the NSS is that it effects[sic] the league table position of subject groups within Universities which may well be a consideration when prospective students are selecting a University.”

Food for thought.

I think it’s food for thought as well. I can find 20 billion things wrong with the survey, but these random effects seem to fit the kind of story people construct (like maths assessment is objective) – and they have implications. Are maths students nervous of handling unfamiliar problems because we have been keeping them very nicely constrained with the problems they do work.

By the way, you’re right to argue about the binary classification (done this way for computational convenience)- I have since reworked it as an ordinal logistic problem but that still hides the fact that there are surprisingly large number of people who just tick 5.5.5.5.5 for everything.