At Shanghai Jiao Tong University they started their "league table" the Academic Ranking of World Universities [WP] to measure the gap between Chinese Universities and "world class" (mostly US) universities I was interested to get some idea of the difference between our School of Mathematics and other top mathematics departments in the United Kingdom. Since our formation from the merger of UMIST and the Victoria University on Manchester (VUM) in 2004 the School of Mathematics at Manchester has been on a generally upward trend, and while crude measures should be treated with extreme caution it helps us to get some idea of how we compare (for example on size and income). I was also interested in the reasons some of the newspaper league tables for university maths departments produce some results that are quite surprising relative to how we perceive research reputation of departments.
I was interested to note a survey by the Sunday Times of the opinions of headteachers about the top five universities for several subjects. The headteachers had this order for mathematics: Cambridge, Oxford, Imperial, Warwick, Bath. Lets see how this compares to some rankings using published data.
One starting point is the 2001 Research Assessment Exercise. Of course we did not exist in 2001 and at the time of writing the process of assessing the 2008 RAE has just begun. For the sake of comparison we can combine the UMIST and VUM entries, although I expect we have changed (upwards!) much more than most UK maths departments since 2001 so in most respects this gives a lower bound.
|University||Total Research Active Staff (FTE)||Weighted average grade by FTE in each unit. 5*=6, 3a=3.5,3b=3||Average grade over three UOA (taken as zero if no return)|
|University of Cambridge||114.5||6||6|
|University of Oxford||81.6||5.59||5.67|
|The University of Manchester (UMIST+VUM)||75.5||4.55||4.5|
|University of Leeds||58.25||5||5|
|Imperial College of Science, Technology and Medicine||54||5.84||5.67|
|University of Nottingham||50.9||5||5|
|University of Edinburgh||48||5.15||5|
|University of Bristol||44||5.75||5.67|
|University of Warwick||43.75||5.42||5.67|
|University of Durham||42||5.22||5|
The numbers of undergraduate maths students is harder to find in published data. However I have found the following:
As far as we can tell from this data Manchester has the biggest population of undergraduate mathematical sciences students (judged by the 2007 intake) by a very small margin over Warwick. Going by the 2001RAE figures for staff it seems unlikely that any other departments would make it in to the top six by size, but Leeds (about 500 total - see brochure), Nottingham (total approx 500 ) and Edinburgh have fairly large undergraduate populations.
On January 7th 2008 the table is as follows, MORE RECENT VERSION
These results should be taken with a very large hand full of salt. Of course they indicate some merit as at least getting a grant means that referees and panel members approved the proposal. Here are some caveats
Hinch, Huppert, Shepherd-Barron, Spiegelhalter, Pedley,Wills +etc
|Gowers is a Fields Medallist|
Ball, J. Ockendon, Silverman, Segal, Birch, Kirwan, James, Lyons
Heath-Brown, Hitchin, Donnelly, Trefethen
|Warwick||MacKay, Reid, Stewart, Preiss|
|Imperial||Donaldson, Hayman, Atkinson,||Donaldson is a Fields Medallist.|
|Manchester||Higham, Taylor, Wilkie||Paris is a Fellow of the British Academy
Buchstabber and Shiryaev are Corr. Memb. Russian Acad. Sci.
|Liverpool||Rees||Mazya is Member of the Royal Swedish Academy of Sciences|
Fields Medalist[WP] are very rare so not really useful for league tables. Probably more important taking a long view is that a department has a culture that will produce one. For example Donaldson and Atiya got their Fields Medals while at Oxford. That said the research culture of a department is likely to be improved by having one there.
It is good for ones research papers to get cited and ISI Highly Cited researchers are ones that have got cited a lot, an indication that their work is valued by other researchers. Some topics in mathematics, for example numerical analysis, seem to generate more citations than others. But maybe that means these areas are more useful anyway?
|University||Highly cited researchers|
|Oxford||Ball, Cox, Quillen, Silverman,Trefethen,|
|Cambridge||Clayton, Spiegelhalter, Fokas, Lickorish,|
|Manchester||Higham, Hammarling (hon post), Dongarra (fractional post)|
|King's College London||Davies|
More up to date information on entry requirements can be found on the UCAS web site, e.g. by a search for course code G100 (Maths). Here are some examples as of Jan 2008 (some are slightly more complicated than stated, follow links for more details). Most of the top universities do not use UCAS points tariff as their entry criterion, in England and Wales the grades on three A-levels is the usual standard. The top maths departments find that this is not sufficient to select on mathematical ability and use things such as STEP and AEA results, module grades, for example on the core mathematics modules C3 and C4, and Further maths A or AS grades. UCAS tariffs for students who are accepted may include things like A-level general studies that are often exluded from entry requirements, as well as stand-alone AS scores.
|Cambridge||AAA + STEP|
|Oxford||AAA (varies by college)|
A(M) B 3-STEP
|Bristol||A(M)AB||Bath||A(M),A,A or A(M),A,B|
|Manchester||A(M with AB in C3-4)AB|
|Nottingham||A(M)AB (A in FM if taken)|
|UCL||A(M),A,B(FM)||Durham||A(M) AB (FM at AS if not A2)|
So the whole there is still basically "COWI" Cambridge Oxford Warwick Imperial asking for three As and some, and then the next bunch who will let you get a B as long as you do well enough in maths. In contrast to the Times GUG based on 2001 entry requirement the current entry requirements are broadly in line with the other rankings..
The GUG is compiled by a consortium called Mayfield University Consultants, largely current or former university administrators, and the University of Sheffield. It seems this group used to be responsible for the Times Good University Guide, but have split from them. The Times GUG are now produced by Exeter Enterprises, owned by Exeter University.
|URL||Page rank||Cambridge www.maths.cam.ac.uk||Oxford www.maths.ox.ac.uk||7||Warwick www.maths.warwick.ac.uk||6||Imperial www.ma.ic.ac.uk||N/A||Bristol www.maths.bris.ac.uk||6||Manchester www.maths.manchester.ac.uk||6||Durham maths.dur.ac.uk||5||Leeds www.maths.leeds.ac.uk||6||Heriot Watt www.ma.hw.ac.uk||6||St Andrews www-maths.mcs.st-andrews.ac.uk||6||Southampton www.maths.soton.ac.uk||6||Birmingham www.mat.bham.ac.uk||6||UCL www.ucl.ac.uk/Mathematics||5||Aberdeen www.maths.abdn.ac.uk||5||Edinburgh www.maths.ed.ac.uk||6|
At the time of writing that does not look very interesting. Most of the reasonably sized maths departments at the time of writing (Jan 2006) have a Page rank of about 6, so it is currently not a very discriminating measure. A list of all maths departments in UK Universities is maintained at Heriot-Watt, if you want to check others. There are some quite respectable departments with Page rank zero. Perhaps because they changed their URL recently. In time there will no doubt be more useful tools to asses the impact of departments on line. Already Webometrics ranks Universities by the impact of their on line publications.
On number of citations no UK departments even made it in to the table! On the "impact" UK departments in the table were 9th Imperial, 11th Cambridge, 15th Oxford, 18th Warwick. Agreeing with the traditional rating as COWI being the top four (but in a different order). Of course many pinches of salt here needed as usual when interpreting citation data. That said it is certainly a good thing to write papers that other researchers cite.
I have recently notcied a paper by Bollen et al that suggests the use of something more like the Page Rank could be a better indicator of quality rather than popularity in networks of journal citations. No doubt such a thing will be implemented and if it is used, eg to allocate funding, people will start to optimise against that criterion. In mathematics citation based measures of the importance of work suffer from the effect that the importance of some mathematical result only shows a considerable time later. For example Fritz John's 1938 paper on the ultrahyperbolic equation had to wait half a century before it found use in 3D x-ray tomography, which had not been invented at the time he did the work.
|University||No. of Pubs in|
MSN in 2007
|St Andrews (several)*||40|
* St Andrews has seven institution codes 4-STAN-? for maths and stats departments so results may be inaccurate.
I have not yet got around to working out papers per individual, but you can do that approximately from the 2001 RAE figures.
The 2007 Lists of Top 10s includes the top 10 on a survey of employers. Out of the UK universities they list Cambridge 1st, Oxford 2nd, LSE 3rd, Manchester 5th and Imperial 8th. It is interesting that the UK does so well so there may be some bias. On the whole large companies concentrate their recruitment effort on a few (usually large) universities and this might be a useful figure for prospective students to choose a univerity within the UK. The scores are given for each university in the Top 200 Universities in the World list.
US universities slot in the gaps with Harvard 4th, MIT 5th and Stanford 6th. By contrast the table of top 10 citations per staff member contains no UK universities, 8 US and one from France and one from Switzerland. However this is not likely to be especially relevant score for mathematics.
There is an increasing tendency in Higher Education to employ "metrics",that is crude numerical values as a substitute for an analysis of quality. I think it is useful for academics and heads of maths departments especially to look at some of the above figures to try to understand if they have created an atmosphere in which excellent mathematics can be done, if they are applying for and being awarded a reasonable number of grants, if the work is getting published and if the academics get to be recognised as leaders in their field. From the point of view of students (undergraduate and postgraduate) and individual academic staff we would like to know if a department has a culture and "climate" in which we can achieve our mathematical potential, and to enjoy ourselves doing so. These are of course very difficult to quantify!
Please feel free to post comments, corrections etc, on this blog entry.
I also wrote some thoughts on advising prospective undergraduates on where to study mathematics in the uk
Bill Lionheart School of Mathematics University of Manchester. January 2008.