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Section III: Panelsí Criteria and Working Methods

3.15 Pure Mathematics, UoA 22

UoA Descriptor

3.15.1 The UoA includes: Group theory, Number Theory, General Algebra, Algebraic and Lie groups, Algebraic geometry, Topology, Geometric analysis, Linear analysis, Operator theory and operator algebras, Complex analysis, ODE and dynamical systems, PDE, Probability theory and stochastic analysis, Harmonic analysis, Mathematical logic, Combinatorics.

UoA Boundaries

3.15.2 The Panel expects that most submissions will fall within the above areas, but that it will also receive some submissions that fall outside them, for example, higher education mathematical pedagogic research and the history of mathematics.

3.15.3 Cross-referrals: the Panel anticipates that it may receive referrals from, and make them to, the following UoAs; Applied Mathematics (UoA 23), Statistics and Operational Research (UoA 24), Computer Science (UoA 25), History (UoA 59) and Education (UoA 68).


3.15.4 The Panel does not anticipate the need for any sub-panels.

Specialist Advice

3.15.5 The Panel will take specialist advice in the following circumstances:

  1. for submissions in any areas for which the Panel does not have the required expertise;
  2. to assist with the review of submissions where Panel members have a declared interest;
  3. in other cases where, in the professional judgement of the Panel, it would be of assistance in reaching decisions.

Interdisciplinary Research

3.15.6 Interdisciplinary work will be treated in the same way as other research output, with such items being referred to other appropriate Panels &/or specialist advisers for additional consideration.

Joint Submissions

3.15.7 The Panel will treat joint submissions as a single submission and assign a single grade.

Treatment of Evidence

3.15.8 The primary criterion of excellence used by the Panel is the quality of the research activity, as evidenced by the research output submitted.

3.15.9 Secondary indicators of excellence are:

  1. the extent of postgraduate research activity as indicated by the number of doctorates awarded relative to the number of research-active staff (RA 3a),
  2. evidence of esteem by external funders as indicated by research support (RA3b and RA4),
  3. evidence of the research vitality of the department,
  4. evidence of national and international research prestige of the department (RA5 and RA6).

3.15.10 For an institution to receive a 5* rating the Panel would expect to record a high score against each of the indicators.

3.15.11 In considering the research vitality of the department, the Panel will have regard, among other things, to access to regular seminars, visiting academics, general postgraduate activity, and the opportunities available for individuals to experience mathematical research culture in the broadest sense.

Research Output (RA2)

3.15.12 The Panel expects that the majority of submitted material will comprise research output published in traditional or electronic formats and that it may be in any of a number of forms, e.g., books, papers, articles, contributions to special volumes. It also anticipates receiving software related to research within the UoA boundaries. If software is submitted, clarification of its research implications should be given in the 'Other relevant details' field of RA2.

3.15.13 All forms of output will be assessed according to their research content. The international excellence of published research output will be determined by comparison with the standard of the leading research output in the area worldwide. The Panel will look for originality, depth, rigour, influence on the discipline and, where appropriate, relevance to users in making its assessment. The value of authoritative and carefully crafted review articles will be recognized.

3.15.14 Although the Panel's final view will take into account the overall volume of output submitted (in proportion to the number of research active staff), the number of items submitted by an individual will not, in itself, be a factor in assessing quality, in the sense that one or two substantial items of output may be of equal/higher quality than four minor items.

3.5.15 It is expected that the author who declares co-authored work will have made a substantial contribution to it. The Panel accepts that a co-authored paper may be returned more than once by the same department. However, departments may wish to submit such an article only once, as the submission of an additional output will give a wider picture of the research in the department.

3.15.16 The Panel will consider all the research submitted and, collectively, will examine in detail at least 50% of the items of research output cited in submissions. In undertaking the examination the Panel will sample across the full range of the research output, and will use the professional expert judgement of appropriate Panel members to identify which items of output are to be sampled.

3.15.17 The output must have existed in a publicly available form at the census date. Where this is not clear from the publication, the Panel will require evidence from the institution. Institutions may wish to bear this in mind, particularly when considering the submission of non-refereed output such as items placed on the World-Wide Web (WWW). For such material the Panel's reviewing process should not be regarded as a substitute for the refereeing process undertaken by recognised journals.

3.15.18 The Panel recognises that leading academic mathematicians publish in a wide variety of different formats and that output of high quality may appear in any of these. It will not, therefore, rank journals in themselves, but nevertheless, the high refereeing and editorial standards of a journal may be used as an indicator of the quality of the output it contains.

Research Students (RA3)

3.15.19 Account will be taken of the numbers of research students, research studentships and research-related higher degrees awarded relative to the number of research-active staff. The relative number of doctorates awarded will carry the greatest weight.

3.15.20 The Panel recognises that funding for research students may come from different sources, but will not distinguish between them. However, the ability to attract research students from outside the institution may be taken as evidence for research vitality.

External Research Income (RA4)

3.15.21 External research support will be used as one measure of peer judgement related to a department's research activity. The perceived rigour of the funding body's reviewing processes will be taken into account.

3.15.22 The Panel does, however, recognize that many pure mathematicians do outstanding work independently of external research support.


Research Structure and Environment

3.15.23 Where it is meaningful so to do, the Panel requests that staff included in RA1, RA2 and RA5 be listed by research areas/groups rather than as individuals.

3.15.24 The Panel wishes to know of other UoAs to which related work has been submitted, with information about any difficulties institutions have encountered in the fit between their own departmental structures and the UoA framework.

3.15.25 Institutions should explain the mechanisms and practices for promoting research and sustaining and developing an active and vital research culture, and should describe the nature and quality of the research infrastructure, including facilities for research students. The Panel will be looking for evidence of vitality in the research environment as indicated by access to regular seminars, postgraduate activities, etc.

3.15.26 If institutions wish to mention any arrangements in place for supporting inter-disciplinary or collaborative research, they should do so here. Similarly, institutions may wish to provide information on relationships with industry and commerce or other research users and, where appropriate, on the account taken of Government policy initiatives and objectives.

Staffing Policy

3.15.27 The Panel requests that the following information be provided:

  1. a description of arrangements for the development and support of the research work of staff;
  2. a description of arrangements in place for developing the research of younger and/or new researchers and for integrating them into a wider, supportive research culture;

and, if relevant:

  1. an explanation of the role and contribution of category A* staff who have joined the department;
  2. a commentary on how the departure of staff in categories A*, B and D has affected the strength, coherence and research culture of the department at the census date.

Research Strategy

3.15.28 The Panel will note with interest any information about the main objectives and activities in research planned for the next five years. However, it will not require any detailed elaboration on this, or on the 1996 research plans, unless there are particular points to which an institution wishes to draw attention.


3.15.29 Institutions may wish to submit a concise self-assessment.


Evidence of esteem

3.15.30 Institutions are invited to list, for each member of staff, up to four specific items which provide evidence of peer esteem. The following are examples:

  1. prizes and awards,
  2. invited lectures at international or national meetings
  3. research grants and studentships attached to the individual
  4. editorial board membership
  5. EPSRC College membership
  6. seminars at other institutions,

Individual Staff Circumstances

3.15.31 Institutions should note any circumstances relating to individual members of staff, which have significantly affected their contribution to the submission, for example, periods of sick leave, career breaks, engagement on long-term projects, major administrative responsibilities, parental leave.

Contributions by Non Research-active Staff

3.15.32 Institutions may also wish to discuss the relative contribution made to research by staff who have not been returned as research active.

Working methods

3.15.33 The Panel will not use a formulaic approach.

3.15.34 The overall process for reaching decisions will be iterative, with each submission being considered more than once during that process. Special care will be taken with submissions identified at some stage of the process as being on the borderline between ratings.


3.15.35 Before the first meeting panel members will familiarize themselves with all submissions and identify those areas within their fields of expertise.

3.15.36 Panel members will play no part in judging the quality of a submission from an institution in which they have a material interest and will withdraw from discussion of such an institution where it is appropriate to do so. Specialist advisers will be appointed to provide advice on those submissions in which Panel members have a declared interest.

3.15.37 At the first meeting, submissions for which

  1. specialist advice, or
  2. cross-referral

is considered necessary will be identified. The remainder of the submissions will be allocated to panel members, each submission being assigned to at least two Panel members, who will consider the profile of the department as a whole in preparation for further meetings. Discussion of anomalies in the submissions may also take place here.

3.15.38 Cross-referrals from the Panel will be forwarded to the UoA which the Panel considers most appropriate. Cross referrals received from other Panels will be considered by the most appropriate member(s) of the Panel, who will provide comments which will assist the referring UoA in making its decisions. Assessment of cross-referred work will normally include discussion at a meeting with at least one member of each panel.

3.15.39 At the second and subsequent meetings, each submission will be discussed taking into account the research output and the information provided in RA5 and RA6 and all other relevant information. These discussions will be led by the Panel members assigned to the submission at the first meeting. The full Panel, taking account of the specialist knowledge within and outside the Panel, will assess the research output of each individual, based on standards of international and national excellence and will then form a view on the overall quality of the research output of the department. The secondary indicators will then be considered and a preliminary overall rating will be determined, again by discussion within the Panel.

3.15.40 The Panel will hold as many meetings as are required to deal with each submission in a consistent and equitable manner.

3.15.41 At the final meetings all submissions will be reviewed and final ratings decided. Decisions will be reached by consensus within the Panel or, failing this, by a simple majority vote.

3.15.42 In interpreting the rating points, the Panel will have regard to the descriptions provided in the Guidance on Submissions (RAE 2/99).

3.15.43 International excellence in research output will be determined by comparison with the standards of the leading research output in the area worldwide. In deciding whether such a standard of excellence has been reached the Panel will use its professional expertise and judgement.

3.15.44 Other standards will be defined with reference to the standard of international excellence.

3.15.45 The Panel proposes that up to 5 non-UK based experts be appointed from pure mathematicians with experience considerably beyond their own institution (e.g. former or current heads of learned societies or research institutes who have acquired an overview of a particular constituency of overseas mathematicians). They will be asked to offer an opinion on the Panel's setting and application of the benchmark standard of international excellence by reference to all submissions provisionally given a rating of 5* and 5 and a sample of those rated 4.

Last updated 17 April 2000

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