London School of Economics and Political Science Department of ...

London School of Economics and Political ScienceDepartment of MathematicsDepartmental StatementTLAC Review of Educational Provision, January 2006ContentsIntroduction Page 21. Issues arising from the 2002 review2. Academic portfolio and teaching methods3. Assessment4. Mechanisms for review, monitoring, quality assuranceand quality enhancement5. Tutorial provision and student support6. MPhil/PhD provision7. Service teaching8. Conclusions9. Appendix APage 2Page 6Page 13Page 20Page 23Page 28Page 31Page 32Page 33

IntroductionThe Department of Mathematics is responsible for the BSc degree in Mathematics and Economics, theMSc in Applicable Mathematics, and a doctoral programme leading to the MPhil/PhD for studentswith research interests falling within the expertise of members of the Department. In addition, theDepartment provides students taking other degrees (particularly Economics, Accounting and Finance,Actuarial Science, Business Mathematics and Statistics, Management) with courses designed toprovide them with the necessary mathematical background. As a result, the Department is heavilyinvolved with undergraduate teaching: of the 1375 first-year undergraduates in the School in 2004-05,approximately 800 took at least one module in mathematics.The Department was externally reviewed under QAA (together with Statistics) in 1999. There was anInternal Review of the Mathematics Department in 2002, which forms the starting point for the currentprocess.We should say at the outset that in the context of UK Mathematics Departments, we are rather unusual.We are smaller relative to the size of our institution, and cover a different range of topics, with anemphasis on discrete mathematics and mathematics related to the social sciences (such as gametheory). This role is reflected in our research interests, in the degrees offered (specifically no singlesubjectMathematics degree), and in our course offerings. We specifically do not attempt to offereducational provision covering the full spectrum of mathematics. However it should be noted that,even given our acceptance of a specialized role, we believe that we are still rather too small, relative tothe size of our commitment, to provide appropriate mathematical grounding to a major institution of thesocial sciences.The most significant innovation in the Department since 2002 is the setting up of our MSc degree inApplicable Mathematics, which ran for the first time in 2004-05. It is proving remarkably successful,and will be discussed more fully below. We see this degree as a significant step towards a substantialprogramme of graduate training at both MSc level and PhD level, based on the acknowledged expertiseof the existing staff. We are now recruiting good numbers of students at both levels.1. Issues arising from the 2002 Review1.1 The distinctive features of the DepartmentOnce upon a time the LSE had a small group of mathematicians who were members of a large anddiffuse Department of Statistical and Mathematical Sciences. The Department of Mathematics was setup in 1995, with the intention of providing the School with a clearly defined focus for its mathematicalactivities. The Department aims to provide a foundation that matches the best international standardsin the mathematical community, with particular emphasis on those areas of Mathematics that areclosely related to the Social Sciences. The Review in 2002 commended us for the progress that hadbeen made in that direction.2

Following the APRC Review in 2003, we appointed three additional staff: Dr Malwina Luczak, whoworks at the interface between probability theory and discrete mathematics, Dr Amol Sasane, whoworks on optimal control theory, and Dr Robert Simon, who is a mathematical game theorist. Theseappointments are both complementary and supplementary to the existing expertise within theDepartment. All three new staff have fitted in well, and have made excellent contributions to theDepartment.The resources for these new posts were expected to come mainly from the MSc fee income, withrelatively little growth in undergraduate numbers. In fact, the undergraduate numbers continue toincrease 1 and the Department feels that it is still underfunded in comparison with larger Departments.In particular, large Departments are better able to spread the workload associated with innovations,such as the development of new courses. The inauguration of five new taught MSc half-units in 2004-05 and two more in 2005-06 has placed a heavy burden on our staff. We have also taken on asubstantial Summer commitment - the supervision of the compulsory full-unit MSc dissertations. Thishas affected all our staff, not just the new appointees. One of our concerns is to ensure that thededication shown by all concerned is seen to be recognized, rather than exploited.At MSc level we have established the following new courses (all new since the last Review).MA407 Algorithms and ComputationMA408 Discrete Mathematics and ComplexityMA409 Continuous Time OptimizationMA410 Information Communication and CryptographyMA411 Probability and MeasureMA412 Functional Analysis and its ApplicationsMA413 Games of Incomplete InformationMA498 Dissertation in Mathematics (which includes a series of dissertation seminars)With these courses, and a few pre-existing ones, we feel that we have constructed a programme that isboth distinctive and of high mathematical quality. Several LSE undergraduates have gone on to takeour MSc as a ‘fourth year’, and the recruitment from overseas has been gratifying. The numbersentering the course were 17 in 2004 (against a target of 10) and 27 in 2005 (against a target of 20).1.2 Quality assurance mechanismsThe 2002 Review commented favourably on our mechanisms, such as the Annual Course Review. Thisis a half-day meeting in the Summer Term, attended by all staff, at which our courses and programmesare discussed in detail in a 5-year cycle. We maintain our commitment to quality assurance, whileremaining distrustful of bogus ‘box-ticking’ procedures, which, in our view, merely avoid frank andopen discussion of problems.Further details of our quality assurance procedures are discussed in Section 4.1 Appendix A shows how our undergraduate teaching commitment has changed since the time of the last review.3

1.3 Other matters arising from the 2002 ReviewIn this section we report on what we have done in response to other matters mentioned in the 2002Review. The references are to the relevant sections of the Review Document. Our plans for the futureare covered later (section 2.9) in this document.Class teaching (2.11, 2.22, 2.23)Our service teaching commitment, already heavy, has recently increased 2 , mainly as a result of twodecisions by other departments. The Economics Department now requires all BSc Economics students(and those on other programmes with a large Economics element) to take our full unit MA100Mathematical Methods, rather than the half-unit MA107. The Statistics Department now recommendsthat all BSc Actuarial Science students take MA103 Introduction to Abstract Mathematics in their firstyear (it was previously only a second-year option).In the light of this heavy and increasing commitment, we have been building up over many years agroup of highly-qualified and dedicated class teachers. It should not be thought that these are all‘graduate teaching assistants’. Some are indeed research students, for which class teaching is seen as auseful part of their training (as endorsed by the School), but many of our class teachers havesignificantly more experience of teaching, at LSE and elsewhere, and many have a PhD. This session,11 of our 22 part-time class teachers are ‘guest teachers’ rather than graduate teaching assistants, and10 of our part-time teachers have a PhD. In the Michaelmas term of this session, for example, over halfof our class teaching conducted by part-time teachers is being carried out by those with PhDs. Weemploy doctoral students for the more basic courses, and in some cases for teaching topics specificallyrelated to their research (such as Game Theory).Doctoral progamme (3.1-3.10)We have been very conscious of the need to increase the number of doctoral students, and we haveused much of our outside funds to support such students. The new MSc has already provided oneresearch student, and we confidently expect to recruit more from that source. As a result of thesemeasures the number is currently 10, which is roughly equal to the number of staff. (At the time of thelast Review, we had 5 research students.) This level is fairly typical in mathematics across the sector.Information for students regarding options (2.7: Recommendation 5.2 (a) (i))In 2002 a few students seemed to be unaware of the full range of options open to them in the third-yearof the Mathematics and Economics degrees. This information is now available in our own BScMathematics and Economics Handbook, on the departmental website, and of course in the LSECalendar. Additionally, at the end of the Lent term, the Departmental Tutor provides “optionsdocuments” (one for each year) which are distributed to all first and second-year students. Inconnection with this, the Departmental Tutor organizes a meeting to explain the degree structure andgives detailed information about all options. The introduction of LSE for You has also helped studentsunderstand the options available to them.2 See Appendix A4

Learning support materials (2.10)The last Review commended the Department for its extensive provision of learning support materials.We have made increasing use of course websites since then, and continue to provide other forms ofsupporting materials. Course materials are distributed in hard copy, and are posted on the website. Thematerials would typically include: course notes, exercise sheets, and model answers to the exercises.For some courses, lecture slides and Maple worksheets are also posted. We have not used WebCT,because we are not convinced that it will be as useful in Mathematics courses as it might be in coursesin other disciplines, and not as useful as our websites.Diagnostic test (2.12; Recommendation 5.2 (a) (ii))In the mathematical community it is widely believed that the standard of A-level examinations hasfallen, particularly in the last 10-15 years. On the other hand, the official view is that standards havebeen improving gradually. In order to monitor the situation the Department decided to introduce ashort diagnostic test for each intake of students. The test was first used in 2001, and the results showedlittle significant change up to the 2003 intake. However the 2004 results were significantly worse, andthis appears to be reflected in the somewhat lower first-year examination performance of this cohort.The results for the 2005 entry are better, but may be distorted by a larger-than-usual number of studentswho did not take the test. We administer the same test each year in order to be able to makemeaningful comparisons over time.We are currently reviewing the way in which the test is managed, and the purposes for which it mightbe used. Currently only the aggregate results have been used formally. The completed test papers arereturned to individual students by their personal tutors, who may recommend remedial action, but thereis no other follow-up.Use of mathematical software packages (2.33; Recommendation 5.2 (a) (iii))We believe that familiarity with a mathematical software package, such as MAPLE, is an integral partof any degree in Mathematics. The Department has been developing its use of MAPLE, which wasfirst introduced on the School network in 2000/01. Use of MAPLE is well-established in MA100Mathematical Methods, where students meet examples from multivariate calculus and linear algebra.The classes in week 5 of this course take place in computer rooms, and MAPLE exercises are set ashomework. Solutions to exercises are often provided in the form of MAPLE worksheets(http://www.maths.lse.ac.uk/Courses/MA100/index.html). It has been our policy to spread the use ofMAPLE throughout the curriculum, and ways of doing this are regularly discussed at DepartmentalMeetings and Annual Course Reviews. We reported in our last Review document some of the stepsmade towards this. Dr. Michele Harvey carried out a project on “Dissemination of MAPLE as aTeaching and Learning Aid” under a grant from the (then) Teaching and Learning Development Office.Four graduate students were employed to adapt the MAPLE base to the specific requirements ofseveral of our courses and a general tutorial for MAPLE was produced and put on the Department’swebsite (http://www.maths.lse.ac.uk/Courses/MA100/maths_tutorial.mws). There have been a numberof developments since then. A tutorial on the use of MAPLE as a programming language has beendeveloped and placed on the Department’s website(http://www.maths.lse.ac.uk/Courses/Tut2prog.mws). Use of MAPLE has been extended into othercourses. Currently, a number of courses (such as MA103, MA200, MA207, MA209, MA303, MA315)5

involve the use of MAPLE for solving exercises, or have examination questions expressed in MAPLEterminology. There are plans to introduce MAPLE into additional courses, such as MA305.The specialist third-year course MA314 (Theory of Algorithms) contains an introduction toprogramming in JAVA, and students are required to produce working versions of basic algorithms.A similar approach is followed in the core MSc course MA407 Algorithms and Computation.MSc students make extensive use of a range of software in preparing their dissertations. Last session,many of the dissertations contained significant amounts of programming and computational work.2. Academic portfolio and teaching methods2.1 IntroductionAs indicated in the Introduction at the very start of this document, the academic provision in thedepartment -- the BSc Mathematics and Economics, the MSc Applicable Mathematics, and serviceteaching -- is quite distinctive in the UK context.The Department has well-functioning course review mechanisms (described later, in Section 4) and wehave been involved in significant amounts of course updating and curricular innovation in recent years.Not least, we have started the new MSc programme (the Department’s first Masters programme) andhave developed brand new graduate courses for it. Although this has been helped in part by theappointment of new staff, the work involved in developing eight new courses, the administrative workinvolved in setting up the programme, and the supervision of MSc students and their dissertations hasgenerated an enormous amount of work for all members of the department. (This has been said earlier,but is worth emphasising.) This pressure has come at a time when we have also experienced an increasein undergraduate teaching loads (see Appendix A) and an overall increase in student:staff ratio (seeFigure 1).The department has an unusually high student:staff ratio. The SSR figures provided to us by thePlanning Office, for years 2001/2 to 2004/5 inclusive, and the estimated SSR for 2005/6, are, in eachyear, the highest among all departments in the School. For example, our SSR in 2004/5 was 26.5,against an overall School figure of 16.8 (and an average across departments/institutes of 16.03). SeeFigure 1.6

Figure 1: student:staff ratios 2001/2 to 2004/528.0026.0024.0022.0020.0018.00Maths SSRSchool SSRAverage departmentalSSR16.0014.002001/02 2002/03 2003/04 2004/052.2 BSc Mathematics and EconomicsAdmissions and aims of the degreeThe Mathematics and Economics degree programme is highly successful. It attracts a very large, andincreasing, number of highly-qualified applicants (over 10 applications per place). Given thecompetition for places, we recently increased the standard offer from ABB to AAB with A inMathematics. It should be noted, however, that this standard offer does not reflect the entrancequalifications of those who eventually register: given the competition, incoming students generallyhave better grades than this.The BSc Mathematics and Economics aims, among other things, to provide students with a knowledgeof mathematics, economics, and the interaction between the two. The comments of external examinersattest to its success, and the QAA Subject Review Report commented that “A good balance betweenflexibility of choice and coherence characterises the degree”.Structure of the degree and courses offeredIn the first year of the BSc Mathematics and Economics, students must take MA100 MathematicalMethods, ST102 Elementary Statistical Theory and EC102 Economics B and are strongly encouragedto take MA103 Introduction to Abstract Mathematics. MA100 is a fairly demanding post A-levelcourse in Calculus and Linear Algebra. ST102 and EC102 are introductory, university-level, courses inStatistics and Economics. MA103 is an introduction to proof, number theory, analysis and abstractalgebra. Strictly speaking, MA103 can be deferred to the second year, but it creates more flexibility for7

students in the second and third year if they take it in the first year. However, the fact that theregulations permit MA103 to be taken in the second year enables students from related degrees, such asBusiness Mathematics and Statistics, or Economics, as well as students from the External Programme,to enter the degree in Year 2. The general principle underlying the second and third years of the degreeis that students should continue to take courses in both mathematics and economics, concentrating onthe parts of each subject most closely related to the other. For instance, one popular third year option isthe full-unit MA300 Game Theory, the second half of which is taught by the Economics Department:this is a subject that would not normally be taught as part of a traditional mathematics curriculum.The compulsory “core” courses in the second and third years are made up of three half-units ofmathematics and two full units of economics: MA200 Further Mathematical Methods (Calculus),MA201 Further Mathematical Methods (Linear Algebra), MA203 Real Analysis, EC202Microeconomic Principles II, and EC319 Mathematical Economics. Beyond this, students have areasonable variety of choice, including the option of taking one unit outside Mathematics andEconomics, with the approval of the Departmental Tutor.The regulations for the degree are formally reviewed by the Mathematics and Economics Departmentsas part of our 5-year cycle of reviews; the next such review will take place later this session.A list of courses taught in the Department, with numbers of students, appears at the end of thedocument, in Appendix A.There is a sequence of “methods” courses, designed for our own students but also popular with others(and compulsory on some other degree programmes): this starts with the full-unit MA100, which leadson to the half-units MA200 and MA201. These courses are in turn pre-requisites for some third yearcourses in mathematics and statistics.The “abstract” mathematics sequence of courses begins with MA103. This is a pre-requisite, or at leasthighly advisable, for many more advanced options, notably MA203, MA208 and MA209.Although our third year courses often follow on from the abstract courses, many are applicationsoriented.Given the nature of the degree programme, we do not offer some courses which one mightexpect to find in a traditional Mathematics degree. Instead we provide courses which take a rigorousapproach to the subject, but are closer to the application areas students experience in other courses.2.3 Service teachingThe Department carries out an enormous amount of teaching to students not registered on our BScMathematics and Economics programme.The course MA100 Mathematical Methods currently has around 560 students (compared with around360 at the time of our last review), and is a compulsory course for first years in most degrees that havea significant Economics component.There are four methods courses we teach that are not available to our own students. These are MA106(a half-unit course for students who have done little or no post-GCSE mathematics), MA110 (a fullunitcourse for students who have done little or no post-GCSE mathematics ), MA107 (a half-unit8

course in mathematics for degrees that don’t require the full MA100 unit, such as Accounting andFinance, Management, and Management Sciences) and MA207 (a follow-on half-unit course forstudents who took MA107 and want to study more mathematics). We recently took on the teaching ofMA110: previously it was taught by the Economics department as EC110. The first half of MA110 isequivalent to MA106, a course that is usually taken in combination with a corresponding statistics halfunitcourse. Current plans, however, are for a full unit Statistics course along the same lines as MA110to be developed, and for students on the Accounting and Finance degree to take MA110 and the newStatistics unit. Therefore, many students currently taking the half-unit course MA106 will instead takethe full unit MA110, increasing our service teaching load a little further. (MA106 may not be needed infuture years, but since it is essentially the first half of MA110, there are no real savings to be gainedshould it be withdrawn.)Our advanced methods courses (such as MA200 and MA201, currently with around 240 students) arealso popular as options for students on other degree programmes (and compulsory on BMS andActuarial Science). The third year Game Theory course (MA300/MA301, with around 150 students) isamong the largest third year courses in the school, drawing students who are interested in gametheoreticaspects of economic theory. Some of our more specialized courses (in particular, MA203 RealAnalysis, MA208 Optimisation Theory, MA209 Differential Equations, and the Game Theory coursesagain) attract significant numbers of General Course students. Those students often comment that theirhome universities don’t offer these kinds of courses, which teach rigorous mathematics related toapplications in the social sciences.Service teaching will be discussed further in Section 7, alongside related matters such as part-timeteaching. Section 4 also discusses quality management of service teaching.2.4 MSc Applicable MathematicsIntroductionIn the 2004/5 session, the Department started a new MSc programme in Applicable Mathematics. Apartfrom some participation in the now-defunct intercollegiate London MSc in Mathematics and a smallcontribution to teaching students on the King’s College MSc in Information Processing and NeuralNetworks, this is the Department’s first foray into Masters teaching. As noted above, the work involvedhas been keenly felt by all our staff, but we are pleased that the new degree programme has been asuccess.We intended to take 10 students in 2004/5, 20 in 2005/6 and 30 thereafter. Both intakes so far havebeen above the target registration figures and we are confident that we will be able to recruit 30 goodstudents each year from next session. What may not be realised in the LSE context is that, for a Mastersprogramme in Mathematics, we have a very large number of students. Information about the sizes ofMSc programmes in many other institutions is not readily available, but this is one of the largest UKMathematics MSc programmes that we know of. (For example, the MSc in Modern Applications ofMathematics at the University of Bath, which has 10 EPSRC funded studentship places and which isregarded as very successful, has 14 students.)9

The programme has attracted some very talented students. In the first year, 8 of the 17 students haveobtained the MSc with distinction. Some very good dissertations have been written. One student haspresented the results of his dissertation at an international workshop. We are encouraging the beststudents to produce research reports for inclusion in the CDAM research report series and we have alsoestablished a prize for the best dissertation, in memory of Haya Freedman, who was a member of theLSE mathematics (sub)department from its inception until her retirement.Aims of the degreeThe MSc in Applicable Mathematics draws together traditional and modern mathematical techniques ina variety of social science ‘contexts’. Students are offered a range of mathematics options, and also theopportunity to take a social science module, such as Economics, Finance, Government, OperationalResearch, or Statistics, where they can see in practice the mathematics they are learning, and achievegreater understanding of social sciences. The skills and knowledge gained are then brought together toprepare an in-depth dissertation on a mathematical topic.It is intended that the MSc opens up to students a wide range of potential careers: in finance, business,government, and industry. It also provides a base for further studies at research level. The programmeis intended to have broad appeal. For pure and applied mathematicians, it provides an opportunity toincrease their knowledge of mathematics, particularly (depending on options chosen) in discretemathematics, algorithms, game theory, and probability and to make themselves more ‘marketable’ byadding some social science aspects to their knowledge and skills base. For social scientists with verystrong quantitative backgrounds, it provides an opportunity to add to and improve their understandingof the mathematics behind much of social science.Structure of the programmeReflecting the emphasis on computational algorithms and techniques, there is one core taught course, ahalf-unit, MA407 Algorithms and Computation. All students must also undertake a full unitDissertation in Mathematics and must take a half-unit course in Game Theory or Discrete Mathematics.They take two or three additional half-units in Mathematics and up to one unit from outside thedepartment (various options in Economics, Finance, Operational Research, Statistics and Governmentbeing listed explicitly in the programme regulations).Dissertation and dissertation seminarsAll MSc students write a full-unit dissertation on some mathematical topic. They are given advice andsupport by individual supervisors, but, also, before that in the Dissertation Seminar MA498. In theseseminars, potential supervisors will describe the projects that they are willing to supervise, and answerquestions about them. We also have talks by experts on various aspects of dissertation writing such aslibrary research, mathematical word processing, mathematical writing, and IT. There is time forstudents to confer individually with the teacher responsible for the course about their choice of project.10

2.5 MPhil/PhD MathematicsLike almost all UK Mathematics PhD programmes, the MPhil/PhD programme in our department doesnot, formally, contain any taught course elements. However, students are encouraged to attend Masterscourses in our department and elsewhere (including mathematics courses at other institutions of theUniversity of London). The development of the MSc has been particularly useful here, providing arange of in-house courses that reflect the research interests of the staff, and which are therefore highlyrelevant to the PhD students. As commented on earlier in this document, the number of PhD students inthe department is now quite appropriate for a department with our number of staff, though we continueto encourage talented applicants interested in working in our areas of research. Funding for PhDstudents has been available from the EPSRC through its doctoral training allowance scheme, thoughmuch of the funding we have provided has come from the Department’s outside funds (generatedlargely as a result of staff involvement in the External Programme).More information on our MPhil/PhD programme is to be found in Section 6 below.2.6 Curricular innovationThe Department has been particularly innovative in curricular matters in recent years. Primarily, thishas been through the introduction of eight new courses for the MSc. But there has, and continues to be,much on-going improvement and updating of undergraduate courses. Developments are discussedformally at departmental meetings and our Annual Course Review, and at a more informal level amongstaff who teach related courses.Some mathematics at undergraduate level, especially abstract mathematics, is ‘classical’ and essentiallythe same material is (and must be) taught from year to year. However, even here there is scope forinnovations and fresh approaches to the courses, and in teaching style and supporting materials. This isencouraged by the fact that, since all of our undergraduate courses can be taught by more than onemember of staff, there is a fair amount of circulation of core undergraduate courses among lecturers.Examples include the re-branding and re-development of the course MA305 Control Theory asOptimisation in Function Spaces. Courses that focus on application, or have large parts that do, areoften updated as new applications or techniques are developed.At the time of our last review, we had just introduced the new courses MA209 Differential Equationsand MA315 Algebra and its Applications. These have proven to be successful and popular.New courses that have been introduced since the last Review are:MA407 Algorithms and ComputationMA408 Discrete Mathematics and ComplexityMA409 Continuous Time OptimizationMA410 Information Communication and CryptographyMA411 Probability and MeasureMA412 Functional Analysis and its ApplicationsMA413 Games of Incomplete InformationMA498 Dissertation in MathematicsMA110 Basic Quantitative Methods11

2.7 Course deliveryTeachingCourses in the department, as at LSE generally, are usually taught in (sometimes very large) lectures,supplemented by small classes. Our department imposes an upper limit of 15 students in all itsundergraduate classes. Teaching is usually supported by fairly extensive lecture notes that have beenprepared by the lecturing staff. Lecture notes material is generally handed out in lectures, although inthe very largest courses it is produced at the start of the course as part of a study pack (for whichstudents pay a small amount as a contribution towards the reprographics costs). In most cases, allhandouts are also available on the web (see http://www.maths.lse.ac.uk/Courses).Use of ICTLectures and classes are augmented by the use of ICT, chiefly, for our department, in the use ofwebsites for the delivery of learning materials. We have not used WebCT, because we are notconvinced that it will be as useful in Mathematics courses as it might be in courses in other disciplines.Most of what we might wish to achieve can be more easily realised through the use of websites. Themain webpage for each course is maintained by the Departmental Manager, but “Course Materials”pages are the responsibility of the individual lecturers. Course websites will generally contain courseinformation, reading lists, lecture notes, lecture slides (where appropriate), class assignments, solutionsto class assignments, links to other useful websites, and past examination papers. For some courses,such as MA100 Mathematical Methods, Maple tutorials and workbooks, and videos of Extra Examplessessions, are available.As discussed in Section 1.3, the Department makes increasing use of MAPLE and Java in its courses.At their induction, MSc students are provided with a CD containing the software they will need fortheir courses and for preparing their dissertations.Library and IT supportWe are supported in the provision of learning materials by the library and IT services. The library hassufficient copies of core texts, and the access to electronic journals is of particular help to our researchstudents and to MSc students in their dissertation research. The standard build for PCs in the Schoolnow includes many of the software packages that our students use, such as MAPLE, Java, MikTeX andScientific Word. Students can also buy a copy of MAPLE for personal use from IT services for only£10.2.8 Course suspension practiceFrom time to time, courses need to be dropped, while new ones are added. Reasons for change include:developments in modern mathematics, new areas of application of mathematics, change in studentdemand, and staff changes. Since the last review, the course MA312 Convexity and Geometry has beenremoved because too few students expressed an interest in taking it. All of our undergraduate coursesand most of our graduate courses can be taught by more than one member of staff, so there is usually12

no need to suspend a course because of sabbatical leave, unless this would result in unusually highteaching loads.2.9 Future developmentsWe aim to continue to provide innovative and up-to-date courses to specialist students, and to meet theneeds of other students through our service teaching courses.Immediate plans, as mentioned above, include an increase in the number of students on the MSc inApplicable Mathematics.The School has already earmarked funds for us to appoint a chair and a lectureship in FinancialMathematics and we hope to make these appointments soon. This will enable us to develop an MScprogramme in the financial mathematics area (complementing rather than duplicating existingprovision within the departments of Accounting and Finance and Statistics).We are also interested in investigating new MSc ventures, probably joint with other departments, toincrease our presence on the graduate teaching side. One possible area in which we could expand ourprovision is in the Algorithms and Theoretical Computer Science area, in which the department hasresearch expertise. We already provide some courses and supervise research students in this area.EPSRC's International Reviews in Computer Science and in Mathematics both identified the interfacebetween Discrete Mathematics and Theoretical Computer Science as an area that should bestrengthened, and there is some possibility that EPSRC will dedicate resources in some form to this.Our Department, perhaps in collaboration with others, would be well placed to take advantage of this.3. Assessment3.1 IntroductionNormal assessment practices in Mathematics are rather different from those in many of the otherdisciplines taught in the School. Our external examiners have continually endorsed the way we set andmark examinations and have verified that where we divert from what is normal practice in otherdisciplines at LSE (for example, blind double marking), we are justified in doing so.3.2 Formative assessmentClassworkFor all of our courses, problems are assigned weekly and these form the basis for discussion in classes.Although the amount of work we require our students to hand in is well above the LSE norm, ourpractices are in line with mathematics courses in other UK institutions. We expect class teachers tomark work that has been handed in on time, so as to give rapid and informative feedback on students’performance: students clearly value this, and tutees complain to us about courses in other departmentswhere this is not common practice. Solutions are discussed in class and usually distributed or postedon course websites. These assignments do not count towards the final, summative, assessment. Rather,13

they are to be considered as part of the learning process, regular working through of problems being anessential part of any mathematics course.Class assignments are generally graded on a letter-based scale from VG (very good) to P (poor).Students are advised of our classwork grading procedures on our website athttp://www.maths.lse.ac.uk/grading.html. One reason for using qualitative grades rather than numericalones is that our previous experience had suggested that students would often regard marks obtained forclasswork as a predictor of their examination mark, which is not necessarily valid because classworkquestions are, for sound pedagogical reasons, often different from exam questions, and because theyare not answered under the same conditions as exam questions. (Generally, a classwork assignment willcontain some questions that are easier than exam questions, to enable the student to develop proficiencyin concepts or techniques, whereas exam-based summative assessment is designed to assess theacquisition of such proficiency after it has been developed in classwork.) We now explicitly warnstudents against inferring too strong a linkage between classwork grades and exam performance. Theclass grading document states that ‘classwork grades reflect performance on a particular piece of workdone in particular circumstances. They are intended to give students an indication of their progress, butthey do not necessarily predict performance in the final examination’.More important than the grades given to a piece of classwork are the comments made by markers onthe student’s work. This is an essential part of our feedback mechanisms: it is important for a student toknow why their answer or approach to a question is incorrect. In the training session we provide fornew class teachers (as part of TLC’s training course), the importance of such written feedback ishighlighted. In our own survey of class teachers (see Section 4), we specifically check with studentsthat such written feedback is being given.Past or mock examinationsFor all existing courses, past examination papers are available either as an integral part of lecture notes(as in MA100 from this year), or on course websites, and are available for purchase (for a nominal feeto offset copying costs) from the Departmental office. Solutions to recent years’ papers are alsoavailable. Students are strongly encouraged to try to answer the questions before looking at thesolutions and, for this reason, we often make solutions available only later in the academic year.Should the content of an existing course be changed substantially (perhaps because the course is beingtaught by someone new, with a different approach, or to adapt to new developments in the coursesubject), then any major differences will be highlighted and mock examination questions set ifappropriate. For new courses, mock examination papers are provided.Past examination papers often form the basis for revision lectures in the summer term, where particularquestions may be worked through and the method of answering them discussed in some detail.3.3 Summative assessmentAssessment in our undergraduate mathematics courses is entirely by means of Summer Termexaminations. For some of the taught graduate courses, there are also elements of assessed coursework.Several have a 10% coursework element, and one, MA407 Algorithms and Computation, has a 30%coursework (programming) element.14

Marking of examinationsAll procedural aspects of our examination procedures are set out in the document MathematicsDepartment Examination Procedures 2005/6, which is to be read in conjunction with the LSEdocument Instructions for Examiners for Taught Programmes. Our document standardises manyaspects of our examination papers. For example, half unit papers (two hour exams) always have 5-6questions, while full unit papers (three hour exams) have 8-10. The rubric on the cover sheet follows auniform style which allows only minor variation. This standardization provides transparency forstudents (and for our external examiners).For each examination, solutions are provided for externals to see, along with an indication of what is“bookwork” and whether students will have seen similar problems before. Each paper is inspectedinternally by a “checker”, and then again at an Internal Scrutiny Meeting, before being sent to theexternal examiners. Comments from the external examiners are considered at the External ScrutinyMeeting. For each course, external examiners are also sent a list of learning outcomes to be assessedin the examination, together with an indication of where in each exam paper each outcome is assessedand they are provided with a draft marking scheme indicating the weight to be given to each part ofeach question. (The intended learning outcomes for each course are also made available to students incourse websites and supporting materials.)It is perhaps worth describing what goes on in the marking process, since it does not conform to blinddouble marking. The exam is set by the lecturer(s), and they will normally also be the person who firstmarks the exam script, having drawn up a very detailed marking scheme. The marking is then checkedby a second examiner, who will verify that everything has been done properly. Their job includesmaking sure that all the work really has been marked, and that the marks have been added up correctly.On large courses, things are necessarily done a little differently, with several people involved in themarking. (Here, to ensure consistency of marking, each individual marker is entirely responsible forfirst marking specified questions on every paper.)Once the marking is complete, the two examiners then agree a formula for converting raw script marksto final marks (a ‘curve’). It is normal practice in mathematics courses throughout the sector to scaleraw exam marks into final reported grades, sometimes changing marks quite significantly. This is inorder to assign marks fairly should the exam turn out to have been more difficult, or easier, thanintended. A drawback is that, if severe scaling is seen as standard practice, it is very difficult to conveyto students what is required of them (for instance) to pass the examination. We decided that we wouldalways set examination papers with the intention of doing little or no scaling to the raw marks, and thatif in fact substantial scaling did prove necessary, this would be discussed extensively with the externalexaminers before being agreed upon, and would be treated as a matter to be remedied in subsequentyears.By its nature, Mathematics is a subject in which very precise marking schemes can be specified, andthis is why it is unnecessary for a second marker to re-mark exams independently of the first marker’smarks. We have been open with students and external examiners about our procedures. Externalexaminers have consistently endorsed our procedures as being appropriate and in keeping with thenorms for mathematical subjects. We have been granted exemption from ‘blind double marking’ by theUndergraduate Studies Subcommittee and the Graduate Studies Subcommittee. However, we havebeen told by GSSC that, each year, we will have to make a separate application for such exemption.15

We would much prefer that the School understood our position and respected our disciplinary normsand did not require us to do this on an annual basis.MSc dissertation and assessed courseworkThe MSc handbook contains documents, ‘Assessed coursework’ and ‘Assessment of your dissertation’outlining how we approach the assessment of MSc coursework and the full-unit dissertation. Here,students are told what it is that examiners are looking for and are given advice about such matters asproper citation of sources.Dissertations are marked independently by two examiners. (Here, we adhere to blind double marking.)Each dissertation is assessed according to the following criteria: analysis, content, presentation,organization, critical judgement, and originality. The two examiners then meet to discuss theirindependent reports and arrive at an agreed mark.MSc coursework is marked in the same way as written exams. The work is set, checked, assigned to thestudents, then marked and checked.Advice given to students about examinationsStudents naturally wish to know in advance what their exams will be like, as well as what is expectedof them. We have published on our website a document Examinations in Mathematics(http://www.maths.lse.ac.uk/examinations_in_mathematics.html) which gives students information on,among other things, how mathematics exams are marked and graded, and what sorts of things theexaminers are looking for. As mentioned above, we provide, in printed form and/or on the website, theexamination paper and solutions from previous years to all our courses. When courses change or newcourses are introduced, we provide additional sample questions, or a full specimen examination paper.Past examination papers often form the basis of revision lectures.MSc students are given extensive advice about preparing their dissertations in the course MA498, andin particular in the document ‘Dissertation Instructions for Candidates’, available on the MA498website at http://www.maths.lse.ac.uk/Courses/MA498/dissertation_instructions.pdf. The MSchandbook also contains a substantial amount of information on what examiners are looking for.Comments from external examinersOur external examiners have unhesitatingly declared themselves satisfied with our assessmentprocedures and their outcomes and have declared our standards to be comparable to those in their owninstitutions. Some quotes from external examiners’ reports and examination sub-board minutes serveto demonstrate this:“The top students achieve a very high standard, whilst the weaker students also get a lot out of thecourses. […] The courses, quite properly, combine rigorous and analytical mathematics with interestingapplications. Some courses are highly innovative and stimulating.” (Professor Robert Curtis, Universityof Birmingham, external examiner’s report, 2000)16

“once again the examination system worked extremely well” (Professor Milne Anderson, UCL, externalexaminer’s report, 2003)“Professor Anderson, who is in his last year as External Examiner, stated that the MathematicsDepartment had been very competent and efficient in its procedures. All exams arrived on time,comments were dealt with properly and he had been kept informed of this, and the marking had beenaccurate and effective. He congratulated the Department for this.’’ (minutes of the 2003 BSc sub-boardmeeting)“the academic standards are generally high. I also liked the apparent degree of integration between themathematics and economics components.” (Professor Mark Roberts, Surrey University, externalexaminer’s report 2004)“[Professor Roberts] felt that the academic standards reflected in the papers were pleasingly high.’’(minutes of 2004 BSc sub-board)“Professor Thomason [of the University of Cambridge] said that in his view the Department had beenvery careful and proper in its procedures, with lots of attention paid to setting and marking.’’ (minutes ofthe MSc exam board meeting, October 2005)“The whole operation seems to me to have been well planned and the outcome successful.” (ProfessorThomason, commenting on the examinations process for the MSc in his report, 2005)3.4 Student achievementStudent achievement in individual coursesTo put statistics about our students’ achievements in context, it is worth quoting the QAA subjectbenchmark statement for Mathematics, Statistics and Operational Research (MSOR) 3 (paragraph5.1.8):“For many types of assessment in MSOR, the variation in marks achieved by students of undoubtedcommitment is typically greater than in other subject areas. This is particularly so in writtenexaminations and tests. Experience is that, on the one hand, perfect or near-perfect solutions fullydeserving of very high marks arise more often than in most other subjects; while on the other hand, theproblem-solving nature of MSOR can lead to weaker students, and sometimes not-so-weak students,having difficulty even starting some questions. It is therefore not unusual for marks in MSORassessments to span the full mark range, and this would be a correct representation of the relative valuesof the students’ work. ”We find it possible to set exams so that the threshold for a pass is not too far from 34% and that for afirst is about 70%; however it is true that, in mathematics courses in general, we see relatively manyexam scripts deserving of what the rest of the School would see as exceptionally high marks, but on theother hand relatively many that cannot realistically be deemed to pass the exam. In this light, it isentirely to be expected that mathematics courses should appear regularly on lists of courses withrelatively high failure rates and/or with a relatively high percentage of first class marks, and this hasindeed been the case.3 http://www.qaa.ac.uk/academicinfrastructure/benchmark/honours/mathematics.asp#117

Undergraduate degree classificationsThe distribution of marks in mathematical subjects manifests itself also in degree classifications. Wehave awarded significantly more first class degrees, proportionally, than the School as a whole, and, atthe same time, we have awarded a greater proportion of degrees classified as lower second or below. Itis generally the case, across the HE sector, that a greater proportion of firsts are awarded in themathematical sciences than in the other areas that the LSE focuses on. Making comparisons betweeninstitutions across the sector is difficult because different institutions can have very differentclassification algorithms. However, data on degree classifications does seem to suggest that, generally,a different sort of distribution of classifications arises in mathematical subjects than in others. This isdemonstrated in Figure 2, below.A recurring concern that has been raised in many of our external examiners’ reports relates to theclassification system in place at the undergraduate level. They have suggested that it is often generous,and allows students to graduate with a higher classification than they might elsewhere when theirmarks are averaged. Any method of aggregating module marks into a degree classification is bound tohave its deficiencies, and making comparisons between institutions and disciplines is very difficult.The School has set up a working group to look at the classification guidelines, and a member of ourdepartment has agreed to be on that group. More generally, the whole process of degree classification isunder consideration at national level by the Measuring and Recording Student Achievement SteeringGroup chaired by Professor Robert Burgess.Figure 2.Degrees awarded nationally 2001/2-2003/4 (% in each class)[Source: HESA]6050403020100Social, Economic, PoliticalStudies/Social Studies1 2A 2B 3 P7.9 49.5 33.3 5.8 3.5Mathematical Sciences 25.4 33.3 26 12.2 3.1Almost all of our advanced courses are half-units, so that the degree classification process involves agood deal of pairing of half-unit courses. The rules for degree classification give a rigid mechanism for18

how this pairing takes place, though this has been queried by externals and students from time to time.It became apparent to us that the rules had some undesirable unintended consequences (namely, that alower mark in one course could in fact result in a paradoxical improvement in classification: detailsavailable on request!). To rectify this, the department (with the support of the Statistics department)made a proposal for an amendment of the regulations to the 17 March 2004 USSC meeting, and thiswas accepted.Undergraduate progression and completionIt has recently been drawn to our attention that the BSc Mathematics and Economics has a lower rate ofcompletion in three years than many of the other degree programmes at the School. We are unsure ofthe reasons for this. One possibility is that students encounter some difficulty in making the transitionfrom A-level mathematics (or equivalent) to the more abstract and rigorous university-levelmathematics. This, and the decline in preparedness of A-level students, is something we have beenaware of and have taken steps to ameliorate. We have introduced Extra Examples sessions for MA100(and, also, for the other first year methods courses). Given extra resources, we could provide additionalteaching support. We send students, once they have been accepted but before registration, some reviewexercises for them to practice, and we have a diagnostic test that alerts tutors to students who may notbe as well prepared as we would wish. We have also recently increased the entrance requirements forthe degree. Additionally, the LSE for You system enables us more easily to monitor students’ progress(assuming that class grades have been entered promptly), so that potential difficulties can be spottedearly. During Michaelmas Term we also send out a request to all class teachers in ST102, MA100 andMA103 who teach our first year students, asking them to alert us to any students they think are havingdifficulty coping with the courses.It is, of course, regrettable that some of our students do not proceed as we would wish. Mathematicalcourses build upon each other and there is clear intellectual progression in the degree, and for thisreason the department does not generally recommend that students who have failed to meet thestandard progression requirements be permitted into the next year of the programme. Our experience,and student feedback, has indicated that students often subsequently perform quite well after a year as aprivate re-sit candidate or as a part-time student and they often, in hindsight, see that year as quiteuseful.MSc degree outcomesThe MSc ran for the first time in 2004/5, so we have not been provided with a statistical analysis ofresults. However, we are pleased with the outcomes of our assessments. The classifications obtainedare as follows:NumberDistinction 8Merit 3Pass 3Fail 1Incomplete 1Withdrawn 1TOTAL 1719

3.5 Feedback on formative and summative assessmentAs mentioned above, feedback on classwork is given both in the form of grades and, moresignificantly, written comments, and all students have access to class teachers in their office hours toask for further guidance and feedback. Although classwork questions are not always the same sort ofquestion that a student would encounter in an exam (since, for one thing, the latter will generallyinclude some ‘bookwork’), parts of exam questions will generally be similar in nature to somequestions that have been assigned for class.Consistent with the Academic Board’s policy on feedback on assessed work, we do not generallyprovide explicit individual feedback on final exams. In large part, this is because it is simply notpossible logistically to offer such feedback given the high numbers of students on many of our courses.However, we think that the feedback on formative assessment (which is weekly for our courses),together with revision lectures and the information we provide about past examinations, preparesstudents adequately for the final exam. But we are aware that students would often value guidance onhow questions should have been answered, in the exam they have just taken, not just in previous years’exams. For that reason, at a recent departmental meeting, we decided that, in order to provide studentswith some feedback on the mathematics examinations they have just sat, we would consider makingsolutions available immediately (rather than in the course of the following session).4. Mechanisms for review, monitoring, quality assurance and quality enhancementCourse review and monitoring has recently been raised as an important issue in the School. Ourdepartment has long had a systematic approach to the review and monitoring of its courses andmaintenance and enhancement of teaching quality. Important aspects of this are: the Annual CourseReview; the Staff/Student Liaison Committees; clear lines of communication between SSLC andDepartmental meetings; extensive staff involvement in Quality issues; peer observation of teaching;support for class teachers; student questionnaires (our own and the School’s).Annual Course ReviewThere is an annual meeting of the entire Department in Summer Term, typically lasting two to threehours, at which reviews of our curriculum take place, and where all our courses are evaluated in asystematic way. The Department operates a 5-year cycle of reviews of its degrees and all of itsindividual courses. Modifications to existing degrees and courses are discussed and agreed, and topicssuch as “first year courses” and “portfolio of third year courses” are also contained within the cycle, toallow for a periodic wide-ranging discussion of new initiatives that the Department might wish topursue, and/or courses that might be discontinued. That this works well is demonstrated by the degreeof curricular innovation that has taken place. It is our standard practice to solicit student views aboutcourses that are being reviewed, and this is found to be informative, particularly by the teachersinvolved with the course. The Mathematics and Economics degree has been reviewed fully, incollaboration with the Economics department, and it is due to be reviewed again this session.Responsibility for the Business Mathematics and Statistics degree has passed to the Statisticsdepartment, but we have a BMS point of contact who will participate in any reviews of that degree.Our Annual Course Review last session also provided an opportunity for us to look back on the firstyear of the new MSc in Applicable Mathematics. For example, one discussion (minute 3(b) of the20

12.05.05 ACR) concerned the possibility of getting students to undertake some preparatory work onJava prior to starting the programme. This was something that the first intake of students had suggested(at an SSLC on 11.11.04, minute 3) would be useful. As a result, incoming students were sent somepreparatory materials for them to work on and some suggestions for reading over the summer beforestarting the programme. It appears that the students who have done the preliminary Java exercisesdefinitely have fewer difficulties than last year, but there is still a great disparity in students’programming abilities because of their differing backgrounds.Monitoring of coursesWe are aware that the development of procedures for monitoring is an important emerging issue at theSchool. We have had, for several years now, procedures by which individual course outcomes areanalysed and discussed openly in a meeting of the whole Department. Each year, statisticalinformation concerning performance in each of our courses is presented to a Departmental meeting andwe seek explanations from lecturers for any unusual distribution of marks, such as an unusually highfailure rate, for example. We also present external examiners’ reports to Departmental meetings, anddiscuss these fully.Staff/student liaison committeesThe department has two SSLCs: one for BSc Mathematics and Economics students and another forgraduate students (MSc and MPhil/PhD). Students are invited to suggest agenda items for the meetingahead of time, and are reminded of the names and email addresses of their year representatives. Theagenda is circulated to all students and staff by email, along with the minutes of the previous meeting.Minutes are distributed soon after the meeting, where possible with updates on responses or actionstaken. Proposed changes to the curriculum are discussed at SSLC meetings. Minutes of SSLCmeetings are discussed at Departmental meetings, so that points are not lost. One valuable feature ofthe ME SSLC meetings is that a member of the Economics Department is invited. As all students onthe degree are tutored in the Mathematics Department, this is a useful formal forum for dialoguebetween them and the Economics Department.Staff involvement in Quality issuesMost members of academic staff in the department are involved to some extent in quality managementissues (over and above those concerned with the courses they teach). For one thing, our departmentdoes not have a separate Teaching Committee consisting only of some subset of the staff. Therefore, allmatters related to teaching are discussed openly by the full department, in departmental meetings and inthe Annual Course Review. For instance, we try to plan teaching assignments well in advance, so thatthere is as little disruption as possible due to staff sabbaticals. As already noted, matters raised at SSLCmeetings and at School committees are also discussed at departmental meetings.One of the administrative roles in the department is that of Quality Officer. It has been useful to havethis as a specified job, and it has evolved since we introduced it in 1999. The Quality officer’s remit,generally, is to advise the Convener on all aspects of the Department's work that affect the quality ofteaching and learning, and to chair the Annual Course Review. Much of the work in monitoring and21

enhancing quality is, however, distributed among the staff in the department, as part of specificadministrative roles. The Class Teaching Officer (possibly with the Convener) deals with the results ofsurveys of class teachers and any problems highlighted by these or the observations of class teachers.The Departmental Manager arranges the schedule of teaching observations, in which all staffparticipate. The Departmental Tutor is responsible for the quality of the undergraduate tutorial system.The MSc Programme Director and Doctoral Programme Director have responsibility for quality on theMSc and MPhil/PhD. We also have a designated Teaching and Learning Centre liaison Officer, anEqual Opportunities Officer, and a Library and IT Services Liaison Officer. Quality management andenhancement is therefore deeply embedded in the department.Staff handbookMuch of the information that academic staff need to know about the School’s and the Department’sprocedures, many connected with maintaining and enhancing quality, is provided in the StaffHandbook. The handbook provides helpful information and guidance to new members of staff in theDepartment about many of the procedures and practices of the LSE and the Mathematics Department.It also serves as one-stop-shop for most of the Mathematics Department’s main documents, and istherefore useful to all Departmental Staff.Observations of teachingWe instituted a scheme for peer observation of teaching in 1999/2000, and extended this to coverobservation of occasional teachers by staff in the following year. This was partly in response to theQAA Review Team’s comment that the quality of our class teaching was “variable”. Our initialexperience of peer observation was mostly positive; those conducting the observations generally foundit to be of more benefit than those being observed. The system we now operate is that all teachers inthe Department are observed every two years, except that new teachers are observed in their first termof teaching and again a year later. (In this context, it is perhaps worth stressing that there areconsiderably more occasional teachers in the Department than there are permanent members of staff.)We cannot point to any instances where observations of teaching have unearthed anything other thanminor deficiencies, but it has been useful to be aware of these. In one instance, for example, a newclass teacher was observed and it was decided (after consultation with Liz Barnett, Director of theTeaching and Learning Centre) that that teacher would be better deployed on a different sort ofmathematics course, and we have now done this. In another instance, as a result of an observation, anew class teacher was invited to observe a class in the same course taught by a more experiencedteacher. Generally, our observation scheme enables us to be more confident than we have beenpreviously that those teaching in the Department are doing so to a high standard.Surveys of Class TeachingThe School conducts its own surveys of student opinion regarding occasional teachers in theMichaelmas Term; we have found this to be of limited use, mostly because the results have not alwaysreached us in time to take action for the start of Lent term. Accordingly, we conduct our own smallscalesurvey, in week 7 of Michaelmas term, of new class teachers and also of those who have beenteaching for us but who are now teaching a course new to them. This is distributed via the classes, andis designed to be very quick to complete. Most of the questions are designed to ensure that the teachers22

are meeting our requirements (which are somewhat different from the School as a whole, especially asregards the marking and returning of weekly exercises); we do also ask one simple question about thebenefit students derive from the class teaching, and allow students to write comments. We are able toprocess the information in our Departmental Office in time to give feedback to teachers before the endof term. Any instances where there are a significant number of negative comments are followed up bythe Class Teaching Officer.Support for part-time teachersThe Teaching and Learning Centre is well aware that what is expected of class teachers in quantitativesubjects is different from the School norm. Accordingly, separate induction sessions have been set upfor teachers in these subjects, including one session (on classes and assessment of classwork)conducted by members of the Mathematics and Statistics Departments. The induction programme iscompulsory for new class teachers and as a whole has been very well-received by teachers who havetaken it. A permanent member of the academic staff in the department acts as Class Teaching Officer.He or she is responsible for hiring new class teachers, for helping with their induction, and forproviding guidance and monitoring. All class teachers in the department are given a copy of the ClassTeachers’ Handbook. This comprehensive booklet brings together several documents that we used toprovide separately; in particular the “Code of Practice” which has been developed over several years.The main purposes of the Handbook are to collect in an accessible form the most important informationabout what the Department does, and to set out how we view class teaching, what we expect of classteachers, and what they can expect of lecturers.5. Tutorial provision and student supportInformation given to students pre-registrationWhen students have been accepted onto the BSc programme, we send them a welcome pack in additionto what the School sends them. This consists of a welcoming letter, information on the Inductionmeeting, some review exercises (for MA100) indicating what they should know by way of preparation,and information on the Cumberland Lodge trip. (http://www.maths.lse.ac.uk/maths-econ1.html#Pos )Incoming MSc students are also sent a welcome back from the department, which contains awelcoming letter, information on Induction and registration, some suggestions for preliminary reading,and detailed information on the structure of the programme and the courses within it. This informationis also on the departmental website at http://www.maths.lse.ac.uk/MSc_new_arrivals.html.Induction of new studentsThe Department holds Inductions for its new students on the BSc and MSc in the week beforeMichaelmas Term teaching begins. These provide an informal environment in which new students canmeet the staff of the Department, and we can give them important information about the Department,the tutorial system and their degree. We also encourage student mentors to attend the BSc induction. Atthe induction meetings, BSc students are given information about their lecture timetable, informationon their first year courses and lists of who to contact regarding any questions or concerns they mayhave. MSc students are given short descriptions of each of the mathematics courses on offer, by those23

teaching them, and are provided with software they will need during their course of study (such asmathematical typesetting software and Java).In the days following these Inductions (but still before teaching begins) students have individualmeetings with their Personal Tutor. Among the items that tutors are advised to discuss are: generalwell-being (including housing and financial situation), course choices, preferred manner of contact,organization of tutorial meetings. For each student, tutors keep a standardized “log-sheet” in whichdates of meeting and specific items that have been discussed are noted. These log-sheets also providevaluable information when there is a change in tutor.Student handbooksThe Department produces special programme-specific Student Handbooks (for the BSc, MSc andMPhil/PhD), and, for the BSc and MSc, these are distributed at the Inductions. These Handbookscontain lots of useful information that we hope will help settle the students in (such as maps of LSE,locations of places to eat, etc) as well as important information about the degree they are taking. Theyare also available on the Department’s website (at http://www.maths.lse.ac.uk/studyinfo.html).Diagnostic test and additional supportAs described in Section 1.3, we conduct a ‘diagnostic test’, the results of which are returned toindividual students by their personal tutors. Tutors are then alerted to potential difficulties thosestudents might have, and they may recommend remedial action, but there is no other follow-up.All first year mathematics methods courses now have Extra Examples sessions designed to augmentlectures and classes and to provide students with further advice on tackling problems.Cumberland LodgeOur first-year BSc ME students and the MSc students are encouraged to attend a 2 day orientationsession at Cumberland Lodge in the October or Novemer of their first year. The purpose of this is tohelp students get to know each other and also to give them the opportunity to meet their lecturers inmore relaxed surroundings. This is achieved in a number of ways, including small group sessions,where students are brought together for fun activities mixed with more serious discussions, and also bytalks on topics related to mathematics, but on more general topics than they might find in their courses.At the end of the event we hand out a feedback questionnaire. This has a very high response rate andshows the event to be extremely popular.Orientation seminarsThe department organises occasional ‘orientation seminars’ for our first year Mathematics andEconomics students. In previous years, jointly with Statistics, we organised a programme of suchseminars and required new students in Mathematics and Economics, Actuarial Science and BusinessMathematics and Statistics to attend. However, after consultation with the students, it was thoughtbetter to organise such seminars specifically for ME students, and to do so on an ad-hoc basis. Theseminars will usually include one on careers, one on study skills (especially as related to mathematics),and some from alumni who share their experiences of work or further study with the students.24

Undergraduate tutorial supportEach student registered to the Mathematics Department is allocated a personal tutor, in accordance withthe School’s regulations. Our policy is that where possible a student has at most two tutors during theirtime at LSE, and most students keep the same tutor for the full 3-year period. All academic membersof staff and the 2/3 FTE instructor act as personal tutors. Each of these has an approximately equalnumber of tutees, with the part-time instructor taking half that amount. (This session, each member ofstaff has around 26 tutees, this figure including MSc and General Course students.) We also try to giveeach tutor a mix of students from different years and from the two degrees. The tutorial system isoverseen by the Departmental Tutor, currently Dr. Jan van den Heuvel. He has additional office hoursspecifically to see students in this capacity, although students must make an appointment for these viathe Undergraduate Course Coordinator, Jackie Everid. She asks students why they want to see theDepartmental Tutor, and hence can prepare documentation that makes these visits more efficient, butdoes also advise students when other parts of the LSE are more suitable for their particular concern.The Departmental Tutor sends advisory emails to all tutors, informing them of new developments andreminding them when they need to invite students for a tutorial visit. The Departmental Tutor alsoreports regularly to the Departmental Meetings.Generally, tutors meet with their tutees at least twice a term. (Tutors meet first year students three timesin their first term.) The Undergraduate Course Coordinator sends emails to all tutees reminding themto see their tutors, and follows this up with additional reminders, phonecalls, and letters if necessary.The LSE for You system enables us to monitor students’ progress (assuming that class grades havebeen entered promptly). During Michaelmas Term we also send out a request to all class teachers inST102, MA100 and MA103 who teach our first year students asking them to alert us to any studentsthey think are having difficulty coping with the courses.Option Choice GuidanceWe produce leaflets for first and second year students on each degree regarding their choice of optionsin the subsequent year. A meeting is also held, at which the degree regulations and special regulationsregarding outside options are explained in detail. The introduction of LSE for You has made the courseselection procedure easier, and it perhaps makes the regulations clearer to students. Tutors discussstudent course choices with their tutees.Advice and support for transfer studentsWe always have a few students in each year who decide that university mathematics is not for them.The idea that mathematics provides a rigorous way of thinking about real problems, based on formaldefinitions and proofs, is not familiar to many entrants. Thus we expect to see transfers from ME to(for instance) Economics or Business Mathematics and Statistics (BMS). Since most of the first yearcourses in the ME degree are compulsory or options in those degrees, such transfers are quite feasiblefor the students concerned. Equally, we receive students who switch to ME from Actuarial Science orBMS, something that is relatively straightforward as these programmes have very similar first years.We additionally have isolated students from degrees such as Economics who are interested in doingmore mathematics after the first year. We usually try to accommodate this at the cost of them having25

somewhat fewer options in later years. Every year there are a couple of students who were accepted fora completely different degree, but who, between the time of applying to the LSE and the actual startingdate, realise that their real interests lie in mathematics and economics, and who ask for a transfer beforethey even start a degree programme.A more recent development is a rising interest from General Course students to transfer into the thirdyear of the ME degree. If possible, such transfers are always made conditional on good exam results inthe LSE exams taken at the end of the General Course year. It usually also involves a careful selectionof courses for the third year to design a total programme comparable with the “normal” ME students.All requests for transfer into the degrees are individually dealt with by the Departmental Tutor. Forearly first year students, he usually consults the Admissions Tutor to assist in assessing the informationcontained in the student’s file. The Departmental Tutor also ensures that possible transfer students areaware of the regulations of the degree, pointing out that the structure is much more rigid andchallenging than in many other degree programmes. Students who go ahead with a transfer are ingeneral well-motivated and obtain excellent results. In the last couple of years, more students havetransferred into the ME degree than out of it.MSc tutorial and supervision supportAll MSc students are assigned a member of staff who acts as their tutor and meets them on a regularbasis. Members of the academic staff will offer dissertation topics that they are willing to supervise andthey speak about these in the seminar MA498. This provides an opportunity for students to discoverwhat kinds of dissertation topic they might be interested in and to choose their project and dissertationsupervisor (usually after further, more detailed, discussion with the member of staff). The supervisorwill monitor progress on a continuing basis and provide appropriate guidance as the work on thedissertation proceeds. The Programme Director can also be consulted on any matter by students.Support for PhD studentsThis is discussed in Section 6.SSLC meetings: undergraduate and graduateAs mentioned above, the department has two SSLCs: one for Mathematics and Economics students andanother for graduate students (MSc and MPhil/PhD). This provides a forum for students to raise issuesof concern, and the minutes of these meetings and actions taken are discussed fully in Departmentalmeetings. (More information on how these committees work can be found earlier in this document.)Study skills supportOn our website we provide a document offering advice to students on the specific topic of studying formathematics courses (http://www.maths.lse.ac.uk/studyskills.html) and one of the Orientation Seminarswe run for our first year students (usually conducted jointly by a member of the MathematicsDepartment and the Director of the Teaching and Learning Centre) also covers much of this material.Additionally, the Teaching and Learning Centre provides opportunities for students to improve their26

study skills, for example through its one-to-one sessions and its Academic and ProfessionalDevelopment Programme. Our BSc Handbook also gives some advice on how to study mathematics.CareersThe Department organises several events at which careers guidance is provided, including anOrientation seminar. In addition students are regularly emailed information about career opportunities,and we provide some useful links in the Careers section of our web pages for students(http://www.maths.lse.ac.uk/students.html#Careers).Although a large proportion of students decide to go into the financial sector, students from our degreeshave gone onto a wide variety of careers, including consultancy, school teaching, student politics, andeven the church. A large number of our students also proceed to graduate study, in all sorts of areas,from mathematics, economics, finance, to law and gender studies.Alumni relations and eventsLast session, with helpful support from the Office of Development and Alumni Relations, theDepartment organised its first alumni get-together. The event took place in the Senior Common Roomat LSE on 27 th April. The Convener of Mathematics welcomed everyone to the event, and as drinks andcanapés were served, the Department's Alumni Events Coordinator outlined what he hoped theMathematics Department could do for its alumni, and described the services that the School is able toprovide to its former students. The evening was a great success and there were representatives fromabout 10 different graduation years going back as far as 1985, with the ‘class of 2001’ best represented.Further similar events are planned in the future and we have also recently established an Alumniwebsite (http://www.maths.lse.ac.uk/Alumni/).Another important aspect of alumni relations, particularly for our current students, is that some of ourgraduates help provide advice to existing students by speaking about their careers or further study inthe Orientation seminars.Study roomsOne area of student support in which the Department feels that its students are let down by the Schoolis that we no longer have a study room for our undergraduate students. We did have a study room in2002 and this was, moreover, when we had fewer students. According to the 2002 Review team report,‘The students made it clear that they appreciated the [study] room as a resource and felt that it hadhelped to integrate the student body into a cohesive whole. It also provided opportunities forcollaborative learning for all students and for first years to seek advice and guidance form their peers onmathematical problems, courses and even careers. ……The Review team would like to suggest that the Estates Office and Accommodation Committeeshould work closely with the Department to see if space can be provided for a study room of adequatesize wihin the Department or as close as possible.’The lack of a study room is a matter that is raised at many SSLC meetings. During the summer term(from week 5) onwards, we have made our own arrangements to help provide study space for our27

students. Our Undergraduate Course Coordinator has booked rooms for our students to study in and hasemailed them to let them know of this. But such ad-hoc arrangements are unsatisfactory. We do have astudy room (joint with Statistics) for MSc students, but it is not sufficient in space or in IT facilities.Recently our space for PhD students has become rather cramped also.Homework Help SessionsAdditional support for undergraduate students is provided by their peers, through the mentoringscheme, but also through Homework help sessions run by the LSE Mathematics and Statistics studentsociety. These take place weekly and are announced in the first year mathematics lectures.Equal OpportunitiesThe Department has an Equal Opportunities Officer, who, among other things, conducted an on-linesurvey of our students last session. The results of the survey were positive, indicating that students hadreceived equal treatment.6. MPhil/PhD provisionIntroductionThe Department offers a non-taught MPhil/PhD in Mathematics for students who already havedeveloped an interest in one of our research specialisations, usually either discrete mathematics orgame theory. Students with only a general interest in mathematics are discouraged from applying.Exceptional applicants are encouraged to apply for financial support through the EPSRC or the School.We also made a policy decision several years ago to support research students from the Department’soutside funds (mainly generated as a result of staff participation in the External Programme). Thedecisions about which students to fund (whether from EPSRC or our Outside funds) are made in thedepartment by a small committee, once applicants have completed an application form.MPhil/PhD programmeOur research students are not required to take any taught courses, although they are encouraged toattend some of our courses. The establishment of the MSc in Applicable Mathematics has proven veryuseful in several ways to our research students. It enables them to attend a range of lecture courses thatreflect the research interests of the staff, and hence are either highly relevant to the PhD students or areuseful in broadening their mathematical education. The presence of a sizeable cohort of MSc students,and the informal links that arise between them and the research students, also helps to foster a betterenvironment for the research student. Research students are expected to attend our weekly departmentalresearch seminar in Discrete and Applicable Mathematics. We also have an informal workshop,primarily organised by a research student, that is attended by staff and research students. Theseworkshops are also an opportunity for LSE research students to meet research students from otherMathematics Departments in the University of London. Each student is expected to present a talk inone of the workshops, and to publish results in our CDAM research report series. This has beenrunning for several years but, on the recommendation of our last review, we have formalized it as partof research student training, giving it the course code MA501 and officially timetabling it. Students are28

encouraged to attend research conferences. The Department provides, for each student, a budget of£500 for this purpose. Additionally, a new fund (The Cyril Offord Trust Award) has recently been setup to provide additional funding for this explicit purpose.Training in established research techniques and development of a capacity in the student for originalresearch in the chosen field of specialization is provided through regular one-to-one meetings with thesupervisor, as well as through directed reading. The final aim is to produce a thesis and subsequentpublications that contribute to the development of and understanding of the chosen area ofmathematics.Students are thus offered a supportive environment so that they feel that they are part of a communityof scholars and are well placed to pursue a career building on their research accomplishments.Supervision and supportThe first or Lead supervisor is agreed during the application process. This is determined by a number offactors, in particular the willingness of an academic member of staff to direct a research programmethat is of interest to both the supervisor and the student. This is obviously guided by the researchexpertise of the academic member of staff. It is the Lead supervisor who is principally responsible forthe student’s research training, but he/she is assisted in this by the second supervisor. Each student alsohas a second supervisor. The supervision ‘team’ is completed by the ‘independent adviser’, usually theDoctoral Programme Director (DPD). This role is intended to be primarily a pastoral one.The Doctoral Programme Director is responsible for monitoring the progress of PhD students, as wellas being in overall charge of the doctoral programme arrangements. He or she also has to approvecontinued annual registration, change of status (such as transferring from full-time to part time), theupgrade from MPhil to PhD, assignments of Second supervisors, and any other special arrangementssuch as the thesis viva examinationThe Department’s policy is that a supervisor should meet with their PhD student on average once aweek during term-time to discuss progress. These regular meetings with the supervisor will constitutethe major part of a student’s research training on a Mathematics PhD and their purpose is to reviewwork done and to agree further work. Advice or guidance may be given as to directed reading and inregard to formal courses to be followed, as well as to participation in conferences and graduate schoolswhen appropriate. Monitoring includes progress reports to the second supervisor and formal termly andannual reporting to the Doctoral Programme Director.Skills TrainingIn addition to the research training provided, all our research students are offered the opportunity toteach for the Department (and to take advantage of the training opportunities available). Training inLinux and some computer programming is likely to be provided during the course of the student’s PhD,though this may vary depending on its appropriateness to the research topic. A PhD significantly aidsthe development of a student’s technical writing skills. Some formal training is provided on this, in theform of written guidance on technical writing and an advisory session. In addition, the Teaching andLearning Centre and Methodology Institute offer courses in study skills and specialist options in arange of aspects of social research.29

Students are given the opportunity (and encouragement) to publish in CDAM’s research report seriesand the informal CDAM workshops provide an ideal opportunity for students to improve theirpresentation skills.Monitoring and review of progressA formal termly report is submitted to the Doctoral Programme Director shortly after the end of eachterm. This includes a summary of meetings between student and supervisor. The report at the end of theSummer Term also serves as the basis of the School’s annual progress report form: this formalassessment is conducted by the DPD on the basis of statements made by the supervisors and the studentand on the termly progress reports submitted to the DPD by the student’s supervisor. This wouldnormally cite any research reports written with the participation of the student. The DPD then presentshis findings to the Convener at the end of the summer term.Major Review and upgrade to PhDAt around the end of the student's first year, and on receipt of the first annual progress report of aResearch student, the DPD, in consultation with the lead supervisor, determines when to conduct thestudent's Major Review and will write to the student indicating when this is expected to occur. It isnormal to hold a Major Review within the first fifteen months of registration.The review is conducted by the Doctoral Programme Director and the first Supervisor and theprocedure is as follows. Initially, the student must submit evidence of research progress (relative to thetasks set by the lead Supervisor). An example of the kind of evidence the DPD would hope to receivefrom research students is an appropriate report of research, written by the student and accompanied bythe Lead Supervisor's assessment. The evidence submitted could also be an early draft of a paper, orearly draft chapter of thesis, or CDAM report, again accompanied by the Lead Supervisor's assessment.In the event of favourable evidence being presented, the outcome of the Major Review would usuallybe an upgrade in the registration from MPhil to PhD status. Where the progress falls short of thetargets, the registration at MPhil level could be maintained. If the progress is deemed to be whollyunsatisfactory, a further review would be set up in order to determine, before the end of the followingSummer Term, whether or not continued registration is in order.Facilities and environmentProvision of desks and computers for our research students is above the School’s requirement, but is indanger of becoming inadequate for mathematical research as the number of students has increased. TheSchool norm of one computer for every three research students is not adequate in mathematics. (Thefact that HEFCE classifies Mathematics under ‘price group C’ 4 indicates that they expect it to be moreexpensive than in many social sciences to provide sufficient facilities to support mathematics students.)4 See http://www.hefce.ac.uk/pubs/hefce/2004/04_24/04_24.pdf30

The Department has followed School and EPSRC proposals in setting up a system of support (orsecondary) supervisors. The small size of our research student cohort results in an unusual‘departmental culture’ in which all students become well-known to the staff, who in many cases alsoknow something of the research project undertaken. This has the consequence that advice andassistance to students comes not only from supervisors, but also more widely. A research student inour Department is very unlikely to go un-noticed.Staff student liaison committeeResearch and MSc students share the graduate SSLC committee, which was introduced in the 2004-2005 session when the masters’ programme was introduced. Prior to that, research students were notrepresented on an SSLC, but the numbers were, and still are, small enough that most issues they mightwant to raise can easily be done so on an informal level.Completion and submission ratesThe recent increase in the number of research students has yet to feed through to completions, though itdoes appear to be the case that all current full-time students are on schedule to complete within 4 years.In the past few years, we have had three students complete (on time): Philipp Reinfeld (algebraiccombinatorics, supervised by Norman Biggs), Arndt von Schemde (mathematical game theory,supervised by Bernhard von Stengel) and Nic Georgiou (probabilistic combinatorics, supervised byGraham Brightwell).7. Service teachingMuch that we want to say about class teaching has been covered elsewhere in this (already ratherlengthy) document. The brevity of this section reflects this rather than the relative importance we placeon service teaching, which is an aspect of our provision that we take extremely seriously.IntroductionAs emphasised earlier, one of the Department’s key aims is to provide students studying other degreecourses with an appropriate quantitative background, specific technical skills, and an understanding ofthe role of mathematics in the social sciences. As mentioned in Section 2.3, many of our courses aretaken (either as options or as a compulsory part of their programmes) by students on other degrees.These courses include MA100, MA103, MA106, MA110, MA107, MA207, MA200, MA201, MA300,MA301 (all described in Sections 2.2 and 2.3). As Appendix A shows, the numbers of studentsinvolved are large and have grwn considerably since the last review. The work involved in teachingcourses of this size should not be underestimated. The economies of scale resulting from teachingseveral hundred students at once are not great. There are significant administrative overheads inensuring the smooth running of such a large course, the provision of suitable support materials requiresparticular attention, and there is much that the lecturer has to do in the way of supervising andsupporting armies of class teachers.Class teachers31

Because some of our courses are so large (notably MA100, MA103, MA107, MA200, MA201), weneed to make extensive use of class teachers. The Class Teaching Officer is responsible for theappointment of class teachers, and as mentioned in Section 1.3, many of our part-time class teachershave significant professional experience and qualifications. As described in Section 4, all new classteachers are required to attend an induction programme and their progress is monitored throughout bysurveys (our own and the School’s) and is overseen by the Class Teaching Officer (as described inSection 4). The quality of our class teachers and the processes by which we monitor them and assurethe quality of their teaching have been discussed elsewhere in this document. What we hope comesthrough clearly is that we take class teaching extremely seriously. We are very careful about who wehire, and there are clear expectations on lecturers as to what they should provide in the way of supportand guidance to class teachers (described in our departmental Staff Handbook and Class Teachers’Handbook).8. ConclusionsThe Department is satisfied that it provides its students with high-quality courses and programmes,taught and supported well. We have continued to demonstrate a high degree of curricular innovation,and we have mechanisms for quality assurance and enhancement that have been developed over thepast several years and which have now bedded down well.At the time of the last review, we were considering introducing an MSc programme in the area ofdiscrete and applicable mathematics, and the Review Team was very supportive of this. Since then, wehave worked very hard to set up our MSc programme in Applicable Mathematics. Although this hasrequired huge effort, we are very happy indeed with the result. It is now a thriving programme, verylarge in size for an MSc Mathematics programme, and we believe that it will continue to attract goodstudents.Enhancement of our provision will require further resourcing, both in staffing and in space, particularlyif, as we would wish, we are to continue to expand our activities to take full advantage of otheropportunities that may arise.The strengths highlighted in our last review remain, and the areas of concern mentioned there havebeen addressed, at least in cases where it was down to us to address them. One concern that hascertainly not been addressed relates to the Review Team’s reservations about the quality of ourundergraduate study room: such a room no longer even exists.32

Appendix A: Courses taught in the department, and student numbersThe following table shows the courses taught by the department, the student numbers at the time of thelast review, and the (provisional) student numbers this session. (Note that there has been a migrationfrom the half-unit course MA107 to the full-unit course MA100 as a result of a decision by theEconomics department that students on Economics-based degrees required a more advanced methodscourse.) Most of our courses are half-unit courses, and for this reason we have taken the number ofhalf-unit equivalent students as the basic unit in these figures. (So each student on a full unit coursegives a contribution of 2 to the total.)CODE TITLE STUDENTNUMBERS 01/02MA100MA103MA106MA107MA110MA200MA201MA203MA207MA208MA209MA300MA301MA303MA305MA310MA311STUDENTNUMBERS 05/06Mathematical Methods 716 1174Introduction To Abstract Mathematics 242 406Introductory Quantitative Methods (Mathematics) 24 15Quantitative Methods (Mathematics) 342 222Basic Quantitative Methods New in 2004/5 24Further Mathematical Methods (Calculus) 152 241Further Mathematical Methods (Linear Algebra) 158 248Real Analysis 41 90Further Quantitative Methods (Mathematics) 21 36Optimisation Theory 36 53Differential Equations 22 61Game Theory 29 70Game Theory I 67 79Chaos In Dynamical Systems 34 3Optimisation in Function SpacesDid not run701/02Mathematics of Finance And Valuation 41 42Discrete Mathematics 15 3MA312 Convexity and Fixed Point Theorems 2 No longerrunningMA313Probability For Finance And Economics 5 6MA314Theory Of Algorithms 8 7MA315Algebra And Its Applications 8 17MA401Computational Learning TheoryDid not run01/02Not running05/0633

MA402Game Theory I 2 22MA406 Theory of Algorithms 6 No longerrunningMA407Algorithms and Computation New in 2004/5 35MA408Discrete Mathematics and Complexity New in 2004/5 9MA409Continuous-Time Optimisation New in 2004/5 18MA410MA411MA412MA413MA498Information, Communication and Cryptography New in 2004/5 9Probability and Measure New in 2004/5 6Functional Analysis and its Applications New in 2005/6 6Games of Incomplete Information New in 2005/6 13Dissertation in Mathematics New in 2004/5 54Total 1971 297634