London School of Economics and Political Science Department of ...
London School of Economics and Political Science Department of ...
London School of Economics and Political Science Department of ...
- No tags were found...
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
<strong>London</strong> <strong>School</strong> <strong>of</strong> <strong>Economics</strong> <strong>and</strong> <strong>Political</strong> <strong>Science</strong><strong>Department</strong> <strong>of</strong> Mathematics<strong>Department</strong>al StatementTLAC Review <strong>of</strong> Educational Provision, January 2006ContentsIntroduction Page 21. Issues arising from the 2002 review2. Academic portfolio <strong>and</strong> teaching methods3. Assessment4. Mechanisms for review, monitoring, quality assurance<strong>and</strong> quality enhancement5. Tutorial provision <strong>and</strong> student support6. MPhil/PhD provision7. Service teaching8. Conclusions9. Appendix APage 2Page 6Page 13Page 20Page 23Page 28Page 31Page 32Page 33
IntroductionThe <strong>Department</strong> <strong>of</strong> Mathematics is responsible for the BSc degree in Mathematics <strong>and</strong> <strong>Economics</strong>, theMSc in Applicable Mathematics, <strong>and</strong> a doctoral programme leading to the MPhil/PhD for studentswith research interests falling within the expertise <strong>of</strong> members <strong>of</strong> the <strong>Department</strong>. In addition, the<strong>Department</strong> provides students taking other degrees (particularly <strong>Economics</strong>, Accounting <strong>and</strong> Finance,Actuarial <strong>Science</strong>, Business Mathematics <strong>and</strong> Statistics, Management) with courses designed toprovide them with the necessary mathematical background. As a result, the <strong>Department</strong> is heavilyinvolved with undergraduate teaching: <strong>of</strong> the 1375 first-year undergraduates in the <strong>School</strong> in 2004-05,approximately 800 took at least one module in mathematics.The <strong>Department</strong> was externally reviewed under QAA (together with Statistics) in 1999. There was anInternal Review <strong>of</strong> the Mathematics <strong>Department</strong> in 2002, which forms the starting point for the currentprocess.We should say at the outset that in the context <strong>of</strong> UK Mathematics <strong>Department</strong>s, we are rather unusual.We are smaller relative to the size <strong>of</strong> our institution, <strong>and</strong> cover a different range <strong>of</strong> topics, with anemphasis on discrete mathematics <strong>and</strong> mathematics related to the social sciences (such as gametheory). This role is reflected in our research interests, in the degrees <strong>of</strong>fered (specifically no singlesubjectMathematics degree), <strong>and</strong> in our course <strong>of</strong>ferings. We specifically do not attempt to <strong>of</strong>fereducational provision covering the full spectrum <strong>of</strong> mathematics. However it should be noted that,even given our acceptance <strong>of</strong> a specialized role, we believe that we are still rather too small, relative tothe size <strong>of</strong> our commitment, to provide appropriate mathematical grounding to a major institution <strong>of</strong> thesocial sciences.The most significant innovation in the <strong>Department</strong> since 2002 is the setting up <strong>of</strong> our MSc degree inApplicable Mathematics, which ran for the first time in 2004-05. It is proving remarkably successful,<strong>and</strong> will be discussed more fully below. We see this degree as a significant step towards a substantialprogramme <strong>of</strong> graduate training at both MSc level <strong>and</strong> PhD level, based on the acknowledged expertise<strong>of</strong> the existing staff. We are now recruiting good numbers <strong>of</strong> students at both levels.1. Issues arising from the 2002 Review1.1 The distinctive features <strong>of</strong> the <strong>Department</strong>Once upon a time the LSE had a small group <strong>of</strong> mathematicians who were members <strong>of</strong> a large <strong>and</strong>diffuse <strong>Department</strong> <strong>of</strong> Statistical <strong>and</strong> Mathematical <strong>Science</strong>s. The <strong>Department</strong> <strong>of</strong> Mathematics was setup in 1995, with the intention <strong>of</strong> providing the <strong>School</strong> with a clearly defined focus for its mathematicalactivities. The <strong>Department</strong> aims to provide a foundation that matches the best international st<strong>and</strong>ardsin the mathematical community, with particular emphasis on those areas <strong>of</strong> Mathematics that areclosely related to the Social <strong>Science</strong>s. 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 <strong>and</strong> discrete mathematics, Dr Amol Sasane, whoworks on optimal control theory, <strong>and</strong> Dr Robert Simon, who is a mathematical game theorist. Theseappointments are both complementary <strong>and</strong> supplementary to the existing expertise within the<strong>Department</strong>. All three new staff have fitted in well, <strong>and</strong> have made excellent contributions to the<strong>Department</strong>.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 <strong>and</strong> the <strong>Department</strong> feels that it is still underfunded in comparison with larger <strong>Department</strong>s.In particular, large <strong>Department</strong>s are better able to spread the workload associated with innovations,such as the development <strong>of</strong> new courses. The inauguration <strong>of</strong> five new taught MSc half-units in 2004-05 <strong>and</strong> two more in 2005-06 has placed a heavy burden on our staff. We have also taken on asubstantial Summer commitment - the supervision <strong>of</strong> the compulsory full-unit MSc dissertations. Thishas affected all our staff, not just the new appointees. One <strong>of</strong> 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 <strong>and</strong> ComputationMA408 Discrete Mathematics <strong>and</strong> ComplexityMA409 Continuous Time OptimizationMA410 Information Communication <strong>and</strong> CryptographyMA411 Probability <strong>and</strong> MeasureMA412 Functional Analysis <strong>and</strong> its ApplicationsMA413 Games <strong>of</strong> Incomplete InformationMA498 Dissertation in Mathematics (which includes a series <strong>of</strong> dissertation seminars)With these courses, <strong>and</strong> a few pre-existing ones, we feel that we have constructed a programme that isboth distinctive <strong>and</strong> <strong>of</strong> high mathematical quality. Several LSE undergraduates have gone on to takeour MSc as a ‘fourth year’, <strong>and</strong> the recruitment from overseas has been gratifying. The numbersentering the course were 17 in 2004 (against a target <strong>of</strong> 10) <strong>and</strong> 27 in 2005 (against a target <strong>of</strong> 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 <strong>and</strong> programmesare discussed in detail in a 5-year cycle. We maintain our commitment to quality assurance, whileremaining distrustful <strong>of</strong> bogus ‘box-ticking’ procedures, which, in our view, merely avoid frank <strong>and</strong>open discussion <strong>of</strong> problems.Further details <strong>of</strong> our quality assurance procedures are discussed in Section 4.1 Appendix A shows how our undergraduate teaching commitment has changed since the time <strong>of</strong> 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 <strong>of</strong> 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 <strong>of</strong> twodecisions by other departments. The <strong>Economics</strong> <strong>Department</strong> now requires all BSc <strong>Economics</strong> students(<strong>and</strong> those on other programmes with a large <strong>Economics</strong> element) to take our full unit MA100Mathematical Methods, rather than the half-unit MA107. The Statistics <strong>Department</strong> now recommendsthat all BSc Actuarial <strong>Science</strong> students take MA103 Introduction to Abstract Mathematics in their firstyear (it was previously only a second-year option).In the light <strong>of</strong> this heavy <strong>and</strong> increasing commitment, we have been building up over many years agroup <strong>of</strong> highly-qualified <strong>and</strong> 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 <strong>of</strong> their training (as endorsed by the <strong>School</strong>), but many <strong>of</strong> our class teachers havesignificantly more experience <strong>of</strong> teaching, at LSE <strong>and</strong> elsewhere, <strong>and</strong> many have a PhD. This session,11 <strong>of</strong> our 22 part-time class teachers are ‘guest teachers’ rather than graduate teaching assistants, <strong>and</strong>10 <strong>of</strong> our part-time teachers have a PhD. In the Michaelmas term <strong>of</strong> this session, for example, over half<strong>of</strong> our class teaching conducted by part-time teachers is being carried out by those with PhDs. Weemploy doctoral students for the more basic courses, <strong>and</strong> 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 <strong>of</strong> the need to increase the number <strong>of</strong> doctoral students, <strong>and</strong> we haveused much <strong>of</strong> our outside funds to support such students. The new MSc has already provided oneresearch student, <strong>and</strong> we confidently expect to recruit more from that source. As a result <strong>of</strong> thesemeasures the number is currently 10, which is roughly equal to the number <strong>of</strong> staff. (At the time <strong>of</strong> 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 <strong>of</strong> the full range <strong>of</strong> options open to them in the third-year<strong>of</strong> the Mathematics <strong>and</strong> <strong>Economics</strong> degrees. This information is now available in our own BScMathematics <strong>and</strong> <strong>Economics</strong> H<strong>and</strong>book, on the departmental website, <strong>and</strong> <strong>of</strong> course in the LSECalendar. Additionally, at the end <strong>of</strong> the Lent term, the <strong>Department</strong>al Tutor provides “optionsdocuments” (one for each year) which are distributed to all first <strong>and</strong> second-year students. Inconnection with this, the <strong>Department</strong>al Tutor organizes a meeting to explain the degree structure <strong>and</strong>gives detailed information about all options. The introduction <strong>of</strong> LSE for You has also helped studentsunderst<strong>and</strong> the options available to them.2 See Appendix A4
Learning support materials (2.10)The last Review commended the <strong>Department</strong> for its extensive provision <strong>of</strong> learning support materials.We have made increasing use <strong>of</strong> course websites since then, <strong>and</strong> continue to provide other forms <strong>of</strong>supporting materials. Course materials are distributed in hard copy, <strong>and</strong> are posted on the website. Thematerials would typically include: course notes, exercise sheets, <strong>and</strong> model answers to the exercises.For some courses, lecture slides <strong>and</strong> 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, <strong>and</strong> 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 st<strong>and</strong>ard <strong>of</strong> A-level examinations hasfallen, particularly in the last 10-15 years. On the other h<strong>and</strong>, the <strong>of</strong>ficial view is that st<strong>and</strong>ards havebeen improving gradually. In order to monitor the situation the <strong>Department</strong> decided to introduce ashort diagnostic test for each intake <strong>of</strong> students. The test was first used in 2001, <strong>and</strong> the results showedlittle significant change up to the 2003 intake. However the 2004 results were significantly worse, <strong>and</strong>this appears to be reflected in the somewhat lower first-year examination performance <strong>of</strong> this cohort.The results for the 2005 entry are better, but may be distorted by a larger-than-usual number <strong>of</strong> 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, <strong>and</strong> 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 <strong>of</strong> mathematical s<strong>of</strong>tware packages (2.33; Recommendation 5.2 (a) (iii))We believe that familiarity with a mathematical s<strong>of</strong>tware package, such as MAPLE, is an integral part<strong>of</strong> any degree in Mathematics. The <strong>Department</strong> has been developing its use <strong>of</strong> MAPLE, which wasfirst introduced on the <strong>School</strong> network in 2000/01. Use <strong>of</strong> MAPLE is well-established in MA100Mathematical Methods, where students meet examples from multivariate calculus <strong>and</strong> linear algebra.The classes in week 5 <strong>of</strong> this course take place in computer rooms, <strong>and</strong> MAPLE exercises are set ashomework. Solutions to exercises are <strong>of</strong>ten provided in the form <strong>of</strong> MAPLE worksheets(http://www.maths.lse.ac.uk/Courses/MA100/index.html). It has been our policy to spread the use <strong>of</strong>MAPLE throughout the curriculum, <strong>and</strong> ways <strong>of</strong> doing this are regularly discussed at <strong>Department</strong>alMeetings <strong>and</strong> Annual Course Reviews. We reported in our last Review document some <strong>of</strong> the stepsmade towards this. Dr. Michele Harvey carried out a project on “Dissemination <strong>of</strong> MAPLE as aTeaching <strong>and</strong> Learning Aid” under a grant from the (then) Teaching <strong>and</strong> Learning Development Office.Four graduate students were employed to adapt the MAPLE base to the specific requirements <strong>of</strong>several <strong>of</strong> our courses <strong>and</strong> a general tutorial for MAPLE was produced <strong>and</strong> put on the <strong>Department</strong>’swebsite (http://www.maths.lse.ac.uk/Courses/MA100/maths_tutorial.mws). There have been a number<strong>of</strong> developments since then. A tutorial on the use <strong>of</strong> MAPLE as a programming language has beendeveloped <strong>and</strong> placed on the <strong>Department</strong>’s website(http://www.maths.lse.ac.uk/Courses/Tut2prog.mws). Use <strong>of</strong> MAPLE has been extended into othercourses. Currently, a number <strong>of</strong> courses (such as MA103, MA200, MA207, MA209, MA303, MA315)5
involve the use <strong>of</strong> 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 <strong>of</strong> Algorithms) contains an introduction toprogramming in JAVA, <strong>and</strong> students are required to produce working versions <strong>of</strong> basic algorithms.A similar approach is followed in the core MSc course MA407 Algorithms <strong>and</strong> Computation.MSc students make extensive use <strong>of</strong> a range <strong>of</strong> s<strong>of</strong>tware in preparing their dissertations. Last session,many <strong>of</strong> the dissertations contained significant amounts <strong>of</strong> programming <strong>and</strong> computational work.2. Academic portfolio <strong>and</strong> teaching methods2.1 IntroductionAs indicated in the Introduction at the very start <strong>of</strong> this document, the academic provision in thedepartment -- the BSc Mathematics <strong>and</strong> <strong>Economics</strong>, the MSc Applicable Mathematics, <strong>and</strong> serviceteaching -- is quite distinctive in the UK context.The <strong>Department</strong> has well-functioning course review mechanisms (described later, in Section 4) <strong>and</strong> wehave been involved in significant amounts <strong>of</strong> course updating <strong>and</strong> curricular innovation in recent years.Not least, we have started the new MSc programme (the <strong>Department</strong>’s first Masters programme) <strong>and</strong>have developed br<strong>and</strong> new graduate courses for it. Although this has been helped in part by theappointment <strong>of</strong> new staff, the work involved in developing eight new courses, the administrative workinvolved in setting up the programme, <strong>and</strong> the supervision <strong>of</strong> MSc students <strong>and</strong> their dissertations hasgenerated an enormous amount <strong>of</strong> work for all members <strong>of</strong> 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) <strong>and</strong> 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, <strong>and</strong> the estimated SSR for 2005/6, are, in eachyear, the highest among all departments in the <strong>School</strong>. For example, our SSR in 2004/5 was 26.5,against an overall <strong>School</strong> figure <strong>of</strong> 16.8 (<strong>and</strong> an average across departments/institutes <strong>of</strong> 16.03). SeeFigure 1.6
Figure 1: student:staff ratios 2001/2 to 2004/528.0026.0024.0022.0020.0018.00Maths SSR<strong>School</strong> SSRAverage departmentalSSR16.0014.002001/02 2002/03 2003/04 2004/052.2 BSc Mathematics <strong>and</strong> <strong>Economics</strong>Admissions <strong>and</strong> aims <strong>of</strong> the degreeThe Mathematics <strong>and</strong> <strong>Economics</strong> degree programme is highly successful. It attracts a very large, <strong>and</strong>increasing, number <strong>of</strong> highly-qualified applicants (over 10 applications per place). Given thecompetition for places, we recently increased the st<strong>and</strong>ard <strong>of</strong>fer from ABB to AAB with A inMathematics. It should be noted, however, that this st<strong>and</strong>ard <strong>of</strong>fer does not reflect the entrancequalifications <strong>of</strong> those who eventually register: given the competition, incoming students generallyhave better grades than this.The BSc Mathematics <strong>and</strong> <strong>Economics</strong> aims, among other things, to provide students with a knowledge<strong>of</strong> mathematics, economics, <strong>and</strong> the interaction between the two. The comments <strong>of</strong> external examinersattest to its success, <strong>and</strong> the QAA Subject Review Report commented that “A good balance betweenflexibility <strong>of</strong> choice <strong>and</strong> coherence characterises the degree”.Structure <strong>of</strong> the degree <strong>and</strong> courses <strong>of</strong>feredIn the first year <strong>of</strong> the BSc Mathematics <strong>and</strong> <strong>Economics</strong>, students must take MA100 MathematicalMethods, ST102 Elementary Statistical Theory <strong>and</strong> EC102 <strong>Economics</strong> B <strong>and</strong> are strongly encouragedto take MA103 Introduction to Abstract Mathematics. MA100 is a fairly dem<strong>and</strong>ing post A-levelcourse in Calculus <strong>and</strong> Linear Algebra. ST102 <strong>and</strong> EC102 are introductory, university-level, courses inStatistics <strong>and</strong> <strong>Economics</strong>. MA103 is an introduction to pro<strong>of</strong>, number theory, analysis <strong>and</strong> abstractalgebra. Strictly speaking, MA103 can be deferred to the second year, but it creates more flexibility for7
students in the second <strong>and</strong> 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 <strong>and</strong> Statistics, or <strong>Economics</strong>, as well as students from the External Programme,to enter the degree in Year 2. The general principle underlying the second <strong>and</strong> third years <strong>of</strong> the degreeis that students should continue to take courses in both mathematics <strong>and</strong> economics, concentrating onthe parts <strong>of</strong> each subject most closely related to the other. For instance, one popular third year option isthe full-unit MA300 Game Theory, the second half <strong>of</strong> which is taught by the <strong>Economics</strong> <strong>Department</strong>:this is a subject that would not normally be taught as part <strong>of</strong> a traditional mathematics curriculum.The compulsory “core” courses in the second <strong>and</strong> third years are made up <strong>of</strong> three half-units <strong>of</strong>mathematics <strong>and</strong> two full units <strong>of</strong> economics: MA200 Further Mathematical Methods (Calculus),MA201 Further Mathematical Methods (Linear Algebra), MA203 Real Analysis, EC202Microeconomic Principles II, <strong>and</strong> EC319 Mathematical <strong>Economics</strong>. Beyond this, students have areasonable variety <strong>of</strong> choice, including the option <strong>of</strong> taking one unit outside Mathematics <strong>and</strong><strong>Economics</strong>, with the approval <strong>of</strong> the <strong>Department</strong>al Tutor.The regulations for the degree are formally reviewed by the Mathematics <strong>and</strong> <strong>Economics</strong> <strong>Department</strong>sas part <strong>of</strong> our 5-year cycle <strong>of</strong> reviews; the next such review will take place later this session.A list <strong>of</strong> courses taught in the <strong>Department</strong>, with numbers <strong>of</strong> students, appears at the end <strong>of</strong> thedocument, in Appendix A.There is a sequence <strong>of</strong> “methods” courses, designed for our own students but also popular with others(<strong>and</strong> compulsory on some other degree programmes): this starts with the full-unit MA100, which leadson to the half-units MA200 <strong>and</strong> MA201. These courses are in turn pre-requisites for some third yearcourses in mathematics <strong>and</strong> statistics.The “abstract” mathematics sequence <strong>of</strong> courses begins with MA103. This is a pre-requisite, or at leasthighly advisable, for many more advanced options, notably MA203, MA208 <strong>and</strong> MA209.Although our third year courses <strong>of</strong>ten follow on from the abstract courses, many are applicationsoriented.Given the nature <strong>of</strong> the degree programme, we do not <strong>of</strong>fer 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 <strong>Department</strong> carries out an enormous amount <strong>of</strong> teaching to students not registered on our BScMathematics <strong>and</strong> <strong>Economics</strong> programme.The course MA100 Mathematical Methods currently has around 560 students (compared with around360 at the time <strong>of</strong> our last review), <strong>and</strong> is a compulsory course for first years in most degrees that havea significant <strong>Economics</strong> 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 <strong>and</strong>Finance, Management, <strong>and</strong> Management <strong>Science</strong>s) <strong>and</strong> MA207 (a follow-on half-unit course forstudents who took MA107 <strong>and</strong> want to study more mathematics). We recently took on the teaching <strong>of</strong>MA110: previously it was taught by the <strong>Economics</strong> department as EC110. The first half <strong>of</strong> 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, <strong>and</strong> for students on the Accounting <strong>and</strong> Finance degree to take MA110 <strong>and</strong> 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 <strong>of</strong> MA110, there are no real savings to be gainedshould it be withdrawn.)Our advanced methods courses (such as MA200 <strong>and</strong> MA201, currently with around 240 students) arealso popular as options for students on other degree programmes (<strong>and</strong> compulsory on BMS <strong>and</strong>Actuarial <strong>Science</strong>). 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 <strong>of</strong> economic theory. Some <strong>of</strong> our more specialized courses (in particular, MA203 RealAnalysis, MA208 Optimisation Theory, MA209 Differential Equations, <strong>and</strong> the Game Theory coursesagain) attract significant numbers <strong>of</strong> General Course students. Those students <strong>of</strong>ten comment that theirhome universities don’t <strong>of</strong>fer these kinds <strong>of</strong> 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 <strong>of</strong> service teaching.2.4 MSc Applicable MathematicsIntroductionIn the 2004/5 session, the <strong>Department</strong> started a new MSc programme in Applicable Mathematics. Apartfrom some participation in the now-defunct intercollegiate <strong>London</strong> MSc in Mathematics <strong>and</strong> a smallcontribution to teaching students on the King’s College MSc in Information Processing <strong>and</strong> NeuralNetworks, this is the <strong>Department</strong>’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 <strong>and</strong> 30 thereafter. Both intakes so far havebeen above the target registration figures <strong>and</strong> 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 <strong>of</strong> students. Information about the sizes <strong>of</strong>MSc programmes in many other institutions is not readily available, but this is one <strong>of</strong> the largest UKMathematics MSc programmes that we know <strong>of</strong>. (For example, the MSc in Modern Applications <strong>of</strong>Mathematics at the University <strong>of</strong> Bath, which has 10 EPSRC funded studentship places <strong>and</strong> which isregarded as very successful, has 14 students.)9
The programme has attracted some very talented students. In the first year, 8 <strong>of</strong> the 17 students haveobtained the MSc with distinction. Some very good dissertations have been written. One student haspresented the results <strong>of</strong> his dissertation at an international workshop. We are encouraging the beststudents to produce research reports for inclusion in the CDAM research report series <strong>and</strong> we have alsoestablished a prize for the best dissertation, in memory <strong>of</strong> Haya Freedman, who was a member <strong>of</strong> theLSE mathematics (sub)department from its inception until her retirement.Aims <strong>of</strong> the degreeThe MSc in Applicable Mathematics draws together traditional <strong>and</strong> modern mathematical techniques ina variety <strong>of</strong> social science ‘contexts’. Students are <strong>of</strong>fered a range <strong>of</strong> mathematics options, <strong>and</strong> also theopportunity to take a social science module, such as <strong>Economics</strong>, Finance, Government, OperationalResearch, or Statistics, where they can see in practice the mathematics they are learning, <strong>and</strong> achievegreater underst<strong>and</strong>ing <strong>of</strong> social sciences. The skills <strong>and</strong> 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 <strong>of</strong> potential careers: in finance, business,government, <strong>and</strong> industry. It also provides a base for further studies at research level. The programmeis intended to have broad appeal. For pure <strong>and</strong> applied mathematicians, it provides an opportunity toincrease their knowledge <strong>of</strong> mathematics, particularly (depending on options chosen) in discretemathematics, algorithms, game theory, <strong>and</strong> probability <strong>and</strong> to make themselves more ‘marketable’ byadding some social science aspects to their knowledge <strong>and</strong> skills base. For social scientists with verystrong quantitative backgrounds, it provides an opportunity to add to <strong>and</strong> improve their underst<strong>and</strong>ing<strong>of</strong> the mathematics behind much <strong>of</strong> social science.Structure <strong>of</strong> the programmeReflecting the emphasis on computational algorithms <strong>and</strong> techniques, there is one core taught course, ahalf-unit, MA407 Algorithms <strong>and</strong> Computation. All students must also undertake a full unitDissertation in Mathematics <strong>and</strong> must take a half-unit course in Game Theory or Discrete Mathematics.They take two or three additional half-units in Mathematics <strong>and</strong> up to one unit from outside thedepartment (various options in <strong>Economics</strong>, Finance, Operational Research, Statistics <strong>and</strong> Governmentbeing listed explicitly in the programme regulations).Dissertation <strong>and</strong> dissertation seminarsAll MSc students write a full-unit dissertation on some mathematical topic. They are given advice <strong>and</strong>support 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, <strong>and</strong> answerquestions about them. We also have talks by experts on various aspects <strong>of</strong> dissertation writing such aslibrary research, mathematical word processing, mathematical writing, <strong>and</strong> IT. There is time forstudents to confer individually with the teacher responsible for the course about their choice <strong>of</strong> 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 <strong>and</strong> elsewhere (including mathematics courses at other institutions <strong>of</strong> theUniversity <strong>of</strong> <strong>London</strong>). The development <strong>of</strong> the MSc has been particularly useful here, providing arange <strong>of</strong> in-house courses that reflect the research interests <strong>of</strong> the staff, <strong>and</strong> which are therefore highlyrelevant to the PhD students. As commented on earlier in this document, the number <strong>of</strong> PhD students inthe department is now quite appropriate for a department with our number <strong>of</strong> staff, though we continueto encourage talented applicants interested in working in our areas <strong>of</strong> research. Funding for PhDstudents has been available from the EPSRC through its doctoral training allowance scheme, thoughmuch <strong>of</strong> the funding we have provided has come from the <strong>Department</strong>’s outside funds (generatedlargely as a result <strong>of</strong> 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 <strong>Department</strong> has been particularly innovative in curricular matters in recent years. Primarily, thishas been through the introduction <strong>of</strong> eight new courses for the MSc. But there has, <strong>and</strong> continues to be,much on-going improvement <strong>and</strong> updating <strong>of</strong> undergraduate courses. Developments are discussedformally at departmental meetings <strong>and</strong> our Annual Course Review, <strong>and</strong> at a more informal level amongstaff who teach related courses.Some mathematics at undergraduate level, especially abstract mathematics, is ‘classical’ <strong>and</strong> essentiallythe same material is (<strong>and</strong> must be) taught from year to year. However, even here there is scope forinnovations <strong>and</strong> fresh approaches to the courses, <strong>and</strong> in teaching style <strong>and</strong> supporting materials. This isencouraged by the fact that, since all <strong>of</strong> our undergraduate courses can be taught by more than onemember <strong>of</strong> staff, there is a fair amount <strong>of</strong> circulation <strong>of</strong> core undergraduate courses among lecturers.Examples include the re-br<strong>and</strong>ing <strong>and</strong> re-development <strong>of</strong> the course MA305 Control Theory asOptimisation in Function Spaces. Courses that focus on application, or have large parts that do, are<strong>of</strong>ten updated as new applications or techniques are developed.At the time <strong>of</strong> our last review, we had just introduced the new courses MA209 Differential Equations<strong>and</strong> MA315 Algebra <strong>and</strong> its Applications. These have proven to be successful <strong>and</strong> popular.New courses that have been introduced since the last Review are:MA407 Algorithms <strong>and</strong> ComputationMA408 Discrete Mathematics <strong>and</strong> ComplexityMA409 Continuous Time OptimizationMA410 Information Communication <strong>and</strong> CryptographyMA411 Probability <strong>and</strong> MeasureMA412 Functional Analysis <strong>and</strong> its ApplicationsMA413 Games <strong>of</strong> 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 <strong>of</strong> 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 h<strong>and</strong>ed out in lectures, although inthe very largest courses it is produced at the start <strong>of</strong> the course as part <strong>of</strong> a study pack (for whichstudents pay a small amount as a contribution towards the reprographics costs). In most cases, allh<strong>and</strong>outs are also available on the web (see http://www.maths.lse.ac.uk/Courses).Use <strong>of</strong> ICTLectures <strong>and</strong> classes are augmented by the use <strong>of</strong> ICT, chiefly, for our department, in the use <strong>of</strong>websites for the delivery <strong>of</strong> 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 <strong>of</strong> what we might wish to achieve can be more easily realised through the use <strong>of</strong> websites. Themain webpage for each course is maintained by the <strong>Department</strong>al Manager, but “Course Materials”pages are the responsibility <strong>of</strong> 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, <strong>and</strong> past examination papers. For some courses,such as MA100 Mathematical Methods, Maple tutorials <strong>and</strong> workbooks, <strong>and</strong> videos <strong>of</strong> Extra Examplessessions, are available.As discussed in Section 1.3, the <strong>Department</strong> makes increasing use <strong>of</strong> MAPLE <strong>and</strong> Java in its courses.At their induction, MSc students are provided with a CD containing the s<strong>of</strong>tware they will need fortheir courses <strong>and</strong> for preparing their dissertations.Library <strong>and</strong> IT supportWe are supported in the provision <strong>of</strong> learning materials by the library <strong>and</strong> IT services. The library hassufficient copies <strong>of</strong> core texts, <strong>and</strong> the access to electronic journals is <strong>of</strong> particular help to our researchstudents <strong>and</strong> to MSc students in their dissertation research. The st<strong>and</strong>ard build for PCs in the <strong>School</strong>now includes many <strong>of</strong> the s<strong>of</strong>tware packages that our students use, such as MAPLE, Java, MikTeX <strong>and</strong>Scientific Word. Students can also buy a copy <strong>of</strong> 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 <strong>of</strong> application <strong>of</strong> mathematics, change in studentdem<strong>and</strong>, <strong>and</strong> staff changes. Since the last review, the course MA312 Convexity <strong>and</strong> Geometry has beenremoved because too few students expressed an interest in taking it. All <strong>of</strong> our undergraduate courses<strong>and</strong> most <strong>of</strong> our graduate courses can be taught by more than one member <strong>of</strong> staff, so there is usually12
no need to suspend a course because <strong>of</strong> sabbatical leave, unless this would result in unusually highteaching loads.2.9 Future developmentsWe aim to continue to provide innovative <strong>and</strong> up-to-date courses to specialist students, <strong>and</strong> to meet theneeds <strong>of</strong> other students through our service teaching courses.Immediate plans, as mentioned above, include an increase in the number <strong>of</strong> students on the MSc inApplicable Mathematics.The <strong>School</strong> has already earmarked funds for us to appoint a chair <strong>and</strong> a lectureship in FinancialMathematics <strong>and</strong> 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 <strong>of</strong> Accounting <strong>and</strong> Finance <strong>and</strong> 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 exp<strong>and</strong> ourprovision is in the Algorithms <strong>and</strong> Theoretical Computer <strong>Science</strong> area, in which the department hasresearch expertise. We already provide some courses <strong>and</strong> supervise research students in this area.EPSRC's International Reviews in Computer <strong>Science</strong> <strong>and</strong> in Mathematics both identified the interfacebetween Discrete Mathematics <strong>and</strong> Theoretical Computer <strong>Science</strong> as an area that should bestrengthened, <strong>and</strong> there is some possibility that EPSRC will dedicate resources in some form to this.Our <strong>Department</strong>, perhaps in collaboration with others, would be well placed to take advantage <strong>of</strong> this.3. Assessment3.1 IntroductionNormal assessment practices in Mathematics are rather different from those in many <strong>of</strong> the otherdisciplines taught in the <strong>School</strong>. Our external examiners have continually endorsed the way we set <strong>and</strong>mark examinations <strong>and</strong> 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 <strong>of</strong> our courses, problems are assigned weekly <strong>and</strong> these form the basis for discussion in classes.Although the amount <strong>of</strong> work we require our students to h<strong>and</strong> 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 h<strong>and</strong>ed in on time, so as to give rapid <strong>and</strong> informative feedback on students’performance: students clearly value this, <strong>and</strong> tutees complain to us about courses in other departmentswhere this is not common practice. Solutions are discussed in class <strong>and</strong> 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 <strong>of</strong> the learning process, regular working through <strong>of</strong> problems being anessential part <strong>of</strong> any mathematics course.Class assignments are generally graded on a letter-based scale from VG (very good) to P (poor).Students are advised <strong>of</strong> 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 <strong>of</strong>ten regard marks obtained forclasswork as a predictor <strong>of</strong> their examination mark, which is not necessarily valid because classworkquestions are, for sound pedagogical reasons, <strong>of</strong>ten different from exam questions, <strong>and</strong> 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 pr<strong>of</strong>iciencyin concepts or techniques, whereas exam-based summative assessment is designed to assess theacquisition <strong>of</strong> such pr<strong>of</strong>iciency after it has been developed in classwork.) We now explicitly warnstudents against inferring too strong a linkage between classwork grades <strong>and</strong> exam performance. Theclass grading document states that ‘classwork grades reflect performance on a particular piece <strong>of</strong> workdone in particular circumstances. They are intended to give students an indication <strong>of</strong> their progress, butthey do not necessarily predict performance in the final examination’.More important than the grades given to a piece <strong>of</strong> classwork are the comments made by markers onthe student’s work. This is an essential part <strong>of</strong> 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 <strong>of</strong> TLC’s training course), the importance <strong>of</strong> such written feedback ishighlighted. In our own survey <strong>of</strong> 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 <strong>of</strong> lecture notes(as in MA100 from this year), or on course websites, <strong>and</strong> are available for purchase (for a nominal feeto <strong>of</strong>fset copying costs) from the <strong>Department</strong>al <strong>of</strong>fice. Solutions to recent years’ papers are alsoavailable. Students are strongly encouraged to try to answer the questions before looking at thesolutions <strong>and</strong>, for this reason, we <strong>of</strong>ten make solutions available only later in the academic year.Should the content <strong>of</strong> 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 <strong>and</strong> mock examination questions set ifappropriate. For new courses, mock examination papers are provided.Past examination papers <strong>of</strong>ten form the basis for revision lectures in the summer term, where particularquestions may be worked through <strong>and</strong> the method <strong>of</strong> answering them discussed in some detail.3.3 Summative assessmentAssessment in our undergraduate mathematics courses is entirely by means <strong>of</strong> Summer Termexaminations. For some <strong>of</strong> the taught graduate courses, there are also elements <strong>of</strong> assessed coursework.Several have a 10% coursework element, <strong>and</strong> one, MA407 Algorithms <strong>and</strong> Computation, has a 30%coursework (programming) element.14
Marking <strong>of</strong> examinationsAll procedural aspects <strong>of</strong> our examination procedures are set out in the document Mathematics<strong>Department</strong> Examination Procedures 2005/6, which is to be read in conjunction with the LSEdocument Instructions for Examiners for Taught Programmes. Our document st<strong>and</strong>ardises manyaspects <strong>of</strong> 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 st<strong>and</strong>ardization provides transparency forstudents (<strong>and</strong> for our external examiners).For each examination, solutions are provided for externals to see, along with an indication <strong>of</strong> what is“bookwork” <strong>and</strong> whether students will have seen similar problems before. Each paper is inspectedinternally by a “checker”, <strong>and</strong> 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 <strong>of</strong> learning outcomes to be assessedin the examination, together with an indication <strong>of</strong> where in each exam paper each outcome is assessed<strong>and</strong> they are provided with a draft marking scheme indicating the weight to be given to each part <strong>of</strong>each question. (The intended learning outcomes for each course are also made available to students incourse websites <strong>and</strong> 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), <strong>and</strong> 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, <strong>and</strong> 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 <strong>of</strong> 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 st<strong>and</strong>ard practice, it is very difficult to conveyto students what is required <strong>of</strong> them (for instance) to pass the examination. We decided that we wouldalways set examination papers with the intention <strong>of</strong> doing little or no scaling to the raw marks, <strong>and</strong> thatif in fact substantial scaling did prove necessary, this would be discussed extensively with the externalexaminers before being agreed upon, <strong>and</strong> 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, <strong>and</strong>this is why it is unnecessary for a second marker to re-mark exams independently <strong>of</strong> the first marker’smarks. We have been open with students <strong>and</strong> external examiners about our procedures. Externalexaminers have consistently endorsed our procedures as being appropriate <strong>and</strong> in keeping with thenorms for mathematical subjects. We have been granted exemption from ‘blind double marking’ by theUndergraduate Studies Subcommittee <strong>and</strong> 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 <strong>School</strong> understood our position <strong>and</strong> respected our disciplinary norms<strong>and</strong> did not require us to do this on an annual basis.MSc dissertation <strong>and</strong> assessed courseworkThe MSc h<strong>and</strong>book contains documents, ‘Assessed coursework’ <strong>and</strong> ‘Assessment <strong>of</strong> your dissertation’outlining how we approach the assessment <strong>of</strong> MSc coursework <strong>and</strong> the full-unit dissertation. Here,students are told what it is that examiners are looking for <strong>and</strong> are given advice about such matters asproper citation <strong>of</strong> 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, <strong>and</strong> originality. The two examiners then meet to discuss theirindependent reports <strong>and</strong> 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 <strong>and</strong> checked.Advice given to students about examinationsStudents naturally wish to know in advance what their exams will be like, as well as what is expected<strong>of</strong> 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 <strong>and</strong> graded, <strong>and</strong> what sorts <strong>of</strong> things theexaminers are looking for. As mentioned above, we provide, in printed form <strong>and</strong>/or on the website, theexamination paper <strong>and</strong> 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 <strong>of</strong>ten form the basis <strong>of</strong> revision lectures.MSc students are given extensive advice about preparing their dissertations in the course MA498, <strong>and</strong>in particular in the document ‘Dissertation Instructions for C<strong>and</strong>idates’, available on the MA498website at http://www.maths.lse.ac.uk/Courses/MA498/dissertation_instructions.pdf. The MSch<strong>and</strong>book also contains a substantial amount <strong>of</strong> information on what examiners are looking for.Comments from external examinersOur external examiners have unhesitatingly declared themselves satisfied with our assessmentprocedures <strong>and</strong> their outcomes <strong>and</strong> have declared our st<strong>and</strong>ards to be comparable to those in their owninstitutions. Some quotes from external examiners’ reports <strong>and</strong> examination sub-board minutes serveto demonstrate this:“The top students achieve a very high st<strong>and</strong>ard, whilst the weaker students also get a lot out <strong>of</strong> thecourses. […] The courses, quite properly, combine rigorous <strong>and</strong> analytical mathematics with interestingapplications. Some courses are highly innovative <strong>and</strong> stimulating.” (Pr<strong>of</strong>essor Robert Curtis, University<strong>of</strong> Birmingham, external examiner’s report, 2000)16
“once again the examination system worked extremely well” (Pr<strong>of</strong>essor Milne Anderson, UCL, externalexaminer’s report, 2003)“Pr<strong>of</strong>essor Anderson, who is in his last year as External Examiner, stated that the Mathematics<strong>Department</strong> had been very competent <strong>and</strong> efficient in its procedures. All exams arrived on time,comments were dealt with properly <strong>and</strong> he had been kept informed <strong>of</strong> this, <strong>and</strong> the marking had beenaccurate <strong>and</strong> effective. He congratulated the <strong>Department</strong> for this.’’ (minutes <strong>of</strong> the 2003 BSc sub-boardmeeting)“the academic st<strong>and</strong>ards are generally high. I also liked the apparent degree <strong>of</strong> integration between themathematics <strong>and</strong> economics components.” (Pr<strong>of</strong>essor Mark Roberts, Surrey University, externalexaminer’s report 2004)“[Pr<strong>of</strong>essor Roberts] felt that the academic st<strong>and</strong>ards reflected in the papers were pleasingly high.’’(minutes <strong>of</strong> 2004 BSc sub-board)“Pr<strong>of</strong>essor Thomason [<strong>of</strong> the University <strong>of</strong> Cambridge] said that in his view the <strong>Department</strong> had beenvery careful <strong>and</strong> proper in its procedures, with lots <strong>of</strong> attention paid to setting <strong>and</strong> marking.’’ (minutes <strong>of</strong>the MSc exam board meeting, October 2005)“The whole operation seems to me to have been well planned <strong>and</strong> the outcome successful.” (Pr<strong>of</strong>essorThomason, 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 <strong>and</strong> Operational Research (MSOR) 3 (paragraph5.1.8):“For many types <strong>of</strong> assessment in MSOR, the variation in marks achieved by students <strong>of</strong> undoubtedcommitment is typically greater than in other subject areas. This is particularly so in writtenexaminations <strong>and</strong> tests. Experience is that, on the one h<strong>and</strong>, perfect or near-perfect solutions fullydeserving <strong>of</strong> very high marks arise more <strong>of</strong>ten than in most other subjects; while on the other h<strong>and</strong>, theproblem-solving nature <strong>of</strong> MSOR can lead to weaker students, <strong>and</strong> 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, <strong>and</strong> this would be a correct representation <strong>of</strong> the relative values<strong>of</strong> the students’ work. ”We find it possible to set exams so that the threshold for a pass is not too far from 34% <strong>and</strong> that for afirst is about 70%; however it is true that, in mathematics courses in general, we see relatively manyexam scripts deserving <strong>of</strong> what the rest <strong>of</strong> the <strong>School</strong> would see as exceptionally high marks, but on theother h<strong>and</strong> 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 <strong>of</strong> courses withrelatively high failure rates <strong>and</strong>/or with a relatively high percentage <strong>of</strong> first class marks, <strong>and</strong> this hasindeed been the case.3 http://www.qaa.ac.uk/academicinfrastructure/benchmark/honours/mathematics.asp#117
Undergraduate degree classificationsThe distribution <strong>of</strong> marks in mathematical subjects manifests itself also in degree classifications. Wehave awarded significantly more first class degrees, proportionally, than the <strong>School</strong> as a whole, <strong>and</strong>, atthe same time, we have awarded a greater proportion <strong>of</strong> degrees classified as lower second or below. Itis generally the case, across the HE sector, that a greater proportion <strong>of</strong> 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 <strong>of</strong> distribution <strong>of</strong> classifications arises in mathematical subjects than in others. This isdemonstrated in Figure 2, below.A recurring concern that has been raised in many <strong>of</strong> our external examiners’ reports relates to theclassification system in place at the undergraduate level. They have suggested that it is <strong>of</strong>ten generous,<strong>and</strong> allows students to graduate with a higher classification than they might elsewhere when theirmarks are averaged. Any method <strong>of</strong> aggregating module marks into a degree classification is bound tohave its deficiencies, <strong>and</strong> making comparisons between institutions <strong>and</strong> disciplines is very difficult.The <strong>School</strong> has set up a working group to look at the classification guidelines, <strong>and</strong> a member <strong>of</strong> ourdepartment has agreed to be on that group. More generally, the whole process <strong>of</strong> degree classification isunder consideration at national level by the Measuring <strong>and</strong> Recording Student Achievement SteeringGroup chaired by Pr<strong>of</strong>essor Robert Burgess.Figure 2.Degrees awarded nationally 2001/2-2003/4 (% in each class)[Source: HESA]6050403020100Social, Economic, <strong>Political</strong>Studies/Social Studies1 2A 2B 3 P7.9 49.5 33.3 5.8 3.5Mathematical <strong>Science</strong>s 25.4 33.3 26 12.2 3.1Almost all <strong>of</strong> our advanced courses are half-units, so that the degree classification process involves agood deal <strong>of</strong> pairing <strong>of</strong> 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 <strong>and</strong> 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 <strong>of</strong> the Statistics department)made a proposal for an amendment <strong>of</strong> the regulations to the 17 March 2004 USSC meeting, <strong>and</strong> thiswas accepted.Undergraduate progression <strong>and</strong> completionIt has recently been drawn to our attention that the BSc Mathematics <strong>and</strong> <strong>Economics</strong> has a lower rate <strong>of</strong>completion in three years than many <strong>of</strong> the other degree programmes at the <strong>School</strong>. We are unsure <strong>of</strong>the reasons for this. One possibility is that students encounter some difficulty in making the transitionfrom A-level mathematics (or equivalent) to the more abstract <strong>and</strong> rigorous university-levelmathematics. This, <strong>and</strong> the decline in preparedness <strong>of</strong> A-level students, is something we have beenaware <strong>of</strong> <strong>and</strong> have taken steps to ameliorate. We have introduced Extra Examples sessions for MA100(<strong>and</strong>, 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, <strong>and</strong> 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 <strong>and</strong>MA103 who teach our first year students, asking them to alert us to any students they think are havingdifficulty coping with the courses.It is, <strong>of</strong> course, regrettable that some <strong>of</strong> our students do not proceed as we would wish. Mathematicalcourses build upon each other <strong>and</strong> there is clear intellectual progression in the degree, <strong>and</strong> for thisreason the department does not generally recommend that students who have failed to meet thest<strong>and</strong>ard progression requirements be permitted into the next year <strong>of</strong> the programme. Our experience,<strong>and</strong> student feedback, has indicated that students <strong>of</strong>ten subsequently perform quite well after a year as aprivate re-sit c<strong>and</strong>idate or as a part-time student <strong>and</strong> they <strong>of</strong>ten, 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 <strong>of</strong>results. However, we are pleased with the outcomes <strong>of</strong> our assessments. The classifications obtainedare as follows:NumberDistinction 8Merit 3Pass 3Fail 1Incomplete 1Withdrawn 1TOTAL 1719
3.5 Feedback on formative <strong>and</strong> summative assessmentAs mentioned above, feedback on classwork is given both in the form <strong>of</strong> grades <strong>and</strong>, moresignificantly, written comments, <strong>and</strong> all students have access to class teachers in their <strong>of</strong>fice hours toask for further guidance <strong>and</strong> feedback. Although classwork questions are not always the same sort <strong>of</strong>question that a student would encounter in an exam (since, for one thing, the latter will generallyinclude some ‘bookwork’), parts <strong>of</strong> 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 <strong>of</strong>fer such feedback given the high numbers <strong>of</strong> students on many <strong>of</strong> our courses.However, we think that the feedback on formative assessment (which is weekly for our courses),together with revision lectures <strong>and</strong> the information we provide about past examinations, preparesstudents adequately for the final exam. But we are aware that students would <strong>of</strong>ten 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 <strong>of</strong> the following session).4. Mechanisms for review, monitoring, quality assurance <strong>and</strong> quality enhancementCourse review <strong>and</strong> monitoring has recently been raised as an important issue in the <strong>School</strong>. Ourdepartment has long had a systematic approach to the review <strong>and</strong> monitoring <strong>of</strong> its courses <strong>and</strong>maintenance <strong>and</strong> enhancement <strong>of</strong> teaching quality. Important aspects <strong>of</strong> this are: the Annual CourseReview; the Staff/Student Liaison Committees; clear lines <strong>of</strong> communication between SSLC <strong>and</strong><strong>Department</strong>al meetings; extensive staff involvement in Quality issues; peer observation <strong>of</strong> teaching;support for class teachers; student questionnaires (our own <strong>and</strong> the <strong>School</strong>’s).Annual Course ReviewThere is an annual meeting <strong>of</strong> the entire <strong>Department</strong> in Summer Term, typically lasting two to threehours, at which reviews <strong>of</strong> our curriculum take place, <strong>and</strong> where all our courses are evaluated in asystematic way. The <strong>Department</strong> operates a 5-year cycle <strong>of</strong> reviews <strong>of</strong> its degrees <strong>and</strong> all <strong>of</strong> itsindividual courses. Modifications to existing degrees <strong>and</strong> courses are discussed <strong>and</strong> agreed, <strong>and</strong> topicssuch as “first year courses” <strong>and</strong> “portfolio <strong>of</strong> third year courses” are also contained within the cycle, toallow for a periodic wide-ranging discussion <strong>of</strong> new initiatives that the <strong>Department</strong> might wish topursue, <strong>and</strong>/or courses that might be discontinued. That this works well is demonstrated by the degree<strong>of</strong> curricular innovation that has taken place. It is our st<strong>and</strong>ard practice to solicit student views aboutcourses that are being reviewed, <strong>and</strong> this is found to be informative, particularly by the teachersinvolved with the course. The Mathematics <strong>and</strong> <strong>Economics</strong> degree has been reviewed fully, incollaboration with the <strong>Economics</strong> department, <strong>and</strong> it is due to be reviewed again this session.Responsibility for the Business Mathematics <strong>and</strong> Statistics degree has passed to the Statisticsdepartment, but we have a BMS point <strong>of</strong> contact who will participate in any reviews <strong>of</strong> that degree.Our Annual Course Review last session also provided an opportunity for us to look back on the firstyear <strong>of</strong> the new MSc in Applicable Mathematics. For example, one discussion (minute 3(b) <strong>of</strong> the20
12.05.05 ACR) concerned the possibility <strong>of</strong> getting students to undertake some preparatory work onJava prior to starting the programme. This was something that the first intake <strong>of</strong> 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 <strong>and</strong> 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 <strong>of</strong> their differing backgrounds.Monitoring <strong>of</strong> coursesWe are aware that the development <strong>of</strong> procedures for monitoring is an important emerging issue at the<strong>School</strong>. We have had, for several years now, procedures by which individual course outcomes areanalysed <strong>and</strong> discussed openly in a meeting <strong>of</strong> the whole <strong>Department</strong>. Each year, statisticalinformation concerning performance in each <strong>of</strong> our courses is presented to a <strong>Department</strong>al meeting <strong>and</strong>we seek explanations from lecturers for any unusual distribution <strong>of</strong> marks, such as an unusually highfailure rate, for example. We also present external examiners’ reports to <strong>Department</strong>al meetings, <strong>and</strong>discuss these fully.Staff/student liaison committeesThe department has two SSLCs: one for BSc Mathematics <strong>and</strong> <strong>Economics</strong> students <strong>and</strong> another forgraduate students (MSc <strong>and</strong> MPhil/PhD). Students are invited to suggest agenda items for the meetingahead <strong>of</strong> time, <strong>and</strong> are reminded <strong>of</strong> the names <strong>and</strong> email addresses <strong>of</strong> their year representatives. Theagenda is circulated to all students <strong>and</strong> staff by email, along with the minutes <strong>of</strong> 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 <strong>of</strong> SSLCmeetings are discussed at <strong>Department</strong>al meetings, so that points are not lost. One valuable feature <strong>of</strong>the ME SSLC meetings is that a member <strong>of</strong> the <strong>Economics</strong> <strong>Department</strong> is invited. As all students onthe degree are tutored in the Mathematics <strong>Department</strong>, this is a useful formal forum for dialoguebetween them <strong>and</strong> the <strong>Economics</strong> <strong>Department</strong>.Staff involvement in Quality issuesMost members <strong>of</strong> academic staff in the department are involved to some extent in quality managementissues (over <strong>and</strong> above those concerned with the courses they teach). For one thing, our departmentdoes not have a separate Teaching Committee consisting only <strong>of</strong> some subset <strong>of</strong> the staff. Therefore, allmatters related to teaching are discussed openly by the full department, in departmental meetings <strong>and</strong> 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 <strong>and</strong> at <strong>School</strong> committees are also discussed at departmental meetings.One <strong>of</strong> the administrative roles in the department is that <strong>of</strong> Quality Officer. It has been useful to havethis as a specified job, <strong>and</strong> it has evolved since we introduced it in 1999. The Quality <strong>of</strong>ficer’s remit,generally, is to advise the Convener on all aspects <strong>of</strong> the <strong>Department</strong>'s work that affect the quality <strong>of</strong>teaching <strong>and</strong> learning, <strong>and</strong> to chair the Annual Course Review. Much <strong>of</strong> the work in monitoring <strong>and</strong>21
enhancing quality is, however, distributed among the staff in the department, as part <strong>of</strong> specificadministrative roles. The Class Teaching Officer (possibly with the Convener) deals with the results <strong>of</strong>surveys <strong>of</strong> class teachers <strong>and</strong> any problems highlighted by these or the observations <strong>of</strong> class teachers.The <strong>Department</strong>al Manager arranges the schedule <strong>of</strong> teaching observations, in which all staffparticipate. The <strong>Department</strong>al Tutor is responsible for the quality <strong>of</strong> the undergraduate tutorial system.The MSc Programme Director <strong>and</strong> Doctoral Programme Director have responsibility for quality on theMSc <strong>and</strong> MPhil/PhD. We also have a designated Teaching <strong>and</strong> Learning Centre liaison Officer, anEqual Opportunities Officer, <strong>and</strong> a Library <strong>and</strong> IT Services Liaison Officer. Quality management <strong>and</strong>enhancement is therefore deeply embedded in the department.Staff h<strong>and</strong>bookMuch <strong>of</strong> the information that academic staff need to know about the <strong>School</strong>’s <strong>and</strong> the <strong>Department</strong>’sprocedures, many connected with maintaining <strong>and</strong> enhancing quality, is provided in the StaffH<strong>and</strong>book. The h<strong>and</strong>book provides helpful information <strong>and</strong> guidance to new members <strong>of</strong> staff in the<strong>Department</strong> about many <strong>of</strong> the procedures <strong>and</strong> practices <strong>of</strong> the LSE <strong>and</strong> the Mathematics <strong>Department</strong>.It also serves as one-stop-shop for most <strong>of</strong> the Mathematics <strong>Department</strong>’s main documents, <strong>and</strong> istherefore useful to all <strong>Department</strong>al Staff.Observations <strong>of</strong> teachingWe instituted a scheme for peer observation <strong>of</strong> teaching in 1999/2000, <strong>and</strong> extended this to coverobservation <strong>of</strong> occasional teachers by staff in the following year. This was partly in response to theQAA Review Team’s comment that the quality <strong>of</strong> our class teaching was “variable”. Our initialexperience <strong>of</strong> peer observation was mostly positive; those conducting the observations generally foundit to be <strong>of</strong> more benefit than those being observed. The system we now operate is that all teachers inthe <strong>Department</strong> are observed every two years, except that new teachers are observed in their first term<strong>of</strong> teaching <strong>and</strong> again a year later. (In this context, it is perhaps worth stressing that there areconsiderably more occasional teachers in the <strong>Department</strong> than there are permanent members <strong>of</strong> staff.)We cannot point to any instances where observations <strong>of</strong> teaching have unearthed anything other thanminor deficiencies, but it has been useful to be aware <strong>of</strong> these. In one instance, for example, a newclass teacher was observed <strong>and</strong> it was decided (after consultation with Liz Barnett, Director <strong>of</strong> theTeaching <strong>and</strong> Learning Centre) that that teacher would be better deployed on a different sort <strong>of</strong>mathematics course, <strong>and</strong> we have now done this. In another instance, as a result <strong>of</strong> 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 <strong>Department</strong> are doing so to a high st<strong>and</strong>ard.Surveys <strong>of</strong> Class TeachingThe <strong>School</strong> conducts its own surveys <strong>of</strong> student opinion regarding occasional teachers in theMichaelmas Term; we have found this to be <strong>of</strong> limited use, mostly because the results have not alwaysreached us in time to take action for the start <strong>of</strong> Lent term. Accordingly, we conduct our own smallscalesurvey, in week 7 <strong>of</strong> Michaelmas term, <strong>of</strong> new class teachers <strong>and</strong> also <strong>of</strong> those who have beenteaching for us but who are now teaching a course new to them. This is distributed via the classes, <strong>and</strong>is designed to be very quick to complete. Most <strong>of</strong> the questions are designed to ensure that the teachers22
are meeting our requirements (which are somewhat different from the <strong>School</strong> as a whole, especially asregards the marking <strong>and</strong> returning <strong>of</strong> weekly exercises); we do also ask one simple question about thebenefit students derive from the class teaching, <strong>and</strong> allow students to write comments. We are able toprocess the information in our <strong>Department</strong>al Office in time to give feedback to teachers before the end<strong>of</strong> term. Any instances where there are a significant number <strong>of</strong> negative comments are followed up bythe Class Teaching Officer.Support for part-time teachersThe Teaching <strong>and</strong> Learning Centre is well aware that what is expected <strong>of</strong> class teachers in quantitativesubjects is different from the <strong>School</strong> norm. Accordingly, separate induction sessions have been set upfor teachers in these subjects, including one session (on classes <strong>and</strong> assessment <strong>of</strong> classwork)conducted by members <strong>of</strong> the Mathematics <strong>and</strong> Statistics <strong>Department</strong>s. The induction programme iscompulsory for new class teachers <strong>and</strong> as a whole has been very well-received by teachers who havetaken it. A permanent member <strong>of</strong> 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, <strong>and</strong> forproviding guidance <strong>and</strong> monitoring. All class teachers in the department are given a copy <strong>of</strong> the ClassTeachers’ H<strong>and</strong>book. This comprehensive booklet brings together several documents that we used toprovide separately; in particular the “Code <strong>of</strong> Practice” which has been developed over several years.The main purposes <strong>of</strong> the H<strong>and</strong>book are to collect in an accessible form the most important informationabout what the <strong>Department</strong> does, <strong>and</strong> to set out how we view class teaching, what we expect <strong>of</strong> classteachers, <strong>and</strong> what they can expect <strong>of</strong> lecturers.5. Tutorial provision <strong>and</strong> 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 <strong>School</strong> sends them. This consists <strong>of</strong> a welcoming letter, information on the Inductionmeeting, some review exercises (for MA100) indicating what they should know by way <strong>of</strong> preparation,<strong>and</strong> information on the Cumberl<strong>and</strong> 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 <strong>and</strong> registration, some suggestions for preliminary reading,<strong>and</strong> detailed information on the structure <strong>of</strong> the programme <strong>and</strong> the courses within it. This informationis also on the departmental website at http://www.maths.lse.ac.uk/MSc_new_arrivals.html.Induction <strong>of</strong> new studentsThe <strong>Department</strong> holds Inductions for its new students on the BSc <strong>and</strong> MSc in the week beforeMichaelmas Term teaching begins. These provide an informal environment in which new students canmeet the staff <strong>of</strong> the <strong>Department</strong>, <strong>and</strong> we can give them important information about the <strong>Department</strong>,the tutorial system <strong>and</strong> 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 <strong>and</strong> lists <strong>of</strong> who to contact regarding any questions or concerns they mayhave. MSc students are given short descriptions <strong>of</strong> each <strong>of</strong> the mathematics courses on <strong>of</strong>fer, by those23
teaching them, <strong>and</strong> are provided with s<strong>of</strong>tware they will need during their course <strong>of</strong> study (such asmathematical typesetting s<strong>of</strong>tware <strong>and</strong> 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 <strong>and</strong> financial situation), course choices, preferred manner <strong>of</strong> contact,organization <strong>of</strong> tutorial meetings. For each student, tutors keep a st<strong>and</strong>ardized “log-sheet” in whichdates <strong>of</strong> meeting <strong>and</strong> specific items that have been discussed are noted. These log-sheets also providevaluable information when there is a change in tutor.Student h<strong>and</strong>booksThe <strong>Department</strong> produces special programme-specific Student H<strong>and</strong>books (for the BSc, MSc <strong>and</strong>MPhil/PhD), <strong>and</strong>, for the BSc <strong>and</strong> MSc, these are distributed at the Inductions. These H<strong>and</strong>bookscontain lots <strong>of</strong> useful information that we hope will help settle the students in (such as maps <strong>of</strong> LSE,locations <strong>of</strong> places to eat, etc) as well as important information about the degree they are taking. Theyare also available on the <strong>Department</strong>’s website (at http://www.maths.lse.ac.uk/studyinfo.html).Diagnostic test <strong>and</strong> additional supportAs described in Section 1.3, we conduct a ‘diagnostic test’, the results <strong>of</strong> which are returned toindividual students by their personal tutors. Tutors are then alerted to potential difficulties thosestudents might have, <strong>and</strong> 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 <strong>and</strong> classes <strong>and</strong> to provide students with further advice on tackling problems.Cumberl<strong>and</strong> LodgeOur first-year BSc ME students <strong>and</strong> the MSc students are encouraged to attend a 2 day orientationsession at Cumberl<strong>and</strong> Lodge in the October or Novemer <strong>of</strong> their first year. The purpose <strong>of</strong> this is tohelp students get to know each other <strong>and</strong> also to give them the opportunity to meet their lecturers inmore relaxed surroundings. This is achieved in a number <strong>of</strong> ways, including small group sessions,where students are brought together for fun activities mixed with more serious discussions, <strong>and</strong> also bytalks on topics related to mathematics, but on more general topics than they might find in their courses.At the end <strong>of</strong> the event we h<strong>and</strong> out a feedback questionnaire. This has a very high response rate <strong>and</strong>shows the event to be extremely popular.Orientation seminarsThe department organises occasional ‘orientation seminars’ for our first year Mathematics <strong>and</strong><strong>Economics</strong> students. In previous years, jointly with Statistics, we organised a programme <strong>of</strong> suchseminars <strong>and</strong> required new students in Mathematics <strong>and</strong> <strong>Economics</strong>, Actuarial <strong>Science</strong> <strong>and</strong> BusinessMathematics <strong>and</strong> Statistics to attend. However, after consultation with the students, it was thoughtbetter to organise such seminars specifically for ME students, <strong>and</strong> to do so on an ad-hoc basis. Theseminars will usually include one on careers, one on study skills (especially as related to mathematics),<strong>and</strong> some from alumni who share their experiences <strong>of</strong> work or further study with the students.24
Undergraduate tutorial supportEach student registered to the Mathematics <strong>Department</strong> is allocated a personal tutor, in accordance withthe <strong>School</strong>’s regulations. Our policy is that where possible a student has at most two tutors during theirtime at LSE, <strong>and</strong> most students keep the same tutor for the full 3-year period. All academic members<strong>of</strong> staff <strong>and</strong> the 2/3 FTE instructor act as personal tutors. Each <strong>of</strong> these has an approximately equalnumber <strong>of</strong> tutees, with the part-time instructor taking half that amount. (This session, each member <strong>of</strong>staff has around 26 tutees, this figure including MSc <strong>and</strong> General Course students.) We also try to giveeach tutor a mix <strong>of</strong> students from different years <strong>and</strong> from the two degrees. The tutorial system isoverseen by the <strong>Department</strong>al Tutor, currently Dr. Jan van den Heuvel. He has additional <strong>of</strong>fice 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 the<strong>Department</strong>al Tutor, <strong>and</strong> hence can prepare documentation that makes these visits more efficient, butdoes also advise students when other parts <strong>of</strong> the LSE are more suitable for their particular concern.The <strong>Department</strong>al Tutor sends advisory emails to all tutors, informing them <strong>of</strong> new developments <strong>and</strong>reminding them when they need to invite students for a tutorial visit. The <strong>Department</strong>al Tutor alsoreports regularly to the <strong>Department</strong>al 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, <strong>and</strong> follows this up with additional reminders, phonecalls, <strong>and</strong> 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 <strong>and</strong> 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 <strong>and</strong> second year students on each degree regarding their choice <strong>of</strong> optionsin the subsequent year. A meeting is also held, at which the degree regulations <strong>and</strong> special regulationsregarding outside options are explained in detail. The introduction <strong>of</strong> LSE for You has made the courseselection procedure easier, <strong>and</strong> it perhaps makes the regulations clearer to students. Tutors discussstudent course choices with their tutees.Advice <strong>and</strong> 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 <strong>of</strong> thinking about real problems, based on formaldefinitions <strong>and</strong> pro<strong>of</strong>s, is not familiar to many entrants. Thus we expect to see transfers from ME to(for instance) <strong>Economics</strong> or Business Mathematics <strong>and</strong> Statistics (BMS). Since most <strong>of</strong> 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 <strong>Science</strong> orBMS, something that is relatively straightforward as these programmes have very similar first years.We additionally have isolated students from degrees such as <strong>Economics</strong> who are interested in doingmore mathematics after the first year. We usually try to accommodate this at the cost <strong>of</strong> them having25
somewhat fewer options in later years. Every year there are a couple <strong>of</strong> students who were accepted fora completely different degree, but who, between the time <strong>of</strong> applying to the LSE <strong>and</strong> the actual startingdate, realise that their real interests lie in mathematics <strong>and</strong> economics, <strong>and</strong> 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 <strong>of</strong> the ME degree. If possible, such transfers are always made conditional on good exam results inthe LSE exams taken at the end <strong>of</strong> the General Course year. It usually also involves a careful selection<strong>of</strong> 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 <strong>Department</strong>al Tutor. Forearly first year students, he usually consults the Admissions Tutor to assist in assessing the informationcontained in the student’s file. The <strong>Department</strong>al Tutor also ensures that possible transfer students areaware <strong>of</strong> the regulations <strong>of</strong> the degree, pointing out that the structure is much more rigid <strong>and</strong>challenging than in many other degree programmes. Students who go ahead with a transfer are ingeneral well-motivated <strong>and</strong> obtain excellent results. In the last couple <strong>of</strong> years, more students havetransferred into the ME degree than out <strong>of</strong> it.MSc tutorial <strong>and</strong> supervision supportAll MSc students are assigned a member <strong>of</strong> staff who acts as their tutor <strong>and</strong> meets them on a regularbasis. Members <strong>of</strong> the academic staff will <strong>of</strong>fer dissertation topics that they are willing to supervise <strong>and</strong>they speak about these in the seminar MA498. This provides an opportunity for students to discoverwhat kinds <strong>of</strong> dissertation topic they might be interested in <strong>and</strong> to choose their project <strong>and</strong> dissertationsupervisor (usually after further, more detailed, discussion with the member <strong>of</strong> staff). The supervisorwill monitor progress on a continuing basis <strong>and</strong> 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 <strong>and</strong> graduateAs mentioned above, the department has two SSLCs: one for Mathematics <strong>and</strong> <strong>Economics</strong> students <strong>and</strong>another for graduate students (MSc <strong>and</strong> MPhil/PhD). This provides a forum for students to raise issues<strong>of</strong> concern, <strong>and</strong> the minutes <strong>of</strong> these meetings <strong>and</strong> actions taken are discussed fully in <strong>Department</strong>almeetings. (More information on how these committees work can be found earlier in this document.)Study skills supportOn our website we provide a document <strong>of</strong>fering advice to students on the specific topic <strong>of</strong> studying formathematics courses (http://www.maths.lse.ac.uk/studyskills.html) <strong>and</strong> one <strong>of</strong> the Orientation Seminarswe run for our first year students (usually conducted jointly by a member <strong>of</strong> the Mathematics<strong>Department</strong> <strong>and</strong> the Director <strong>of</strong> the Teaching <strong>and</strong> Learning Centre) also covers much <strong>of</strong> this material.Additionally, the Teaching <strong>and</strong> Learning Centre provides opportunities for students to improve their26
study skills, for example through its one-to-one sessions <strong>and</strong> its Academic <strong>and</strong> Pr<strong>of</strong>essionalDevelopment Programme. Our BSc H<strong>and</strong>book also gives some advice on how to study mathematics.CareersThe <strong>Department</strong> organises several events at which careers guidance is provided, including anOrientation seminar. In addition students are regularly emailed information about career opportunities,<strong>and</strong> we provide some useful links in the Careers section <strong>of</strong> our web pages for students(http://www.maths.lse.ac.uk/students.html#Careers).Although a large proportion <strong>of</strong> students decide to go into the financial sector, students from our degreeshave gone onto a wide variety <strong>of</strong> careers, including consultancy, school teaching, student politics, <strong>and</strong>even the church. A large number <strong>of</strong> our students also proceed to graduate study, in all sorts <strong>of</strong> areas,from mathematics, economics, finance, to law <strong>and</strong> gender studies.Alumni relations <strong>and</strong> eventsLast session, with helpful support from the Office <strong>of</strong> Development <strong>and</strong> Alumni Relations, the<strong>Department</strong> organised its first alumni get-together. The event took place in the Senior Common Roomat LSE on 27 th April. The Convener <strong>of</strong> Mathematics welcomed everyone to the event, <strong>and</strong> as drinks <strong>and</strong>canapés were served, the <strong>Department</strong>'s Alumni Events Coordinator outlined what he hoped theMathematics <strong>Department</strong> could do for its alumni, <strong>and</strong> described the services that the <strong>School</strong> is able toprovide to its former students. The evening was a great success <strong>and</strong> there were representatives fromabout 10 different graduation years going back as far as 1985, with the ‘class <strong>of</strong> 2001’ best represented.Further similar events are planned in the future <strong>and</strong> we have also recently established an Alumniwebsite (http://www.maths.lse.ac.uk/Alumni/).Another important aspect <strong>of</strong> alumni relations, particularly for our current students, is that some <strong>of</strong> ourgraduates help provide advice to existing students by speaking about their careers or further study inthe Orientation seminars.Study roomsOne area <strong>of</strong> student support in which the <strong>Department</strong> feels that its students are let down by the <strong>School</strong>is that we no longer have a study room for our undergraduate students. We did have a study room in2002 <strong>and</strong> 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 <strong>and</strong> felt that it hadhelped to integrate the student body into a cohesive whole. It also provided opportunities forcollaborative learning for all students <strong>and</strong> for first years to seek advice <strong>and</strong> guidance form their peers onmathematical problems, courses <strong>and</strong> even careers. ……The Review team would like to suggest that the Estates Office <strong>and</strong> Accommodation Committeeshould work closely with the <strong>Department</strong> to see if space can be provided for a study room <strong>of</strong> adequatesize wihin the <strong>Department</strong> or as close as possible.’The lack <strong>of</strong> 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 <strong>and</strong> hasemailed them to let them know <strong>of</strong> 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 <strong>and</strong> Statistics studentsociety. These take place weekly <strong>and</strong> are announced in the first year mathematics lectures.Equal OpportunitiesThe <strong>Department</strong> has an Equal Opportunities Officer, who, among other things, conducted an on-linesurvey <strong>of</strong> our students last session. The results <strong>of</strong> the survey were positive, indicating that students hadreceived equal treatment.6. MPhil/PhD provisionIntroductionThe <strong>Department</strong> <strong>of</strong>fers a non-taught MPhil/PhD in Mathematics for students who already havedeveloped an interest in one <strong>of</strong> 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 <strong>School</strong>.We also made a policy decision several years ago to support research students from the <strong>Department</strong>’soutside funds (mainly generated as a result <strong>of</strong> 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 <strong>of</strong> our courses. The establishment <strong>of</strong> the MSc in Applicable Mathematics has proven veryuseful in several ways to our research students. It enables them to attend a range <strong>of</strong> lecture courses thatreflect the research interests <strong>of</strong> the staff, <strong>and</strong> hence are either highly relevant to the PhD students or areuseful in broadening their mathematical education. The presence <strong>of</strong> a sizeable cohort <strong>of</strong> MSc students,<strong>and</strong> the informal links that arise between them <strong>and</strong> 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 <strong>and</strong> Applicable Mathematics. We also have an informal workshop,primarily organised by a research student, that is attended by staff <strong>and</strong> research students. Theseworkshops are also an opportunity for LSE research students to meet research students from otherMathematics <strong>Department</strong>s in the University <strong>of</strong> <strong>London</strong>. Each student is expected to present a talk inone <strong>of</strong> the workshops, <strong>and</strong> to publish results in our CDAM research report series. This has beenrunning for several years but, on the recommendation <strong>of</strong> our last review, we have formalized it as part<strong>of</strong> research student training, giving it the course code MA501 <strong>and</strong> <strong>of</strong>ficially timetabling it. Students are28
encouraged to attend research conferences. The <strong>Department</strong> provides, for each student, a budget <strong>of</strong>£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 <strong>and</strong> development <strong>of</strong> a capacity in the student for originalresearch in the chosen field <strong>of</strong> 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 <strong>and</strong> subsequentpublications that contribute to the development <strong>of</strong> <strong>and</strong> underst<strong>and</strong>ing <strong>of</strong> the chosen area <strong>of</strong>mathematics.Students are thus <strong>of</strong>fered a supportive environment so that they feel that they are part <strong>of</strong> a community<strong>of</strong> scholars <strong>and</strong> are well placed to pursue a career building on their research accomplishments.Supervision <strong>and</strong> supportThe first or Lead supervisor is agreed during the application process. This is determined by a number <strong>of</strong>factors, in particular the willingness <strong>of</strong> an academic member <strong>of</strong> staff to direct a research programmethat is <strong>of</strong> interest to both the supervisor <strong>and</strong> the student. This is obviously guided by the researchexpertise <strong>of</strong> the academic member <strong>of</strong> 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 <strong>of</strong> PhD students, as wellas being in overall charge <strong>of</strong> the doctoral programme arrangements. He or she also has to approvecontinued annual registration, change <strong>of</strong> status (such as transferring from full-time to part time), theupgrade from MPhil to PhD, assignments <strong>of</strong> Second supervisors, <strong>and</strong> any other special arrangementssuch as the thesis viva examinationThe <strong>Department</strong>’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 <strong>of</strong> a student’s research training on a Mathematics PhD <strong>and</strong> their purpose is to reviewwork done <strong>and</strong> to agree further work. Advice or guidance may be given as to directed reading <strong>and</strong> inregard to formal courses to be followed, as well as to participation in conferences <strong>and</strong> graduate schoolswhen appropriate. Monitoring includes progress reports to the second supervisor <strong>and</strong> formal termly <strong>and</strong>annual reporting to the Doctoral Programme Director.Skills TrainingIn addition to the research training provided, all our research students are <strong>of</strong>fered the opportunity toteach for the <strong>Department</strong> (<strong>and</strong> to take advantage <strong>of</strong> the training opportunities available). Training inLinux <strong>and</strong> some computer programming is likely to be provided during the course <strong>of</strong> the student’s PhD,though this may vary depending on its appropriateness to the research topic. A PhD significantly aidsthe development <strong>of</strong> a student’s technical writing skills. Some formal training is provided on this, in theform <strong>of</strong> written guidance on technical writing <strong>and</strong> an advisory session. In addition, the Teaching <strong>and</strong>Learning Centre <strong>and</strong> Methodology Institute <strong>of</strong>fer courses in study skills <strong>and</strong> specialist options in arange <strong>of</strong> aspects <strong>of</strong> social research.29
Students are given the opportunity (<strong>and</strong> encouragement) to publish in CDAM’s research report series<strong>and</strong> the informal CDAM workshops provide an ideal opportunity for students to improve theirpresentation skills.Monitoring <strong>and</strong> review <strong>of</strong> progressA formal termly report is submitted to the Doctoral Programme Director shortly after the end <strong>of</strong> eachterm. This includes a summary <strong>of</strong> meetings between student <strong>and</strong> supervisor. The report at the end <strong>of</strong> theSummer Term also serves as the basis <strong>of</strong> the <strong>School</strong>’s annual progress report form: this formalassessment is conducted by the DPD on the basis <strong>of</strong> statements made by the supervisors <strong>and</strong> the student<strong>and</strong> on the termly progress reports submitted to the DPD by the student’s supervisor. This wouldnormally cite any research reports written with the participation <strong>of</strong> the student. The DPD then presentshis findings to the Convener at the end <strong>of</strong> the summer term.Major Review <strong>and</strong> upgrade to PhDAt around the end <strong>of</strong> the student's first year, <strong>and</strong> on receipt <strong>of</strong> the first annual progress report <strong>of</strong> aResearch student, the DPD, in consultation with the lead supervisor, determines when to conduct thestudent's Major Review <strong>and</strong> will write to the student indicating when this is expected to occur. It isnormal to hold a Major Review within the first fifteen months <strong>of</strong> registration.The review is conducted by the Doctoral Programme Director <strong>and</strong> the first Supervisor <strong>and</strong> theprocedure is as follows. Initially, the student must submit evidence <strong>of</strong> research progress (relative to thetasks set by the lead Supervisor). An example <strong>of</strong> the kind <strong>of</strong> evidence the DPD would hope to receivefrom research students is an appropriate report <strong>of</strong> research, written by the student <strong>and</strong> accompanied bythe Lead Supervisor's assessment. The evidence submitted could also be an early draft <strong>of</strong> a paper, orearly draft chapter <strong>of</strong> thesis, or CDAM report, again accompanied by the Lead Supervisor's assessment.In the event <strong>of</strong> favourable evidence being presented, the outcome <strong>of</strong> the Major Review would usuallybe an upgrade in the registration from MPhil to PhD status. Where the progress falls short <strong>of</strong> 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 <strong>of</strong> the followingSummer Term, whether or not continued registration is in order.Facilities <strong>and</strong> environmentProvision <strong>of</strong> desks <strong>and</strong> computers for our research students is above the <strong>School</strong>’s requirement, but is indanger <strong>of</strong> becoming inadequate for mathematical research as the number <strong>of</strong> students has increased. The<strong>School</strong> norm <strong>of</strong> 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 <strong>Department</strong> has followed <strong>School</strong> <strong>and</strong> EPSRC proposals in setting up a system <strong>of</strong> support (orsecondary) supervisors. The small size <strong>of</strong> 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 <strong>of</strong> the research project undertaken. This has the consequence that advice <strong>and</strong>assistance to students comes not only from supervisors, but also more widely. A research student inour <strong>Department</strong> is very unlikely to go un-noticed.Staff student liaison committeeResearch <strong>and</strong> 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, <strong>and</strong> still are, small enough that most issues they mightwant to raise can easily be done so on an informal level.Completion <strong>and</strong> submission ratesThe recent increase in the number <strong>of</strong> 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) <strong>and</strong> 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 <strong>of</strong> this section reflects this rather than the relative importance we placeon service teaching, which is an aspect <strong>of</strong> our provision that we take extremely seriously.IntroductionAs emphasised earlier, one <strong>of</strong> the <strong>Department</strong>’s key aims is to provide students studying other degreecourses with an appropriate quantitative background, specific technical skills, <strong>and</strong> an underst<strong>and</strong>ing <strong>of</strong>the role <strong>of</strong> mathematics in the social sciences. As mentioned in Section 2.3, many <strong>of</strong> our courses aretaken (either as options or as a compulsory part <strong>of</strong> 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 <strong>and</strong> 2.3). As Appendix A shows, the numbers <strong>of</strong> studentsinvolved are large <strong>and</strong> have grwn considerably since the last review. The work involved in teachingcourses <strong>of</strong> this size should not be underestimated. The economies <strong>of</strong> scale resulting from teachingseveral hundred students at once are not great. There are significant administrative overheads inensuring the smooth running <strong>of</strong> such a large course, the provision <strong>of</strong> suitable support materials requiresparticular attention, <strong>and</strong> there is much that the lecturer has to do in the way <strong>of</strong> supervising <strong>and</strong>supporting armies <strong>of</strong> class teachers.Class teachers31
Because some <strong>of</strong> our courses are so large (notably MA100, MA103, MA107, MA200, MA201), weneed to make extensive use <strong>of</strong> class teachers. The Class Teaching Officer is responsible for theappointment <strong>of</strong> class teachers, <strong>and</strong> as mentioned in Section 1.3, many <strong>of</strong> our part-time class teachershave significant pr<strong>of</strong>essional experience <strong>and</strong> qualifications. As described in Section 4, all new classteachers are required to attend an induction programme <strong>and</strong> their progress is monitored throughout bysurveys (our own <strong>and</strong> the <strong>School</strong>’s) <strong>and</strong> is overseen by the Class Teaching Officer (as described inSection 4). The quality <strong>of</strong> our class teachers <strong>and</strong> the processes by which we monitor them <strong>and</strong> assurethe quality <strong>of</strong> 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, <strong>and</strong> there are clear expectations on lecturers as to what they should provide in the way <strong>of</strong> support<strong>and</strong> guidance to class teachers (described in our departmental Staff H<strong>and</strong>book <strong>and</strong> Class Teachers’H<strong>and</strong>book).8. ConclusionsThe <strong>Department</strong> is satisfied that it provides its students with high-quality courses <strong>and</strong> programmes,taught <strong>and</strong> supported well. We have continued to demonstrate a high degree <strong>of</strong> curricular innovation,<strong>and</strong> we have mechanisms for quality assurance <strong>and</strong> enhancement that have been developed over thepast several years <strong>and</strong> which have now bedded down well.At the time <strong>of</strong> the last review, we were considering introducing an MSc programme in the area <strong>of</strong>discrete <strong>and</strong> applicable mathematics, <strong>and</strong> the Review Team was very supportive <strong>of</strong> 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, <strong>and</strong> we believe that it will continue to attract goodstudents.Enhancement <strong>of</strong> our provision will require further resourcing, both in staffing <strong>and</strong> in space, particularlyif, as we would wish, we are to continue to exp<strong>and</strong> our activities to take full advantage <strong>of</strong> otheropportunities that may arise.The strengths highlighted in our last review remain, <strong>and</strong> the areas <strong>of</strong> 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 <strong>of</strong> ourundergraduate study room: such a room no longer even exists.32
Appendix A: Courses taught in the department, <strong>and</strong> student numbersThe following table shows the courses taught by the department, the student numbers at the time <strong>of</strong> thelast review, <strong>and</strong> 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 <strong>of</strong> a decision by the<strong>Economics</strong> department that students on <strong>Economics</strong>-based degrees required a more advanced methodscourse.) Most <strong>of</strong> our courses are half-unit courses, <strong>and</strong> for this reason we have taken the number <strong>of</strong>half-unit equivalent students as the basic unit in these figures. (So each student on a full unit coursegives a contribution <strong>of</strong> 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 <strong>of</strong> Finance And Valuation 41 42Discrete Mathematics 15 3MA312 Convexity <strong>and</strong> Fixed Point Theorems 2 No longerrunningMA313Probability For Finance And <strong>Economics</strong> 5 6MA314Theory Of Algorithms 8 7MA315Algebra And Its Applications 8 17MA401Computational Learning TheoryDid not run01/02Not running05/0633
MA402Game Theory I 2 22MA406 Theory <strong>of</strong> Algorithms 6 No longerrunningMA407Algorithms <strong>and</strong> Computation New in 2004/5 35MA408Discrete Mathematics <strong>and</strong> Complexity New in 2004/5 9MA409Continuous-Time Optimisation New in 2004/5 18MA410MA411MA412MA413MA498Information, Communication <strong>and</strong> Cryptography New in 2004/5 9Probability <strong>and</strong> Measure New in 2004/5 6Functional Analysis <strong>and</strong> its Applications New in 2005/6 6Games <strong>of</strong> Incomplete Information New in 2005/6 13Dissertation in Mathematics New in 2004/5 54Total 1971 297634