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UCL DEPARTMENT OF MATHEMATICS
MSc in Mathematical Modelling
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CONTENTS Section 1: General Information ........................................................................... 1 1. Introduction.................................................................................................... 1 2. Dates of Term................................................................................................ 1 3. Addresses...................................................................................................... 1 4. List of staff and locations in the Department.................................................. 2 5. Advice and guidance ..................................................................................... 6 6. Teaching and learning ................................................................................... 8 7. Library, computing and other resources ........................................................ 9 8. Examinations (formal).................................................................................. 11 9. Paying Fees................................................................................................. 14 SECTION 2: COURSE INFORMATION............................................................ 15 10. Introduction.................................................................................................. 15 11. Programme Structure .................................................................................. 15 12. Programme Aims......................................................................................... 16 13. Compulsory modules................................................................................... 16 MATHGM01 Advanced Modelling Mathematical Techniques....................................... 16 MATHGM02 Nonlinear Systems ................................................................................... 17 MATHGM03 Operational Research .............................................................................. 17 MATHGM04 Computational and Simulation Methods .................................................. 18 MATHGM05 Frontiers in Mathematical Modelling and its Applications ........................ 19 14. Optional Modules......................................................................................... 19 MATHGM21 Quantitative and Computational Finance ................................................. 20 MATHG302 Asymptotic Methods and Boundary Layers Theory .................................. 21 MATHG303 Hyperbolic PDEs with Applications ........................................................... 21 MATHG304 Geophysical Fluid Dynamics..................................................................... 22 MATHG305 Mathematics for General Relativity ........................................................... 22 MATHG306 Cosmology ................................................................................................ 23 MATHG307 Biomathematics......................................................................................... 23 MATHG501 Theory of Traffic Flow ............................................................................... 24 MATHG505 Evolutionary Games and Population Genetics.......................................... 24 MATHG506 Mathematical Ecology ............................................................................... 25 MATHG508 Financial Mathematics .............................................................................. 25 15. MATHGM10 MSc Project ............................................................................ 26 16. Requirements to Pass the Course............................................................... 28 17. Tutors .......................................................................................................... 28 18. Module Timetable ........................................................................................ 29
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MSc and Post Graduate Diploma in Mathematical Modelling Frontiers in the application of mathematics
Handbook
Section 1: General Information
1. Introduction
This booklet contains information for students reading for the Postgraduate Diploma or Master’s degree in Mathematical Modelling at UCL. Another relevant document is the UCL Student handbook which is distributed to all students at college enrolment containing general information for all students at UCL. The UCL Student Handbook can be obtained from the Registry or viewed on the Registry website at: http://www.ucl.ac.uk/current-students/. More details about sources of information is given later in this booklet, but you can consult the Departmental Office (Room 610) or the MSc Tutor, Dr S Baigent (Room 802b). Information is also available at the Mathematics Department website: http://www.ucl.ac.uk/Mathematics/ where any updates/corrections will also be posted.
2. Dates of Term
Autumn: Monday 27 September 2010 – Friday 17 December 2010 (reading week 8 – 12 November)
Spring: Monday 10 January 2011 – Friday 25 March 2011
(reading week 14 – 18 February) Summer:
Tuesday 3 May 2011 – Friday 17 June 2011
You are expected to be available to attend college during all of the above terms. The course runs for a full 12 months with the Project deadline usually set for mid September.
3. Addresses
It is very important that we have your correct term-time and home addresses. If you change your address it is your responsibility enter the changes on PORTICO, the Registry website, at: http://www.ucl.ac.uk/portico/. If we do not have your up-to-date address (and telephone number), we will not be able to contact you if anything urgent arises, and we may not be able to send you important documentation. Please also see the relevant section of the UCL Student Handbook.
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4. List of staff and locations in the Department
If no extension is given, please use the office extension 32839 or look on the departmental web-site or notice boards for updated information. Most internal numbers have the prefix of 3. To dial from outside UCL use 020 7679 followed by the last 4 digits. For example, the main Department Office is on extension 32839 or externally 020 7679 2839. Head of Department Prof D Vassiliev Deputy Head of Department Prof N R McDonald Departmental Tutor Dr M L Roberts Admissions Tutor Dr R I Bowles Postgraduate Tutor (Pure Maths) Dr J Talbot Postgraduate Tutor (Applied Maths) Prof V Smyshlyaev Course Director Mathematical Modelling programmes Prof F T Smith Departmental MSc Tutor Dr S A Baigent Affiliate Tutor Dr I Petridis Joint Honours Exams Sub-Boards Dr J A Haight Chair of the Maths Exams Sub-Board Dr R Hill Chair of the Departmental Teaching Committee Prof S R Bishop Staff E-mail address Room Extension Professors of Mathematics Ball, K M [email protected] 607 32843 Bárány, I [email protected] 605 32836 Bishop, S [email protected] KLB 340 33082 Csörnyei, M [email protected] 712 32862 Johnson, E R [email protected] 805 32854 Johnson, F E A [email protected] 705 32845 Kim, M [email protected] KLB M203 31333 Kurylev, Y [email protected] KLB M205 37896 Laczkovich, M [email protected] 800 (T1) 32836 McDonald, N R [email protected] 604 32853 McGlade, J [email protected] 32839 Parnovski, L [email protected] 709 32847 Seymour, R M [email protected] 809 32858 Smith, F T [email protected] 609 32837 Smyshlyaev, V [email protected] 708 33854 Sobolev, A [email protected] 710 32863 Sokal, A D [email protected] 800 (T2) 32844 Vanden-Broeck, J-M [email protected] 814 32835 Vassiliev, D [email protected] 608 32442 Zaikin, A [email protected] 711 34375 Professor of Operational Research Utley, M, Director of CORU
[email protected] 24506
Professorial Research Associate Davey, Dr M [email protected] 504a 30170 Readers in Mathematics
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Esler, Dr G [email protected] 700 32842 Hill, Dr R M [email protected] 808 32404 Petridis, Dr I [email protected] 504b 37897 Timoshin, Dr S N [email protected] 803 32205 Wilson, Dr H J [email protected] 802a 31302 Yafaev, Dr A [email protected] 812 32861 Fellows Halburd, Dr R [email protected] 703 32973 Talbot, Dr J [email protected] 812a 34102 Senior Lecturers and Tutors Bowles, Dr R I [email protected] 603 33501 Roberts, Dr M L [email protected] 604a 32833 Lecturers Baigent, Dr S A [email protected] 802b 33593 Böhmer, Dr C [email protected] KLB 342 33597 Ovenden, Dr N C [email protected] 701 32128 Page, Dr K M [email protected] 810 33683 Sidorova, Dr N [email protected] KLB 341 37864 Teaching Fellows Ahmad, Dr R [email protected] 806 32839 Burnett, Mr J [email protected] 712 32862 Gray, Prof J Haight, Dr J A [email protected] 600 34309 Larman, Prof D G [email protected] 600 32855 López Peña, Dr J [email protected] 813 54068 Ronan, Prof M [email protected] 605 32836 Rose, Mr S [email protected] 600 34309 Strouthos, Dr I [email protected] 813 54068 Van der Heijden, Dr G [email protected] Civil Eng 32727 Walton, Dr J 806 32856
Postdoctoral Researchers Baudains, Mr P [email protected] 51099 Bosi, Dr R [email protected] 602 32831/32840 Caldera-Cabral, Dr G [email protected] 806 32856 Cooper, Dr F [email protected] 602 32831/32840 Fry, Ms H [email protected] 602 32831/32840 Hicks, Dr P [email protected] 602 32831/32840 Kakde, Dr M [email protected] 602 32831/32840 Kang, Dr H 602 32831/32840 Morozov, Dr S [email protected] 602 32831/32840 Obukhov, Dr Y [email protected] 602 32831/32840 White, Dr A [email protected] 602 32831/32840
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Clinical Operational Research Unit (CORU) – 4 Taviton Street Crowe, Dr S [email protected] 24953 Fiorentino, Dr F [email protected] 24505 Gallivan, Prof S [email protected] 24508 Pagel, Dr C [email protected] 24501 Reddy, Mr B [email protected] 24504 Skeen, Dr A 28549 Utley, Prof M [email protected] 24506 Vasilakis, Dr C [email protected] 24507
Departmental Administrator Higgins, Ms H [email protected] 611 32838 General Office Abdul Ghafoor, Mrs M Assistant Administrator
Undergraduate Teaching from April 2011 610 32894
Carboo, Mrs B Examinations Officer/ MSc Administrator 610 32841
Datta, Miss S Assistant Administrator 610 32939 Lawrie, Ms K Secretary 610 32881 Milich, Miss N Assistant Administrator
Undergraduate Teaching to March 2011 610 32894
Other room locations Postgraduate Room 713 32851 Postgraduate Room KLB M201 37881 Staff Room 606 - Student Reading Room 503 - Student Common Room 502 MSc Room 501 32834
Note that all rooms are in Mathematics Department, except those marked KLB (Kathleen Lonsdale Building). Access to this building is restricted, so if you wish to meet a member of staff whose office is there, you should contact the tutor by phone or email in advance to make arrangements.
Honorary Professors Hunt, J [email protected] 37743 Fraenkel, LE [email protected] 605 32836 Ronan, Prof M [email protected] 605 32836
Emeritus Staff and Honorary Research Fellows Anderson, Prof J M [email protected] 806 32839 Banaji, Dr M [email protected] 806 32856 Bangert, Dr P Belinfante, Dr D C Brown, Dr A L [email protected] 806 32856 Brown, Prof S N [email protected] Davies, Mr H L 712a 32249 Davis, Prof A M Eames, Dr I [email protected] Mech Eng Fenwick, Dr C
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Grimshaw, Prof R Grossman, Prof S I [email protected] Hocking, Prof L M [email protected] Jansons, Dr K M [email protected] 806 32856 Jayne, Prof J E [email protected] 806 32856 Jillians, Dr W Levitin, Prof M Martin, R Mathias, Dr A McMullen, Prof P [email protected] 600 34309 Morgan, Dr C J G [email protected] 806 32856 O’Neill, Prof M E [email protected] 600 34309 Pepper, Dr J V [email protected] Roth, Prof K F Rothman, P E [email protected] 605 32836 Sherlaw-Johnson, C Singmaster, Prof D B Stephenson, Dr W [email protected] Van der Heijden, Dr G [email protected] Civil Eng 32727 Williams, P G
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5. Advice and guidance
If you have any problems or difficulties, please discuss them with a member of staff. Specific questions about mathematical problems in your courses should in the first instance be taken up with the appropriate course lecturer. For more general questions (academic, personal, financial, accommodation, etc), you can talk with the following (see below for more details): (1) Your personal tutor;
(2) The MSc Tutor, Dr S. Baigent
(3) The Departmental Post-graduate Tutor, Prof FT Smith
(4) The Head of Department, Professor Dmitri Vassiliev (Room 608), or any other
member of staff you know
(5) In the maths office (Room 610), where a secretary will deal with matters concerned with MSc students, although you might also need to see the Departmental Administrator, Ms Helen Higgins, about matters to do with finance.
(6) Outside the Department, there are the College support services, which include:
• the Dean of Students (Welfare), Dr Ruth Siddall, [email protected] • the UCL Union, The Rights and Advice Centre, First Floor of the Bloomsbury
Theatre, 15 Gordon Street, http://www.ucl.ac.uk/disability/services/ucl-services/ucl-union
• the UCL Counselling Service, located at 3 Taviton Street (first floor, Room 101) (5 minutes walk from the Department): students can just go along there or phone (020 7679 1487). The student counselling service provides completely confidential help on all personal issues, http://www.ucl.ac.uk/disability/services/ucl-services/counselling-service
• the advisor to women students – appointments can be made through the Dean of Students Office, extension 24545.
If you become unhappy with your programme of study, or feel that you are falling behind and cannot cope, or are experiencing other problems, it is very important that you contact the Course Director, Prof FT Smith or the MSc Tutor Dr S Baigent (or another member of staff of the Department) straightaway. These difficulties can often be resolved but it is much easier if they are dealt with promptly (this is true regardless of whether you need some help to continue with the course, wish to change course, or even to give up the course). If you experience racial or sexual harassment, please discuss it with someone from the list above. More details on this are given in the UCL Student Handbook at: http://www.ucl.ac.uk/current-students/ .
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Careers The UCL Careers Service is located at: 4th Floor, ULU Building Malet Street London WC1E 7HY http://www.ucl.ac.uk/careers/ They can provide a variety of services. For more information, see the relevant section of the UCL Student Handbook. The careers officer in the Department is Prof Robb McDonald (Room 604). Various career talks take place in the Department each year. References You may well wish to use members of staff (e.g. your personal tutor, the MSc Tutor, or another member of staff who knows you) as referees for jobs or further study. Please seek the permission of whoever you are going to use as a referee. In any case, it is a good idea to talk briefly to your referee, and perhaps to give them your CV. Please also see information below under "Data Protection Act". Unless you request otherwise, references will be provided on request to companies and educational institutions during your time of study here and for two years afterwards without specific permission from you. If you require references after this time, you will need to contact the referee. Accommodation The UCL Student Residences Office is located at 117 Gower Street (Tel: 020 7679 6322) and has information about Halls and Houses administered by the College or the University. http://www.ucl.ac.uk/accommodation The University of London Housing Services, University of London Union, Malet Street, London WC1E 7HY (Tel: 020 7862 8880) and has information on private and other accommodation. http://www.housing.lon.ac.uk/ For more details, please see the UCL Student Handbook. Disabilities The college has a Committee for People with Disabilities; the Co-ordinator of this Committee is Ms Marion Lamb (020 7679 0100), whom you can contact if you have any queries. There are some special arrangements possible for students with disabilities, e.g. for taking examinations. If you wish to enquire about such arrangements, please contact the MSc Tutor in the first instance. Data Protection Act At the start of session you will have been given a form setting out the Department’s normal procedures (in relation to your rights under the Data Protection act). If you have agreed to the Department administering your student career in the way described, you will have signed the form; if not, you will have discussed the matter
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with the MSc Tutor, and alternative arrangements will have been made. The normal procedures specified on the form are as follows: Photographs: (i) We will take a photo of you, which may be stored digitally; these photos may be displayed in the Student Common Room, for ease of identification. (ii) We may also wish to display photographs of departmental activities to publicise these. (iii) The Department maintains its own WebPages; we may wish to publish student names and e-mail addresses here. Academic procedures: Marked written work will be put out for collection in the relevant lecture or left at a collection point in the main Department Office or returned to your pigeonhole in Room 501.
6. Teaching and learning
The primary method of teaching and learning in the MSc is by means of lectures, reinforced by coursework, self-study, and in some cases computer classes. There is also a substantial project component for the MSc. Student assessment of lectures Students are asked at the end of each Mathematics course to fill in an anonymous questionnaire on their assessment of the course. The forms will be analysed, and the summary of results posted on the noticeboard in the Student Common Room. Reading weeks Mathematics Department lectures and problem classes will not take place during the ‘reading weeks’ of 8-12 November 2010 or 14-18 February 2011. These weeks provide a time to go through what you have studied so far and make sure you understand it. Important: If you are taking courses from other departments, such lectures may continue during the reading weeks. Certain other activities may also take place during reading week. Coursework: problem sheets In some courses regular coursework is set. In most courses, this consists of problem sheets given out to be completed and handed in a week later. This is a very important part of the course - working on problems is one of the best ways of getting a good understanding of the topics (as well as learning how to solve problems!). Requirements for each course may vary; students should check individual course units. Keeping coursework Please note that you should keep all your returned marked coursework: you may be required to re-submit them for scrutiny at the end of the year. You will also find your coursework useful when you come to revise. Co-operation and plagiarism Plagiarism, which includes copying the work of other students, or copying from books, research papers or websites without proper acknowledgment and citation, is strictly
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forbidden, and could lead to severe penalties. When you are working on a problem, it may well be helpful to discuss it with other students, and indeed you may sometimes be asked to work in groups. However, you must write the work up independently and on your own. All written project work should be carefully referenced to acknowledge sources of information. Students will be required to submit both hard and electronic copies of their written work and you should be aware that, if deemed necessary, a project will be submitted to the Turnitin plagiarism detection system for evaluation. Please also read the entry on Plagiarism in the UCL Student Handbook, available online at: http://www.ucl.ac.uk/current-students/guidelines/policies/plagiarism Office hours The lecturer for each course will allocate an office hour each week, when they will normally be available in their office to answer questions on the course. This time will be advertised on the office doors. A list of lecturers with their room numbers is given above; you can also find photographs of members of staff in the Student Common Room, Room 502. Assessment Assessment is predominantly by formal written exams, held in the Third Term (Tuesday 3 May 2011 until Friday 17 June 2011). Some courses have a coursework component (e.g.10%). It is necessary to attend the lectures and complete the coursework satisfactorily in order to pass a course. If inadequate coursework is attempted, you may be considered to be "Not complete" and withdrawn from the exam, resulting in automatic failure in that course. The normal criterion for coursework to be considered adequate is that you make a reasonable attempt at a minimum of 50% of the coursework sheets. Please also note the section on Examinations later in this booklet and the information in the UCL Student Handbook. Attendance You are expected to be available to attend classes during all of term time, and therefore to attend all lectures, problem classes, etc. If your attendance is very poor, you may be asked to leave the MSc course. Absence due to illness or other unavoidable cause If you have to be absent for a period of more than 2 days, please let the Mathematics Departmental Office know (telephone: 020 7679 2841). If your absence is longer than a week, please see the MSc Tutor when you return to college, providing a doctor's note if relevant.
7. Library, computing and other resources
Library UCL has a substantial collection of Mathematics books in the library. The Mathematics collection is on the 3rd floor of the Science Library in the DMS Watson Building, at the south end of college. There may be relevant material, particularly in applied mathematics, elsewhere in the Science Library.It is worth while getting to know about the facilities of the library.
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Computing facilities MSc students have computers provided for their use in the MSc room, Room 501. There are also various workstation cluster rooms around college which are available for general student use. Departmental Office The Mathematics Department general office is Room 610. Photocopying All the Library's staffed sites have self-service photocopying facilities, operated by cards. Rechargeable cards are required to use the photocopiers. You need only buy one card and then keep it for the whole of your time at UCL. • Cards cost £1 each (this does not include any copy credit) • The minimum copycredit you can add to a copycard is 20p, the maximum is £50. • If you lose your copycard you will have to buy a new one. Therefore, we
recommend that you do not charge your copycard with large amounts of copy credit. It is also sensible to write your name on your card or record the individual number on the back of the card. You can then reclaim the card if it is found and handed in to library staff.
• All 8 participating library sites have card vending and card re-charging machines. MSc room Room 501 is specifically for use by MSc students of the Maths Department. It contains a number of desks, chairs and computers, but not enough for one per student, so sharing arrangements will have to be worked out. MSc students can also use the Common Room, Room 502, and Study Room, Room 503 (see below). Student Common Room and Study Room Room 502 is a student common room. Room 503 is a study room intended for working quietly. Smoking is not permitted anywhere in the department. Lockers are provided in Room 503 on a first-come-first-served basis. You must not leave anything in there over the summer. If you do, the padlock will be cut and the contents of your locker disposed of. Informal use of lecture rooms on 7th and 8th floor If unoccupied, you may use these for quiet study, but you must leave promptly if asked to do so. Mail Any physical mail that comes for you will be put in the MSc post tray in Room 501. This includes anything from members of staff, library etc. Please check the post tray in Room 501 regularly. Notices Although we endeavour to update the information on the website regularly, further details of all courses, including tutorials, exams, any change of time of classes, are placed on the information boards on the 5th and 6th floors.
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E-mail and web page Please check your email regularly, and also look at notices on the departmental web-page. The Department will send all important information to your main UCL account only. Mathematics Society There is a student Mathematics society, called the ADM Society, which organizes events in the Department, publishes a newsletter, etc. Mathematics Department Staff Student Consultative Committee This is a committee made up of representatives from the undergraduate and postgraduate students (chosen by election) and from the staff of the Department, which meets twice a year, approximately in the middle of the Spring and Autumn. It provides a forum for students to raise issues relating to the course or the Department. Some issues may be dealt with immediately informally; others may be referred to the Departmental Teaching Committee or the Head of Department. The minutes are posted on the Student Common Room noticeboard, and also go to staff in the Department and to the College Staff Student Committee as well as the Dean of the Faculty. Graduate School The Graduate school offers a variety of skills courses for all postgraduates. These can be viewed at: http://courses.grad.ucl.ac.uk/list-training.pht This page also contains a link to a list of courses aimed specifically at Masters students.
8. Examinations (formal)
General Information The examinations are normally set by the lecturer for the course, checked by a second internal examiner and also by a Visiting (or External) Examiner (from outside the college). Student scripts are similarly marked by the two internal examiners, and the marking checked by the Visiting Examiner. Examination scripts are marked anonymously. Recommendations about the results of individual courses and degrees awarded are made by the Taught Postgraduate Courses in Mathematics Board of Examiners to the College Board, which makes the final decisions. The Taught Postgraduate Courses in Mathematics Board of Examiners includes the MSc internal Examiners and Visiting Examiners. Extenuating Circumstances If there are any circumstances which affect your performance, either during the period of study or during the exam period, and which you would like taken into account, you should discuss this with the MSc Tutor as early as possible. If the issue relates to an examination then you should inform the MSc Tutor no later than 7 days after the exam. Typical circumstances which might be taken into account are serious or prolonged illness, disability or bereavement. Documentation is normally required (e.g. doctor's note). Information will be kept confidential and special circumstances will be discussed by a small committee of examiners.
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Missing exams due to illness or other unavoidable cause If you miss an examination due to illness or some other unavoidable cause, please inform a member of staff, preferably the MSc Tutor, as soon as possible. The MSc Tutor should be given a doctor's note if the absence is due to illness, and any possible documentary evidence supporting absences due to other reasons. Withdrawal from examinations If you wish to apply to withdraw from some or all your examinations, you must do so before the end of the first week of the summer term. You will need to see the MSc Tutor, and fill in a form for approval by the Faculty Tutor. Withdrawal after this date is only permitted in exceptional circumstances, namely ill health supported by a medical certificate or the death of a near relative. The examinations Before the exams start, please check your timetable for the dates, times and locations of your examinations. It is your responsibility to turn up to the right place at the right time with the right equipment (usually just pens, your personal exam timetable and your ID for a Mathematics examination). You will be provided with a candidate number - please make sure that you have this number with you, as it must be entered on your script. Your seat number also has to be entered on the script (this will change for each exam). Please make sure that you read and follow instructions on the paper. It is important to write legibly. Calculators are not permitted in most Mathematics exams and where used elsewhere they must be of UCL standard type as sold in the UCL shop (these are unable to store characters). Past papers will be on the UCL website and in some cases past solutions are sold by the Department of Mathematics via the Department Office. Cheating and plagiarism Cheating or attempts to cheat may lead to serious consequences, including the degree not being awarded. Unless you are explicitly informed otherwise, you are not allowed to take any written material into the examination - for example, you are not allowed to write formulae on your timetable, which you take into the examination. Please also see information on plagiarism in the UCL Student Handbook. Results Please note that if you owe money to the college or residences, or have unreturned library books, your degree results are likely to be withheld - so please make sure that you have cleared any debts to college, and returned any library books! Students should make sure that they can be contacted after the provisional exam results are processed. This is particularly important for anyone who has failed examinations and may prefer not to proceed to the project component. The Examiners’ Meeting to finalise the marks usually takes place in late September. The marks will then be entered on PORTICO for students to access. Graduation ceremony The graduation ceremony (for students who have completed their degree) normally takes place in early September (so the following year for MSc students).
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Arrangements for this are made by the Registry, and not the Department, and you should receive your application form for places from the Registry, which you must return by the specified date if you wish to attend. Transcripts are also provided by the Registry, and not the Department. Retakes You can normally retake any examination you have failed or been absent from the following year (unless you have graduated). You must re-enter at the first possible opportunity (usually one year later). You cannot retake any examination you have passed. Please note that students will normally be allowed only one retake of any failed examination. Complaints/appeals If you are unhappy with your results or any aspect of your course in the first place please discuss your concerns with the MSc Tutor. If you then wish to pursue matters further, there are procedures for formal appeals. You should first contact the MSc Tutor or the MSc Programme Director, Professor FT Smith. You should also consult the UCL current student pages on the Registry website. You may also contact the following: Academic Registrar: Christopher Hallas Academic Registrar’s Office UCL Registry University College London Gower Street London WC1E 6BT Tel: 020 7679 3203 MAPS Faculty Tutor: Dr Caroline Essex MAPS Faculty Office 1st floor, South Wing, Gower Street London WC1E 6BT Email: [email protected] UCL Students’ Union The Rights and Advice Centre, First Floor of the Bloomsbury Theatre, 15 Gordon Street, London WC1H 0AY Tel: 020 7679 2998 http://www.uclunion.org/get-advice/
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9. Paying Fees
All new postgraduate students who have not provided proof of sponsorship, or payment of at least the first installment of fees, will be provisionally enrolled. Provisional enrolment usually expires on 31 October. Students who have not paid or provided proof of sponsorship will be deregistered after this date. New students with a UK address will have their invoices sent out to them, those with only an overseas address will be able to collect an invoice at enrolment. Returning students will have had their invoices sent to their home addresses during the summer. Students can pay fees online at: http://www.ucl.ac.uk/portico/ if they have a UCL login (for full details please login and you will be given instructions on how to pay within the on line enrolment facility) or at: https://payonline.ucl.ac.uk/ if they have not. Alternatively fees can be paid in the Registry, Room G19, Ground Floor, South Wing, Main Campus. There will be no facility for staff to gain authorisation on any card payments that require it and we ask that students contact their card issuers prior to payment to ensure no authorisation will be requested. Information relating to tuition fees including fee levels, instalment forms, bank transfer instructions and credit card forms can be found on the UCL website at: http://www.ucl.ac.uk/current-students/money/fees-payment/invoices
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SECTION 2: COURSE INFORMATION
MSc in Mathematical Modelling : Frontiers in the application of mathematics
10. Introduction
The MSc programme aims to teach students the basic concepts which arise in a broad range of technical and scientific problems and illustrates how these may also be applied in a research context to provide powerful solutions. This said, the emphasis is placed on generic skills which are transferable across disciplines so that the programme is a suitable foundation for anyone hoping to advance their scientific modelling skills. The Mathematics Department at UCL is at the forefront of research and this programme will allow students to experience the excitement of obtaining solutions to complex physical problems. Students will initially consolidate their mathematical knowledge and formulate basic concepts of modelling before moving on to case studies in which models have been developed for specific issues motivated by industrial, biological or environmental considerations. The programme will provide a unique blend of analytical and computational methods with applications at the frontiers of research. Successful students will be well placed to satisfy the growing demand for mathematical modelling in commerce and industry. The programme will alternatively form a strong foundation for any student who wishes to pursue further research.
11. Programme Structure
The programme lasts for one calendar year formally starting in the last week of September. The programme is full time consisting of taught components which are usually examined in the Third Term (Tuesday 3 May 2011 – Friday 17 June 2011). The programme normally consists of 5 compulsory components, 3 optional components, plus an individual project. Each component corresponds to approximately 30 hours of lectures. Four of the compulsory components are held in the First Term (Monday 27 September 2010 to Friday 17 December 2010). The other compulsory component and optional components are usually taught in the Second Term (Monday 10 January 2011 to Friday 25 March 2011). Examinations for all components are held usually in the Third Term (Tuesday 3 May 2011 – Friday 17 June 2011). Some components may include assessment by an element of coursework in addition to an examination. After the examinations, all students will then embark on an individual project with the submission early in September. The taught modules account for 2/3 of the final mark with the project making up 1/3. The course is equivalent to 72 ECTS, on the European Credit Transfer Scheme.
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If students are unable to, or do not wish to, complete the project element, they may register for the Postgraduate Diploma in Mathematical Modelling which only covers the taught elements. They should see the MSc tutor to discuss this option.
12. Programme Aims
The Masters level programme in Mathematical Modelling has three main aims:- • To provide an understanding of the processes undertaken to arrive at a
suitable mathematical model • To teach the fundamental analytical techniques and computational methods
used to develop insight into system behaviour • To introduce a range (industrial, biological and environmental) of problems,
associated conceptual models and their solutions.
13. Compulsory modules
MATHGM01 Advanced Modelling Mathematical Techniques This component aims to ensure that students possess knowledge of the analytical techniques and theoretical aspects of computational methods used in mathematical modelling. 1. An introduction to modelling concepts, dimensionality, scale analysis,
perturbation techniques, PDEs versus ODEs, modes, modelling of environmental, biological and industrial problems.
2. A selection of topics from:
(i) Waves and instability (e.g. KH instability, TS instability, waves in the ocean, atmosphere and aerodynamics, phase and group velocity, inverse scattering, WKB methods)
(ii) Integral equations (iii) Asymptotic methods (e.g. matched asymptotics, WKB, multi-scale methods,
triple-deck and related methods) (iv) Stochastic calculus and partial differential equations (v) Vortex dynamics (laws of motion, line vortices, 2D vortex patches,
calculation of trajectories, stability of arrays of vortices, contour dynamics, vortex rings)
(vi) solid mechanics (elasticity) (vii) DEs (e.g. ODEs with periodic coefficients, Mathieu eq.), (viii) Feedback systems, control (ix) Pattern formation (x) Power spectra and correlation functions.
3. Relevant theoretical aspects of computational methods, finite-element and finite-difference methods, methods of CFD, solution path following methods.
Assessed via a 2 hour examination.
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MATHGM02 Nonlinear Systems This component aims to give an overview of the main aspects of nonlinear systems and to provide definitions and theoretical background. 1. Continuous Dynamical Systems:
Equilibria. Local and global stability. Liouville’s Theorem. Conservative and dissipative mechanical systems. Periodic solutions and Poincare-Bendixson theorem. Perturbation methods. Bifurcation analysis for one- and two-dimensional systems, including Hopf bifurcation. Applications: non-linear oscillators, Hamiltonian systems, dissipative systems.
2. Discrete Dynamical systems:
Iterated maps as dynamical systems in discrete time. The logistic map as main example. Equilibria, cycles and their stability. Period doubling bifurcations. Simple random properties of discrete trajectories. Elementary properties of maps in two dimensions. Lyapunov exponents, attractors and the butterfly effect.
3. Non-linear waves:
Linear waves, dispersion relations, dispersion versus dissipation, stable and unstable waves. Travelling wave solutions of non-linear partial differential equations, for example the Korteweg-de Vries, non-linear Schrodinger equations. Phase-plane analysis, solitons.
Recommended Books : S.H.Strogatz, Nonlinear Dynamics and Chaos, Perseus Books, 1994. J.M.T.Thompson & H.B. Stewart, Nonlinear Dynamics and Chaos, Wiley 2003. E.Ott, Chaos in Dynamical Systems, CUP, 1993. D.K.Arrowsmith & C.M.Place, Dynamical Systems, Chapman Hall J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Springer L.D.Landau & E.M.Lifshitz, Course of Theoretical Physics, Vol. 1 Mechanics, Pergamon Drazin and Johnson, Solitons, Cambridge Texts and other books by Drazin, e.g. Nonlinear Systems Assessed via a 2 hour examination. MATHGM03 Operational Research The component will discuss a range of methods used in Operational Research for assisting with the analysis of problems from a wide range of real life settings. Many of the examples given will concern the application of Operational Research to clinically related problems, although examples will also be given related to other areas such as transport and manufacturing industry. The component will introduce mathematical modelling methods frequently used in Operational Research, including linear programming, integer programming, stochastic analysis, queuing theory and compartmental modelling. Students will also be introduced to the practical problem solving methodology of Operational Research and the processes involved in developing a mathematical modelling structure.
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1. Brief history of Operational Research.
2. Introduction to optimisation methods. An overview of linear programming and integer programming algorithms. Examples of applications.
3. Compartmental models.
4. Heuristic methods. Methods that cannot guarantee optimality and methods of judging how 'good' resulting solutions are.
5. Network analysis: theory and application.
6. Introduction to stochastic analysis. Markov chains and Markov processes.
7. Introduction to queuing theory.
8. Exposure to the `open ended' practical problem-solving methodology of Operational Research using a real-life case study. Identifying key elements of a practical problem. Relating them in a mathematical framework. The process of developing a modelling structure.
Recommended Books : S. Ross, An Introduction to Probability Models. 9th Ed, Academic Press, 2006. W.L.Winston, Operations Research: Applications and algorithms, Duxbury Press, Boston, 1987. M.Pidd, Tools for thinking - modelling in management science, 2nd Ed, John Wiley & Son, 2003. Assessed via a 2 hour examination. MATHGM04 Computational and Simulation Methods This module will consider various computational methods which may be used when mathematical modelling. The aim is for the students to investigate the mathematics behind various numerical processes and also the use of software for simulation and visualisation of outcomes. Specific mention will be made of computational experiments which will be linked to issues raised in other components of the Masters course in Mathematical Modelling. The syllabus is broad with the emphasis placed on research applications. 1. Introduction and ODEs:
Preliminary concepts, including formulation of physical problems from continuum mechanics in terms of ODEs and PDEs. Solution of ODEs by finite difference methods. Euler, Runge-Kutta, linear stability, implicit methods, systems of ODEs, higher order ODEs and the shooting method for boundary problems.
2. PDEs: Categorization into parabolic, elliptic, hyperbolic types. Examples to include reduction of linear elliptic PDEs to eigenvalue problems using normal mode approach (e.g. plane Poiseuille flow). Direct methods (Gaussian elimination, LU
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decomposition), iterative techniques (Jacobi and Gauss-Seidel, SOR), vector norms. Finite-differencing for parabolic and hyperbolic PDEs. Explicit, implicit and Crank-Nicholson schemes. Stability criteria.
3. Finite element modelling: Detailed introduction to finite elements for 1D and 2D problems, variational formulation, weak formulation, Galerkin approximation, application to archetypal second-order (heat equation) and fourth-order (beam equation) problems, nonlinear problems.
4. Computer classes. Introduction to programming in C++ and Matlab; the use of both languages for solving problems derived in lectures.
Assessed via a 2 hour examination worth 60% plus coursework worth 40% of the component. MATHGM05 Frontiers in Mathematical Modelling and its Applications This module will introduce a range of problems, their associated mathematical model and solutions. Topics will be introduced covering problems motivated by industry, biology and the environment. By referring to texts or papers, the aim is to highlight the modelling approach taken and discuss the appropriateness of the model based on selective analytical or numerical solutions. Where appropriate, students will utilise knowledge and skills developed in the compulsory components to perform simulations or to visualise behaviour. The detailed syllabus is likely to change from year to year with the use of guest lecturers and visitors but examples may include 1. Applications of techniques of nonlinear dynamics 2. Climate modeling 3. Environmental related phenomena 4. Biomedical modeling 5. Industrial case studies This module introduces the students to research carried out by the staff and is designed to assist students in their choice a suitable project. Students should also attend the department’s weekly Applied Mathematics seminars to broaden their knowledge. Assessed via a 2 hour examination.
14. Optional Modules
The options chosen by each student for the 1st and 2nd term are subject to the
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approval of the programme coordinator. A range of options will be available for students to select within UCL Mathematics Department. The options may vary each year, and some are listed in the timetables at the back of the handbook. It is the student’s responsibility to seek out and select appropriate options allowing for timetableling. For each student, the selected optional courses must be agreed by the MSc Tutor. By special arrangment, it may also be possible for students to take components run by other departments such as Statistics, etc. MATHGM21 Quantitative and Computational Finance Prerequisites: Probability theory and Differential Equations Structure: 3 hour lectures per week Course Outline and Objectives: This is a course in the applied aspects of mathematical finance, in particular derivative pricing. The theme of the course is to develop the PDE approach to the pricing of options. Excel spreadsheets will be used for the computational work. Simulation Methods in Finance: Brief introduction to Stochastic Differential Equations (SDEs) – drift, diffusion, Itô’s Lemma. Simulating asset price SDEs. Examining asset price returns. Financial Products and markets: Introduction to the financial markets and the products which are traded in them: Equities, indices, foreign exchange, fixed income world and commodities. Options contracts and strategies for speculation and hedging. Black-Scholes framework: Black-Scholes PDE: simple European calls and puts; put-call parity. The PDE for pricing commodity and currency options. Discontinuous payoffs – Binary and Digital options. The Greeks: theta, delta, gamma, vega & rho and their role in hedging. The mathematics of early exercise - American options: perpetual calls and puts; optimal exercise strategy and the smooth pasting condition. Computational Finance: Solving the pricing PDEs numerically using Explicit, Implicit and Crank-Nicholson Finite Difference Schemes. Stability criteria. Monte Carlo Technique for derivative pricing. Fixed-Income Products: Introduction to the properties and features of fixed income products; yield, duration & convexity; yield curves & forward rates; swaps & zero coupon bonds. Stochastic interest rate models: stochastic differential equation for the spot interest rate; bond pricing PDE; popular models for the spot rate (Vasicek, CIR and Hull & White); solutions of the bond pricing equation; Multi-factor interest rate modelling. Calibration/yield curve fitting: the importance of matching theoretical and market prices; time dependent one factor models (Ho & Lee, extended Vasicek). Recommended Text: Paul Wilmott Introduces Quantitative Finance: Wilmott, Paul (Wiley) April 2001.
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Assessed via a 2 hour examination worth 90% plus coursework worth 10% of the component. MATHG302 Asymptotic Methods and Boundary Layers Theory This module is about the fluid mechanics of flows with high Reynolds number, for which the viscous effects are concentrated in thin boundary layers that are important features of such flows, for example with regard to surface stresses and drag. The main content is boundary layer theory, which is treated as the leading term in a rational approximation to the Navier-Stokes equations that govern viscous flow. The mathematical basis of this interpretation is singular perturbation theory, and part of the course will cover the associated techniques of matched asymptotic expansions in the more general context of ordinary differential equations. Various types of classical boundary layers are analysed in the course, such as those occurring in two-dimensional steady and unsteady flows past flat plates, wedges and cylinders, and flows in jets and wakes. Flows near stagnation points are investigated in detail, and triple deck boundary layer theory is introduced. Recommended Texts: Batchelor, G.K. An introduction to fluid mechanics. CUP. Schlichting, H. Boundary layer theory, McGraw Hill Sobey, I.J. Introduction to interactive boundary layer theory. OUP Van Dyke, M. Perturbation methods in fluid mechanics. Parabolic Press Hinch, E.J. Perturbation methods. CUP Nayfeh, A. Introduction to perturbation techniques. Rosenhead L. (ed) Laminar boundary layers. OUP Assessed via a 2 hour examination. MATHG303 Hyperbolic PDEs with Applications This module is planned as an introduction to compressible inviscid flow. To derive the equations that describe the behavior of such a fluid, which now involve variable temperature and density in addition to the velocity components and pressure of an incompressible flow, it is necessary to study some of the properties of gases. This is termed thermodynamics and leads to an equation of state that will be taken in the form appropriate to an ideal gas. Definitions of the speed of sound and Mach number follow. A number of varied problems can be solved fairly simply if it is assumed that the flow properties depend on two independent variables only, either time and one space variable, or two space variables. In the former category come one-dimensional wave motion, sound waves and flow in a shock tube. The two-dimensional steady flow equations, on the other hand, are either elliptic or hyperbolic depending on whether the flow is sub or supersonic. The course will include examples of both types of flow, the underlying application being that of flow over an aerofoil. For supersonic flow there will be a study of compression, expansion, Mach lines and oblique shocks. The method of characteristics and the techniques of perturbation theory will be required for the advanced problems.
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Recommended Texts: Chapman, High Speed Flow, Cambridge, Liepmann & Roshko, Elements of Gas Dynamics, Wiley White, Fluid Mechanics, McGraw Hill Assessed via a 2 hour examination. MATHG304 Geophysical Fluid Dynamics This module uses mathematics to discuss the global environment. Basic fluid dynamics and simple physics for the atmosphere and oceans are used to discuss briefly the greenhouse effect, and at greater length some of the mechanisms involved in the dispersion of pollutants along coasts and the four-yearly (on average) El Nino oscillation in the equatorial Pacific, with its attendant Australia drought and blight of the Peruvian anchovy industry. Typical analysis involves the solution of linear partial differential equations for the velocity and density of the flows. Recommended Books: J. Pedlosky, Geophysical Fluid Dynamics, Springer-Verlag. A. E. Gill, Atmosphere-Ocean Dynamics, Academic Press. P. H. Le Blond and L. Bysak, Waves in the Ocean, Elsevier. Assessed via a 2 hour examination. MATHG305 Mathematics for General Relativity The course introduces students to Einstein's theories of special and general relativity. Special relativity shows how measurements of physical quantities such as time and space can depend on an observer's frame of reference. Relativity also emphasizes that there exists an underlying physical description independent of observers. This physical description uses mathematical objects called vectors and tensors. The Maxwell equations provide a description of electromagnetism compatible with special relativity. However, no similar equations exists for gravitation. Instead, a more general form of relativity is needed where spacetime has curvature. Objects no longer accelerate due to gravitation forces; instead they move along geodiscs whose shape is determined by the curvature. Furthermore, rather than mass being the source of the gravitational field, a massive object warps the space around it, generating curvature. Recommended Texts: J Foster & JD Nightingale, A short course in General Relativity, 1994. S. Weinberg, Gravitation and Cosmology (1972); R.D'Inverno, Introducing Einstein's Relativity (1992). Assessed via a 2 hour examination worth 90% plus coursework worth 10% of the component.
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MATHG306 Cosmology Cosmology is the study of the history and structure of the universe. Cosmologists usually assume that the universe is highly symmetric on large scales; under this assumption the equations of general relativity reduce to two simple ordinary differential equations. These equations govern the expansion of the universe. We study these equations in detail, and show how observations are affected by the expansion and curvature of the universe. The course then covers the astronomical methods used to determine the expansion rate (i.e. the Hubble constant) and the mass density of the universe. Physical processes in the early universe such as nucleosynthesis, the formation of the microwave background, and galaxy formation will also be studied. The course begins with a description of black holes and ends with speculative topics including inflation and cosmic strings. Students will be required to have completed a pre-requisite course in general relativity. Recommended Texts: A. Liddle, An Introduction to Modern Cosmology (2003); Rowan-Robinson, Cosmology, (1996); J Silk, The Big Bang (1989). Assessed via a 2 hour examination worth 90% plus coursework worth 10% of the component. MATHG307 Biomathematics1 This module introduces students to biomathematics, an increasingly important branch of applied mathematics. It also serves to reinforce students' skills in mathematical modelling. This component consists of mathematics, principally mechanics, applied to the understanding of the structure and functioning of animals. This course begins with the theory of scaling applied to classes of whole animals of similar shape. For example, we determine how high an animal can jump, how fast it can walk or run, how big a bird must be before it can fly, and so on. We go on to use similar arguments to study the mechanics of bones, muscles and other organs of the body in more detail. Proceeding down in scale, we consider problems of microscopic dimensions, including diffusion through membranes. The emphasis of the component will be on mathematical models, and no special knowledge of Biology is required or assumed only a background in mechanics. The URL http://en.wikipedia.org/wiki/Biomechanics has a lot of background material that is useful. Recommended Texts: Andrew A Biewener. Animal Locomotion. Oxford Animal Biology Series. CUP, 2003. Knut Schmidt-Nielsen. Scaling: Why is animal size so important? CUP, 1984. Ove Sten-Knudson. Biological Membranes: Theory of Transport, Potentials and
2 Please note - MATHG307, Biomathematics, is taught in the first semester.
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Electric Impulses, Cambridge University Press, 2002. J. Keener & J. Sneyd. Mathematical Physiology. Interdisciplinary Applied Mathematics 8. Springer-Verlag, New York 1998. Assessed via a 2 hour examination worth 90% plus coursework worth 10% of the component. MATHG501 Theory of Traffic Flow Traffic problems beset large cities and many smaller towns throughout the world. Consulting firms and local authorities employ teams of professional staff to tackle these problems in ways that help to make cities better places to live in. The methods of solving these problems rely on a mathematical understanding of traffic flow, which covers not only the detailed movement of traffic along individual roads or through particular junctions but also the broad patterns of traffic movement across whole cities. The purpose of this component is to provide an introduction to the mathematical modelling of traffic flow. Examples of modelling at each of the levels of detail described above are considered. Mathematical models are developed from first principles and related to more widely applicable techniques of operational research. Recommended Texts: C.F. Daganzo, Fundamentals of Transportation and Traffic Operations, Pergamon (1997) M.G.H. Bell & Y. Iida, Transportation Network Analysis, Wiley (1997). Assessed via a 2 hour examination worth 90% plus coursework worth 10% of the component.
MATHG505 Evolutionary Games and Population Genetics This component introduces the fundamentals of Mathematical Population Genetics, which gives mathematical expression to the genetic aspects of evolution in natural populations. Also some of the ideas from Game Theory will be described which have recently been used to illuminate the evolution of various properties and behaviours of animals. The emphasis in the component is on Mathematical models. The topics to be discussed will be chosen from: 1. Population Genetics. Mathematical description of Mendelian genetics. The
Hardy-Weinberg law. Natural selection on gene-frequencies (discrete and continuous-time models). Fisher's Fundamental Theorem. Dominance, fixation-time and heterozygote advantage. Mutation-selection balance. Stochastic environment. Recombination. The evolution of sex-ratios.
2. Evolutionary Game Theory. Fitness pay-offs. Evolutionarily-stable-strategies.
Nash equilibria. Evolutionary dynamics and learning. Hawk-Dove games. Paper-
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scissors-stone game. Asymmetric games. The battle of the sexes. The evolution of cooperation.
Recommended Texts: J. Hofbauer and K. Sigmund, Evolutionary Games and Population Dynamics, Cambridge Univ. Press 1998. Assessed via a 2 hour examination. MATHG506 Mathematical Ecology2
Mathematical models are used extensively in many areas of the Biological Sciences. This course aims to give a sample of the construction and use of such models in Population Biology. The fundamental question to be addressed is: what natural (or human) factors control the abundance and distribution of the various populations of animals and plants that we see in Nature? The emphasis of the course will be on mathematical models, and no special knowledge of Biology is required or assumed. However, an interest in, and willingness to learn about, concepts and problems in this area are essential.
• Population models for a single species (discrete and continuous-time models).
Malthusian models of resource limitation. Constant, periodic and random environments. Simple spatial models. Discrete time population models, logistic map.
• Demography. Simple age-structured models. Stable age-structure. The Euler Lotka demogaphic equation. Applications to the theory of life-history strategies.
• Two-species interactions. Competition and niche-theory. Predator-prey models. Models of disease transmission (epidemics).
• Many-species interactions. General Lotka-Volterra models. Applications of Lyapunov functions.
Recommended Texts: Mark Kot, Elements of Mathematical Biology, (CUP 2001). Joseph Hofbauer and Karl Sigmund, Evolutionary games and population dynamics, (CUP 2002). J.D. Murray , Mathematical Biology (Springer-Verlag Biomathematics Texts, 1989). N.J. Gotelli, A Primer in Ecology, (Sinaur Associates Inc.) Assessed via a 2 hour examination. MATHG508 Financial Mathematics This module is an introduction to an exciting and relatively new area of applied mathematics, the valuation (i.e. pricing) of `financial derivatives'.
• A review of a variety of financial contracts involving payments at a future date will be carried out. The module will define the concept of hedging and give
2 Please note – MATHG506, Mathematical Ecology, is taught in the first semester.
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examples of hedging strategies. Explanation of: (i) pricing based on the assumption of no arbitrage opportunities, and (ii) of the Stochastic model of share price changes.
• Revision of elementary probability. • Introduction of tools from calculus and from linear algebra in order to: (i)
deduce the Black-Scholes equation and the risk-neutral valuation principle, (ii) solve some simple partial differential equations arising in finance, (iii) enable the determination of the synthetic probability distribution of share prices at a future date, (iv) establishment of discrete models in particular the Binomial model.
• Calculation of the value of European put and call options (the Black-Scholes formula) using continuous time calculus and using discrete time approximation. Calculation of American and other options using approximative techniques.
Recommended Books: S. R. Pliska, Introduction to Mathematical Finance-Discrete Time Models, Blackwell, 1997, ISBN 1-55786945-6; J. C. Hull, Options, Futures and other Derivatives, Prentice Hall, 1989, ISBN 013-264367-7. Assessed via a 2 hour examination worth 90% plus coursework worth 10% of the component.
15. MATHGM10 MSc Project
A list of topics and corresponding supervisors will be prepared and made available during the first term. Titles and summaries should be agreed by supervisors and the MSc Tutor by the end of the second term. The projects must be completed and submitted by early September, usually the same day as the project presentations - the date will be fixed and students informed of the date. MSc Project Guidelines and Information The MSc summer project MATHGM10 contributes 1/3 of the overall MSc mark, with the 8 taught components making up the remaining 2/3. The module MATHGM10 itself has two components: the written project, and the project presentation. The written project carries 90% of the module marks and the project presentation 10%. Each year the project submission deadline is early September, the actual date to be announced. All students should submit two hard copies of their Project to the Mathematics Departmental Office in Room 610 by this deadline. Students will also be required to email an electronic version of the project in pdf (portable document format, see http://www.adobe.com/downloads/) format to [email protected]. Project Presentations The MSc presentations will commence 10am on the same day as the submission deadline, with the venue to be announced. Each student will be allocated a 20-minute time slot: 15 minutes for their presentation and 5 minutes for questions. Data projection facilities will be available for use of laptops if required. Members of staff in
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the audience will grade the presentations. Students will be expected to stay for all the presentations. General Project Guidelines Given the wide range of topics, the various focuses of projects, and the different aspirations of students, the rules and requirements for the MSc project are suitably flexible. The project can range from an extensive survey and critique of existing research to the development of a new model or an extension of an existing one. Each project will be assessed taking into account where the main focus of effort lies. A component of original research is not a requirement of the project, but will be given due credit if present. A student should discuss these details with their supervisor. Whatever the student decides with their supervisor, there are some things that all projects should include:
• An introduction outlining the project and giving a clear statement of the objectives of the project.
• A relevant literature survey with discussion. • Details of mathematical calculations that can be checked. Where it makes the
text more readable, an appendix could be used for some calculations. • Listings of any innovative computer code (C++, MatLab, Mathematica, etc) that
is central to the project in an appendix. (Standard code, or minor modifications of such, need not be listed.)
• Clear referencing of all material sourced, whether from books, published journals, the internet, personal communication, or similar. Essentially, if it is not the student’s idea or work, it needs to be referenced. Failure to reference material may be construed as plagiarism. The college takes a firm stance on plagiarism http://www.ucl.ac.uk/current-students/guidelines/policies/plagiarism . If in doubt the student should ask their supervisor.
• Conclusions, including a summary of the project findings, and, where new research was carried out, a discussion of the strengths and weaknesses of the model/method, and possible improvements.
Style and Presentation There is no imposed style, nor specification of the word-processing package to be used, as long as it is capable of out-putting the final document in pdf format. Projects that are hand-written or typed on a manual typewriter will not be accepted. Some marks will be allocated for the quality of the written work, including its readability, clarity of argument and overall presentation. There is no word limit for the dissertation. Supervision Students should agree with their supervisor how often they meet for supervision. The role of the supervisor is to help guide the student in the production of the project. It is expected that the student will be able to do a significant amount of the project work independently. Writing up Students should be warned to leave ample time for writing-up the project. Penalties will be incurred on projects that are submitted after the deadline.
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Project Assessment Each project will be marked by the student’s supervisor and also by a second examiner. A final mark will then be agreed between the two examiners, combined with the presentation score to give a final mark in percent.
16. Requirements to Pass the Course
For the MSc students must take 8 taught modules and submit a project. For the Postgraduate diploma students must take 8 taught modules only. The pass mark for taught modules and the project are both 50%. The final weighted average is calculated as 2/3 times the mean of the 8 taught modules plus 1/3 times the project mark (all marks in %). The normal requirements for a pass are 8 passes in the taught modules plus a pass in the project. However, 2 condoned passes (i.e. not less than 40%) of taught modules are permitted provided that the final weighted average is not less than 50% and the project is passed. A distinction is obtained if the average mark on the taught modules equals or exceeds 70%, and the project mark equals or exceeds 70%. A distinction cannot be obtained if some modules or the project are retaken, or if condoned failures are obtained in any modules.
17. Tutors
Each student will normally be assigned a personal tutor who forms their first contact in case of general difficulties.
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18. Module Timetable
DEPARTMENT OF MATHEMATICS University College London
MSC COURSES - FIRST TERM Monday 04 October - Friday 17 December 2010
Reading Week 8 - 12 November 2010
Monday Tuesday Wednesday Thursday Friday
9.00 - 10.00 G307 (707) GM04* (RG11) G508 (706)
10.00 - 11.00 GM01 (706)
GM04* (RG11)
GM04 (707)
11.00 - 12.00 GM01 (706) GM04* (RG11)
GM04 (707)
G307 (707) G508 (706)
12.00 - 1.00 GM01 (706) GM04* (RG11)
GM04 (707)
G307 (707) G508 (706)
1.00 - 2.00
2.00 - 3.00 GM02 (707)
G506 (707) GM03 (707)
3.00 - 4.00 GM02 (707)
GM02* (RG11, weeks 8-10, 12-15)
G506 (707) GM03 (707)
4.00 - 5.00 GM02 (707)
GM02* (RG11, weeks 8-10, 12-15)
GM03 (707) G508
(HMLT) G506 (707)
5.00 - 6.00 G508 (HMLT)
500, 505, 706,707 and 807 are in the Maths Department RG11 = Room G11, Rockefeller, Public Cluster HMLT = Harrie Massey Lecture Theatre * indicates a Computer Practical Session
Compulsory Courses
GM01 Advanced Modelling Techniques Dr S Timoshin and Prof N R McDonald GM02 Non-linear Systems Prof S Bishop GM03 Operational Research CORU GM04 Computational and Simulation
Methods Dr G van der Heijden, Dr S. Timoshin and Mr S E Glavin*
Optional Courses
G307 Biomathematics Dr S Baigent and Prof A. Zaikin G506 Mathematical Ecology Dr S Baigent G508 Financial Mathematics Dr J Walton G508 has additional small group classes at Fri 9.00, Fri 11.00 and Fri 12.00 (all in 706): students will be assigned to one of these.
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DEPARTMENT OF MATHEMATICS
University College London MSC COURSES - SECOND TERM
Monday 10 January - Friday 25 March 2011 Reading Week 14 - 18 February 2010
. Monday Tuesday Wednesday Thursday Friday
9.00 - 10.00 GM21 (BENTHB10)
10.00 - 11.00 GM05 (707) G304 (FC130) G303 (807) G505 (807)
11.00 - 12.00 G303 (807) G505 (807) GM05 (707) G304 (FC216) 12.00 - 1.00 G303 (807) G505 (807) GM05 (707) G304 (FC216)
1.00 - 2.00
2.00 - 3.00 GM21 (706) G501 (706) G306 (807)
3.00 - 4.00 GM21 (706) G501 (706) G306 (807)
4.00 - 5.00 G501 (706) G306 (807)
500, 505, 706, 707 and 807 are in the Maths Department BENTHB10 = Bentham House B10 FC130 = Foster Court 130, Foster Court FC216 = Foster Court 216, Foster Court
Compulsory Course
GM05 Frontiers in Mathematical Modelling Dr S Baigent, Prof J-M Vanden- Broeck, Dr M Davey
Optional Courses
GM21 Quantitative and Computational
Finance Dr R Ahmad
G303 Hyperbolic PDEs with applications Dr M Davey G304 Geophysical Fluid Dynamics Prof E R Johnson G306 Cosmology Dr Y Obukhov G501 Theory of Traffic Flow I Prof B Heydecker G505 Evolutionary Games and
Population Genetics Prof A Zaikin and Dr S Morozov
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