1 [MSci Mathematics degrees] Mathematics, Statistics ... - Workspace

Programme Specification for the MSci in Mathematics PLEASE NOTE. This specification provides a concise summary of the main features of the programme and the learning outcomes that a typical student might reasonably be expected to achieve and demonstrate if he/she takes full advantage of the learning opportunities that are provided. This specification provides a source of information for students and prospective students seeking an understanding of the nature of the programme and may be used by the College for review purposes and sent to external examiners. More detailed information on the learning outcomes, content and teaching, learning and assessment methods of each module can be found on-line at http://www3.imperial.ac.uk/mathematics/students/undergraduate/courseguides. The accuracy of the information contained in this document is reviewed by the College and may be checked by the Quality Assurance Agency. 1. Awarding Institution:

Imperial College London

2. Teaching Institution:

Imperial College London

3. External Accreditation by Professional / Statutory Body: Not applicable, but approved by the Institute of Mathematics and its Application, Institute of Actuaries, etc. Associate of the Royal College of Science (ARCS) 4. Name of Final Award (BEng / BSc / MEng etc):

MSci (Honours)

5. Programme Title (e.g. Biochemistry with Management):

Mathematics, Mathematics with a Year in Europe

6. Name of Department / Division:

Mathematics

7. Name of Faculty:

Natural Sciences

8. UCAS Code (or other coding system if relevant):

G103, G104

9. Relevant QAA Subject Benchmarking Group(s) and/or other external/internal reference points

Mathematics, Statistics and Operational Research 10. Level(s) of programme within the Framework for Higher Education Qualifications (FHEQ): Bachelor’s (BSc, BEng, MBBS) Integrated Master’s (MSci, MEng)

Level 6 Levels 6 and 7

11. Mode of Study FULL TIME 12. Language of Study: English 13. Date of production / revision of this programme specification (month/year):

July 2013

1 [MSci Mathematics degrees]

14. Educational aims/objectives of the programme The programme aims/objectives are to:       

Provide high quality education in Mathematics within an environment committed to excellence in both teaching and research. Attract well-qualified students and to provide intellectual challenge in a structure containing an appropriate amount of flexibility, so that students can develop their specialist interests. Teach and provide the opportunities to learn a core of mathematics fundamental to the education of all mathematicians, together with a wide range of higher level options in Mathematics and allowing some broadening of study through a range of Management and Co-curricular options. Introduce students to a wide-range of applications of Mathematics. Equip students with a range of mathematical skills – in problem-solving, project work, computation and presentation – to enable them to take prominent roles in a wide spectrum of employment and research. Provide further breadth and depth of Mathematics beyond BSc to a level approximating that of a taught MSc. [Mathematics with a Year in Europe] prepare students for, and give students the experience of, the outlook and learning/working practices in a partner university in another European country – 4 year course with year 3 away from Imperial College.

15. Programme Learning Outcomes 1. Knowledge and Understanding Knowledge and Understanding of 1. 2. 3. 4. 5. 6. 7.

The fundamentals of Mathematics as a living discipline in its own right. The development of the application of Mathematics as a language in a wide range of situations relevant to research and industry. The importance of precision of argument. Problem-solving strategies and methods. Basic computational skills. A selection of subjects which students study in greater depth, according to their interests (and degree coding) leading to current developments at the frontiers of the subject. [Mathematics with a Year in Europe] The way Mathematics is taught and structured in a continental European country – together with the appropriate language.

Teaching/learning methods and strategies Outcomes 1 to 6 is through compulsory courses in years 1 and 2 together with more advanced specialist options in year 3 [and year 4 for Mathematics with a Year in Europe]. Lectures are an integral part of course delivery in this programme, supported by problems classes, tutorial groups, computational work, office hours, individual tutorials. In each year students engage in private study in which they work through set problem sheets and individual assignments as well as assimilating lecture content. There is compulsory project work in each of years 1[individual poster] and 2 [group]. In the final year (year 4) there is a compulsory major research project. Outcome 7 is acquired through language teaching at Imperial College in years 1 and 2 followed by attending for a year at a partner university in continental Europe. Assessment of knowledge and understanding is through a combination of unseen written examinations, th assessed coursework/tests, assignments, 4 year mastery examination, written projects and presentations.

2. Skills and other Attributes Intellectual Skills 1. 2. 3. 4. 5.

Ability to assimilate and understand a large body of complex concepts and their inter-relationships. Knowledge and understanding of the role of logical mathematical argument and deductive reasoning, together with formal processes of mathematical proof and development of mathematical theories. Use of a structured mathematical analytical approach to problem solving, including the importance of assumptions made and consequences of their violation. Use of Mathematics to describe and model in applications, including appropriate solution method, and interpretation of results. Carry out extended investigative mathematical work as an individual and as part of a small group.

Teaching/learning methods and strategies


All lecture courses are accompanied by problem sheets, which students work through privately, and supported by group tutorials/problems classes; which are separately timetabled for compulsory/core courses in years 1 and 2, and integrated within the timetabled lecture periods for option courses in years 2 and 3 (4). There is access to lecturers informally and through a formal ‘office hours’ system. Assessment is primarily by unseen examination, together with assessed courseworks/tests and assignments and projects. Skill 5 is acquired through a compulsory poster project in year 1 and a compulsory group project in year 2. In the final year (year 4) there is a compulsory major research project.

Practical Skills 1. 2.

Carry out investigative project work as an individual and as part of a small group. Use symbolic and numerical software as part of practical computation.

Teaching/learning methods and strategies There is compulsory supervised project work in years 1 (individual poster) and 2 (group). In the final year (year 4) there is a compulsory major research project. Projects are assessed through production of hard copy and oral presentation. 2 is developed through a programme of lectures/classes/assignments in year 1 (currently using MAPLE and MATLAB). There is opportunity for more advanced computation (e.g. in C and in R) in option courses.

Transferable Skills 1. 2. 3. 4. 5. 6. 7.

Solve open-ended problems and problems with well-defined solutions by formulating problems in precise terms, identifying key issues and trying different approaches in order to make progress. Carry out an independent investigation using textbooks and other available literature, searching databases and interacting with colleagues and staff to extract important information. Communicate effectively by listening carefully and presenting complex information in a clear and concise manner orally, on paper and using IT. Use analytical skills, paying attention to detail and using technical language correctly, to manipulate precise and intricate ideas, to construct logical arguments. Use IT skills for communication and analysis. Work independently, use their initiative, organize themselves to meet deadlines, plan and execute an extended project. Work in groups, interacting constructively with others.

Teaching/learning methods and strategies Acquisition of 1 is partly through the methods and strategies outlined in Practical Skills above. Acquisition of 2, 3, 4 comes through courseworks, through supervised preparation of a poster and group projects in years 1 and 2 and through final year projects. Acquisition of 5 is through the programme of lectures/classes/ assignments in year 1 – see Practical Skills 2 above and through guided preparation of project presentations. Acquisition of 6 is developed progressively through courseworks, through successive years of the course as students take control of their own learning, through private study, project work, classes. Acquisition of 7 is mainly through the compulsory group project in year 2. In the final year these skills are developed to a particularly high level. Students need to plan their pattern of work very carefully since their programme of lectures will depend on their particular option choice and they need to balance this with the demands of a research project which continues for the whole academic session.

16. The following reference points were used in creating this programme specification 

Subject benchmarking information for Mathematics, Statistics and Operational Research (QAA)


17. Programme structure and features, curriculum units (modules), ECTS assignment and award requirements Each degree programme is offered as a full-time 4-year course and leads to the MSci Honours degree. The programme is organised into course units with 4 units in each year. Typically the course unit value of each components of the programme is ½ a course unit, with the exception of projects, and this corresponds approximately to its contribution to the overall programme each year and its honours weighting. The first and second year projects are outside the course unit system, but count towards overall honours. Written examinations are held in May/June of each year. There are Resit examinations in September at the end of year 1 and at the end of year 2 for all courses. In the final year there is a compulsory research project (valued at 1 course unit) and the 6 lectured courses which make up the programme must be taken from suitably enhanced final year BSc course options and those offered also as part of the Imperial College taught course MSc programmes in Pure Mathematics, Applied Mathematics. ECTS assignment is contained within a separate document http://www3.imperial.ac.uk/mathematics/students/undergraduate/programmeinformation

Year One: All students normally attend 8 half unit lecture courses in the first two terms – currently these are Foundations of Analysis, Geometry and Linear Algebra, Mathematical Methods I, Mathematical Methods II, Analysis I, Algebra I, Probability and Statistics I, Mechanics. The total number of lectures, including numerical methods/computation is about 260, supported by about 100 tutorials/classes. Across terms 1 and 2 there is a course in Computational Mathematics (Computation). In the third term there are examinations, followed by a poster project. Each course component is credited with a certain number of ECTS, roughly proportional to the study time of the component. st In the 1 Year: the 8 lectured half-unit courses each count at 6.5 ECTS, while the computational module M1C st earns 4 ECTS and the Poster project 4.5 ECTS. Thus a successful 1 year earn 8*6.5+4+4.5 = 60.5 ECTS. (Students on the Year in Europe coding would normally also be required to take a language course, for an extra 6 ECTS). Students must normally pass all course elements including Computation and project to proceed to the second year. Students who fail one or more course modules, must resit (up to twice) the examination component the next two time(s) it is offered. For first-year students, the first resit is before the start of the next academic year.

Year Two During the first two terms all students normally take 8 half unit courses Multivariable Calculus, Differential Equations; Real Analysis; Complex Analysis . Probability and Statistics II; Introduction to Numerical Analysis, Algebra II. To complete their 8 half unit courses students then take 1 course from (currently): Nonlinear Waves; Metric Spaces and Topology, Statistical Modelling I Typically the total number of lectures is about 230, supported by about 70 classes. In the third term there are examinations, followed by a supervised group project. Each course component is credited with a certain number of ECTS, roughly proportional to the study time of the component. nd In the 2 Year: the 8 lecture courses (including the option) earn 7 ECTS, while the Group Project earns 5 ECTS, for a total of 61.5 ECTS. Students must pass all courses and the group project to proceed to the next year. Resits of failed courses are available for all courses – as for those in first year, with the first resit before the start of the next academic year. To remain on these MSci codings into years 3 and 4 performance at upper second class or better is required. If this requirement is not met then students will be transferred to a BSc coding.

Year Three Mathematics with a Year in Europe Students follow an arranged programme of study at a partner institution in Continental Europe [valued at 4 course units]. Students must register at least a pass on the year away at a partner institution. Students must normally pass all courses to progress to year 4. Each course component is credited with a certain number of ECTS, roughly proportional to the study time of


the component.

Mathematics Students take 8 courses to the equivalent of 4 course units. Within the Department there are over 60 half-unit courses, the majority of which are available every session. rd

Students are not permitted to take a project course in 3 year. There are also some courses in Business School, and Co-Curricular Studies (non-language) from which a very limited choice may be made.

Year Four Students follow 6 lectured half-unit courses from an extensive list made up of, ‘with Advanced Study’ final year BSc options (having enhanced coursework and the list of courses made available as part of the taught course MSc programmes in Pure Mathematics, Applied Mathematics. They also carry out a supervised individual research project. Fourth Year Mastery Examination The Mastery Examination is taken by all Fourth Year students and consists of advanced topics from all Fourth Year courses on offer. Thus if they are taking six mathematics examinations, they will have six questions on the Mastery Examination paper. They will be expected to answer five of the six in a three hour paper. Those taking a Humanities/Business option that does not have an extended Fourth Year version will have no choice and have to answer all five questions in three hours. Some courses will choose to set extended project work, rather than submit a question to the Mastery Examination. Students taking one or more of these project courses will have a proportionally shorter Mastery Examination. Thus, for example, a student taking a Humanities option and two courses with an enhanced project will have a 108 minute examination consisting of three compulsory questions from each of their remaining courses. As this is the first year of the Mastery Examination, some of the details may change. At their discretion, individual Course Lecturers may give some indication of the kind of advanced questions they will offer. Students must pass all courses to gain the degree. Each course component is credited with a certain number of ECTS, roughly proportional to the study time of the component. th In the MSci 4 year, a typical student would take 6 courses of 8 ECTS each, as well as the full-unit project (16 ECTS) and the Mastery exam (6 ECTS) totally 70 ECTS. They may take one course from a different department, and so the ECTS count is in the range 68-70. MSci students may also optionally undertake extra Summer project work, potentially earning 20 additional ECTS.

18. Support provided to students to assist learning (including collaborative students, where appropriate). 

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In attracting the ablest students the Department is strongly involved with schools and colleges on an individual basis and through Open Days. The Department has its own Open Day as well as taking part in the annual College Open Day; it also normally runs each session a one-day Conference for Teachers. In selection the Department has a policy of inviting all well-qualified home applicants to visit the Department. Through presentations and discussion we try to ensure that we make offers to students who will most benefit from the course. Before successful students arrive they receive academic and other advice about their induction into the Department. On arrival students receive the UG Handbook. This contains details of the course structure and assessment as well as general advice, College safety information, Libraries, computing facilities and timetables. During the first week, as part of the induction process, there is a diagnostic test on ‘A level’ mathematical technique to assess the range and depth of knowledge of new students [there is a wide variety of syllabuses which have been covered by the incoming class]. Early in the first term the Senior Tutor and Director of Undergraduate Studies talk informally to all first year students about study methods and their reactions to the school/university interface. For years 2,3,4 (where appropriate) there are detailed course documents – blue, yellow, mauve – indicating course descriptors, assessment details (Year Handbooks) The Department’s staff is our major resource. Most Academic Staff are involved in teaching/learning/project support, which have strong research input. The Academic Staff also provide Service Teaching in Mathematics throughout the College. Each student has a Personal Tutor to assist with personal and academic problems (normally for the duration of the degree course) allocated by the Senior Tutor as well as Year Tutors to deal with day-to-day matters as well as the Undergraduate Liaison Officer. There is also access to the College Tutor. In Year 1 students have weekly group tutorials for each course, normally led by an academic member of staff. In Year 2 there are problem classes for compulsory courses which are each normally led by 2 or more tutors. For optional courses, classes are held regularly during the


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timetabled lecture periods. All courses are included within the ‘office-hour’ system, where there is a timetabled period for individual student/lecturer consultations. For compulsory courses in Years 1 and 2, as well as for many course options, there is regular assessed coursework/tests, which provides feedback during each course as well as counting in its final assessment (normally up to a total of 10% for each course). In addition to the main College Library here is a new Mathematics Learning Centre within the Department. This, together with other supporting facilities provides an excellent environment for private study and group working – with extensive computation facilities (desktop, docking ports, wifi).

Other facilities include:          

Dedicated computing, printing and copying facilities with extended daily access, providing email and on-line facilities. Departmental licensing of software to enable relatively inexpensive student purchase. A student common room facility. A staff-student committee meets regularly during the session. There are student representatives from each year spanning the programme degree codings. Open access to the Senior Tutor/Year Tutors and the Director of Undergraduate Studies, Undergraduate Liaison Officer. MathSoc – a society for all members of the Department for academic and non-academic events. PLUS – a group for those (students and staff) interested in ‘non-standard’ problem-solving. Careers advice within the Department as well as a College Careers Service. Access to student counsellors on the South Kensington site and a Health Centre. Access to a Union advisor. Access to College Teaching and Learning Support Services.

19. Criteria for admission: The minimum qualifications for admission are a successful performance in the Mathematics Admissions Test (MAT) and three full GCE A-levels, two which must be Mathematics and Further Mathematics at A* and a third subject at grade A. Applicants who are not able to take the MAT will need to sit STEP II or III. In order to take full advantage of the options available in the degree courses and to present a competitive application, an A-level combination including science subjects such as Physics and also Chemistry is recommended; however, we will consider strong applicants who are taking a third subject which not sciencebased, particularly if they are sitting STEP II or III. Scottish qualifications (Advanced Highers) are considered on the basis of their equivalence under the UCAS tariff. There are a number of eligible overseas qualifications including the International, European and French Baccalaureates, the German Abitur and many others which allow university entrance in other countries. BTEC applicants are not eligible. There is no formal language requirement for the course Mathematics with a Year in Europe, although evidence of basic competence in the language of the country for the year away may be requested. As part of this degree language courses for academic credit are normally taken during years 1 and 2. It should be noted that the entry requirements for MSci courses are the same as for the corresponding BSc courses. However, progression into year 4 requires a good level of performance on the course: currently upper second class honours level or better. Suitably qualified students may transfer from BSc codes to MSci codes (or from MSci to BSc) at a later stage.

20. Processes used to select students:  Primarily UCAS Admission, Examination Grades, Interviews for Special Cases, Open Days. From 2013, all entrants will be required to take the the MAT (Mathematics Admissions Test). 21. Methods for evaluating and improving the quality and standards of teaching and learning a) Methods for review and evaluation of teaching, learning, assessment, the curriculum and outcome standards:   

Individual course review initiated through the Director of Undergraduate Studies. Annual course review through the Departmental Examinations Committee. Departmental Staff-Student committee.


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Policy and general curriculum and course review through the Departmental Teaching Strategy and Undergraduate Course Committee (with e.g. inputs from the above). Questionnaires. Occasional Peer review of Lecturer/Course Teaching – approximately biennial. Biennial appraisal of individual staff by Section Heads. External Examiner Reports. Periodic review of departmental teaching by external review panel – members invited by the Rector and from another university, a research institute and industry. This is organised through the College Science Studies Committee Review by the Quality Assurance Agency.

The external examiner system and Boards of Examiners are central to the process by which the College monitors the reliability and validity of its assessment procedures and academic standards. Boards of Examiners comment on the assessment procedures within the College and may suggest improvements for action by relevant departmental teaching Committees. The Faculty Studies Committees and the Graduate School’s Master’s Quality Committees review and consider the reports of external examiners and accrediting bodies and conduct periodic (normally quinquennial) and internal reviews of teaching provision. Regular reviews ensure that there is opportunity to highlight examples of good practice and ensure that recommendations for improvement can be made. At programme level, the Head of Department/Division has overall responsibility for academic standards and the quality of the educational experience delivered within the department or division. Most of the College’s undergraduate programmes are accredited by professional engineering and science bodies or by the General Medical Council. Accreditation provides the College with additional assurance that its programmes are of an appropriate standard and relevant to the requirement of industry and the professions. Some postgraduate taught courses are also accredited. b)

Committees with responsibility for monitoring and evaluating quality and standards:          

Departmental Staff – Student Committee. Departmental Teaching Strategy Committee. Departmental Staff Meeting. Departmental Examination Committee. Departmental Management Committee. Board of Examiners. Faculty of Natural Sciences Teaching Committee Imperial College, Science Studies Committee. Imperial College Quality Assurance and Enhancment Committee Imperial College Senate

The Senate oversees the quality assurance and regulation of degrees offered by the College. It is charged with promoting the academic work of the College, both in teaching and research, and with regulating and supervising the education and discipline of the students of the College. It has responsibility for approval of changes to the Academic Regulations, major changes to degree programmes and approval of new programmes. The Quality Assurance and Enhancement Committee (QAEC) is the main forum for discussion of QA policy and the regulation of degree programmes at College level. QAEC develops and advises the Senate on the implementation of codes of practice and procedures relating to quality assurance and audit of quality and arrangements necessary to ensure compliance with national and international standards. QAEC also considers amendments to the Academic Regulations before making recommendations for change to the Senate. It also maintains an overview of the statistics on completion rates, withdrawals, examination irregularities (including cases of plagiarism), student appeals and disciplinaries. The Faculty Studies Committees and Graduate School’s M a s t e r ’ s Quality Committees are the major vehicle for the quality assurance of undergraduate / postgraduate courses respectively. Their remit includes: setting the standards and framework, and overseeing the processes of quality assurance, for the areas within their remit; monitoring the provision and quality of e-learning; undertaking reviews of new and existing courses; noting minor changes in existing programme


curricula approved by Departments; approving new modules, changes in module titles, major changes in examination structure and programme specifications for existing programmes; and reviewing proposals for new programmes, and the discontinuation of existing programmes, and making recommendations to Senate as appropriate. The Faculty Teaching Committees maintain and develop teaching strategies and promote interdepartmental and inter-faculty teaching activities to enhance the efficiency of teaching within Faculties. They also identify and disseminate examples of good practice in teaching. Departmental Teaching Committees have responsibility for the approval of minor changes to course curricula and examination structures and approve arrangements for course work. They also consider the details of entrance requirements and determine departmental postgraduate student numbers. The Faculty Studies Committees and the Graduate School’s Master’s Quality Committees receive regular reports from the Departmental Teaching Committees. c) Mechanisms for providing prompt feedback to students on their performance in course work and examinations and processes for monitoring that these named processes are effective: Extensive programme of Assessed Coursework/Tests – marked by GTAs and returned. Assessments and Projects – written feedback and an oral presentation.

d) Mechanisms for gaining student feedback on the quality of teaching and their learning experience and how students are provided with feedback as to actions taken as a result of their comments:  Departmental Staff – Student Committee. Departmental Teaching Strategy Committee. Individual Course questionnaires. Personal Tutors, Senior Tutor, Director of Undergraduate Studies, Year Tutors, TOLE, SOLE, NSS e)

Mechanisms for monitoring the effectiveness of the personal tutoring system:

Feedback via Senior Tutor/Reports/Staff-Student Committee f)

Mechanisms for recognising and rewarding excellence in teaching and in pastoral care:

Staff are encouraged to reflect on their teaching, in order to introduce enhancements and develop innovative teaching methods. Each year College and Faculty awards are presented to academic staff for outstanding contributions to teaching, pastoral care or research supervision. A special College award for Teaching Innovation, available each year, is presented to a member of staff who has demonstrated an original and innovative approach to teaching. Nominations for these awards come from across the College and students are invited both to nominate staff and to sit on the deciding panels. g) Staff development priorities for this programme include: 

     22.

Very active research programme in Mathematics. During probation, lecturers attend a series of College organised workshop on teaching and learning. Probationary lecturers are assigned a mentor. Staff are appraised, approximately biennially. Staff have available to them College courses and occasional seminars on teaching and learning. Graduate Teaching Assistants attend a Workshop on demonstrating, and are informally ‘apprenticed to academic staff for their teaching assignments.

Regulation of Assessment

a) Assessment Rules and Degree Classification:


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Within the Department the total raw mark from each course assessment is RESCALED so that overall performances can be compared. For each half-unit course – with only very few exceptions for courses involving extra computational assignments rescaled (honours) marks are then awarded on a notional 0-100 scale with the fixed nd st points at 0, 30 (P  Pass), 60 (T lower/upper 2 class boundary), 75 (E  lowest 1 class), 100 (M  nominated maximum mark). [THESE ARE NOT PERCENTAGES]. Other than for courses which are assignment/project based, assessed coursework typically contributes in total to no more than 10% of each of the course raw mark totals. Details of assessment are contained within the overall First, Second, Third, Fourth Year Course documents [PINK, BLUE, YELLOW, MAUVE respectively]. Honours marks for each year then total: First Year 900 ( 8  100 + 50 + 50) for the eight course assessments and computation and the first year poster project. Second Year 850 ( 8  100 + 50) for the eight course assessments and the second year group project. Third Year 800 ( 8  100) for the eight course assessments, which may include project work depending on degree coding and option choice. Fourth Year 800 ( 6  85, 1  200 project, 1 for Mastery Examination) for the six course assessments and the final year compulsory project.

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The course unit requirements and year weightings for the various MSci degrees are as follows:

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All candidates who pass in each year are awarded a degree and are considered for honours classification. Within the Department final honours assessment is based on total scaled marks after the corresponding year weighting has been applied

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G013, G104: Length (Yrs): 4; Units Taken: 16; Year Honours Weighting: 1:3:4:5 TOTAL MARK First Class

 750

Upper Second Class

600 - 650

Lower Second Class

450 - 550

Third Class

300- 350

Separation lines are set in collaboration with the External Examiners somewhere between the automatic bands. Candidates close to these lines are discussed individually at the Final Meeting of the Mathematics Examining Sub-Board on the basis of the full spectrum of academic performance during the programme.


[It should be noted that reporting of marks for individual courses on course transcripts is carried out by translation to the common College scale on which the grades for individual courses are::GRADE

MARKS

INTERPRETATION

A

70% - 100%

Marks represent a First Class performance

B

60% - 69%

Marks represent an Upper Second Class performance

C

50% - 59%

Marks represent a Lower Second Class performance

D

40% - 49%

Marks represent a Third Class performance

E

0% - 39%

Marks represent a Fail performance

A student who is unable to complete their final year exams because of illness, or the death of a near relative, may be considered for a degree under the ‘aegrotat’ provisions.

b) Marking Schemes for undergraduate and postgraduate taught programmes: On the College Scale (see above), the Pass Mark for all undergraduate modules is 40%. From October 2008 entry all undergraduates are required to pass all their course elements in order to progress to the next year, and then to graduate. c) Processes for dealing with mitigating circumstances: For undergraduate programmes: Candidates with mitigating circumstances are not subject to the borderline restrictions but should be considered individually. However, as a general principle, candidates whose marks are more than 5% below the borderline should not normally be raised to the next higher classification. Resit opportunities are available for students who do not achieve a Pass in examinations – according to College rules. Applications for such to be ‘First attempts’ – normally on medical grounds - which must be accompanied by a medical certificate or other statement of the grounds on which the application is made. These shall be submitted to the Academic Registrar who will submit them to the Board of Examiners. A similar process applied for Appeals against other decision of the Board of Examiners. d) Processes for determining degree classification for borderline candidates: For undergraduate programmes: Candidates who fall no more than 2.5% below the minimum mark for a higher honours classification shall be eligible for review of their final classification; this review could include an oral examination or practical test or other mechanism appropriate to the discipline. Candidates whose marks are below the 2.5% borderline may be considered for a higher honours classification where certain provisions apply. Detailed records of all decisions should be recorded in the minutes of the meeting of the Board. e) Role of external examiners: The visiting examiners (from other universities in the UK) are nominated by the Mathematics Board of Examiners and approved by the Science Studies Committee. Visiting examiners normally serve for 4 years. The role of visiting examiner is that of moderator. In order to do this they:     

approve examination papers; th see all examination scripts/assignments/4 year Mastery examination and research project dissertations; attend the Board of Examiners; provide recommendations for borderline candidates. complete a report to the College.


The primary duty of external examiners is to ensure that the degrees awarded by the College are consistent with that of the national university system. External examiners are also responsible for approval of draft question papers, assessment of examination scripts, projects and coursework (where appropriate). Although external examiners do not have power of veto their views carry considerable weight and will be treated accordingly. External examiners are required to attend each meeting of the Board of Examiners where recommendations on the results of individual examinations are considered. External examiners are required to write an annual report to the President and Rector of Imperial College which may include observations on teaching, course structure and course content as well as the examination process as a whole. The College provides feedback to external examiners in response to recommendations made within their reports. 23. Indicators of Quality and Standards     

Favourable comments by External Examiners. High proportion of students achieving a high degree classification. First destination data for graduates, showing a high proportion find employment or further postgraduate training and related areas. Independent External review invited by the College through its Quality Assurance procedures. This was previously carried out in 2004 with an excellent report. The most recent review was in 2010. Independent review of the quality of the educational provision of the Mathematics Department by the


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Quality Assurance Agency subject review process in 2000, achieving an excellent grading. The best of the Final Year projects have consistently won awards at National level (e.g. SET awards).

24. Key sources of information about the programme can be found in This specification provides a concise summary of the main features of the programme and learning outcome s that a typical student might reasonably be expected to achieve and demonstrate if she/he takes full advantage of the learning opportunities that are provided. The accuracy of the information contained in this document is reviewed by the College and may be checked by the Quality Assurance Agency for Higher Education (QAA). Key sources of information about this course can be found in: 

Undergraduate Prospectus, Imperial College London (available on-line www.imperial.ac.uk)

QAA Subject Review Report (Mathematics, Statistics and Operational Research), 2000 Imperial College of Science, Technology and Medicine (www.qaa.ac.uk). 

ECTS assignment (available on-line at www.ma.imperial.ac.uk)

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Mathematics Undergraduate Courses (available on-line at www3.imperial.ac.uk/mathematics/students/undergraduates/courseguides

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Mathematics: Scheme for the Award of Honours (available on-line at http://www3.imperial.ac.uk/mathematics/students/undergraduate/programspecifications
