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Programme Approval 2006/07 THE PROGRAMME SPECIFICATION 1. Programme title and designation Mathematics Single honours Joint Major/minor X 2. Final award Award Title BSc Mathematics 3. Nested awards Award Title N/A N/A 4. Exit awards Award Title Ordinary Degree (BSc) Undergraduate Diploma Credit Value 360 ECTS equivalent 180 Any special criteria Credit Value N/A ECTS equivalent N/A Any special criteria Credit Value 300 ECTS equivalent 150 Any special criteria 120 N/A 60 N/A Mathematics Natural and 240 Mathematical Sciences Undergraduate Natural and 120 Certificate Mathematical Sciences 5. Level in the qualifications framework 6. Attendance X Minimum length of programme 3 years Maximum length of programme 10 years 7. Awarding institution/body 8. Teaching institution 9. Proposing department 10. Programme organiser and contact Details 11. UCAS code (if appropriate) 12. Relevant QAA subject benchmark/ professional and statutory body guidelines PAF Originally Approved: 26th June 2007 PAF Modified for 2010/11 by ASQ: 5th May 2010 PAF finalised for 2010/11: 18 October 2010 PAF modified by ASQ for 2011/12: 28th February 2011 PAF finalised for 2011/12: 5 September 2011 PAF modified re exit award title: 29 March 2012 PAF finalised for 2012/13: 20 September 2012 N/A N/A H Full-time Mode of attendance N/A Part-time N/A Distance learning N/A King’s College London King’s College London Mathematics First & Second Year – Dr Giuseppe Tinaglia Tel.: 020 7848 2981 E-mail: [email protected] Third Year – Dr Mahesh Kakde: Room 407a, Strand Building Tel.: 020 7848 2852 E-mail: [email protected] G100 Mathematics, Statistics and Operational Research 1 Programme Approval 2006/07 13. Date of production of specification 14. Date of programme review April 2005, Updated in November 2007 for the CF 2014/15 16. Educational aims of the programme To teach the broadly accepted canon of university level undergraduate mathematics. To develop, through the study of mathematics, habits of independent rigorous thought and skill at solving problems, and to enable students to experience the excitement and satisfaction of discovery and solution. To train students to think logically and to present reasoned arguments clearly. To show the power of mathematics as an intellectual activity. To provide demanding courses within the capabilities of the students admitted to the Department; to give them confidence through the acquisition of technical and transferable skills and so encourage them to develop the ability to work and think for themselves. To provide an environment which offers students the opportunity to become active members of the mathematics community. Ensure that students acquire an understanding of their professional and ethical responsibilities. 17. Educational objectives of the programme/programme outcomes The student should acquire: An understanding of the depth of the main areas of modern mathematics at a level comparable with that of major national mathematics departments and at a standard comparable with that of the bachelor degree in other subjects. An appropriate level of understanding of the compulsory material in the programme. An appropriate level of skill in calculation and manipulation within this body of knowledge. Application of core concepts and principals at least in a well defined context. Appreciation of the importance of mathematics and its applications, and of the excitement and satisfaction of discovery. A range of transferable skills including the ability to think logically, to solve problems and to present reasoned arguments clearly, as well as some IT skills. The ability to work independently, pursuing meaningful independent study. In the final year students are expected to consolidate the understanding of year 1 and 2 compulsory material, demonstrating ability to use this in a variety of contexts, and a critical awareness of its range of application and validity. Students are expected to increase their knowledge in some areas of either abstract pure mathematics or application, or both. Knowledge and understanding The programme provides a knowledge and understanding of the following: 1. The fundamental principles of a selection of key areas of pure, applicable or applied mathematics. 2. The professional and ethical responsibilities of mathematicians. These are achieved through the following teaching/learning methods and strategies: The main teaching method is the lecture, but there are also tutorials, problem classes and an optional project. Assessment: th PAF Originally Approved: 26 June 2007 PAF Modified for 2010/11 by ASQ: 5th May 2010 PAF finalised for 2010/11: 18 October 2010 PAF modified by ASQ for 2011/12: 28th February 2011 PAF finalised for 2011/12: 5 September 2011 PAF modified re exit award title: 29 March 2012 PAF finalised for 2012/13: 20 September 2012 2 Programme Approval 2006/07 Usually solely by unseen written examination in May, but for some modules also by course work. Skills and other attributes Intellectual skills: 1. To formulate mathematical models of problems and solve them. 2. To reason logically, and to present arguments clearly. 3. To be self directed in solving problems and understanding new material. These are achieved through the following teaching/learning methods and strategies: Intellectual skills are developed via lectures and the work the students are required to carry out in order to understand the material and to solve the set problems. The questions asked by students and answers given by the lecturer during lectures also play an important part. Assessment: Analysis and problem solving skills are assessed through examination. Practical skills: 1. Use of `Maple’, a computer algebra package and programming language. 2. Verbal communication These are achieved through the following teaching/learning methods and strategies: supervised teaching sessions in computer laboratories. Assessment: First year students are required to pass a test in the use of Maple. Verbal communication is assessed by student presentations of a mathematical topic. Generic/transferable skills: 1. Apply mathematical skills to problems 2. Manage time and plan work load. 3. Learn independently with a spirit of actual enquiry. 4. Effective note taking. These are achieved through the following teaching/learning methods and strategies: These skills are essential by-products of learning the material given in lectures and solving the problems set. Assessment: 1 is assessed by means of the unseen May examinations in each module. The other skills are not directly assessed but are a necessary pre-requisite for learning material presented in lectures and for solving problems set. PAF Originally Approved: 26th June 2007 PAF Modified for 2010/11 by ASQ: 5th May 2010 PAF finalised for 2010/11: 18 October 2010 PAF modified by ASQ for 2011/12: 28th February 2011 PAF finalised for 2011/12: 5 September 2011 PAF modified re exit award title: 29 March 2012 PAF finalised for 2012/13: 20 September 2012 3 Programme Approval 2006/07 18. Statement of how the programme has been informed by the relevant subject benchmark statement(s)/professional and statutory body guidelines The programme is consistent with the relevant heading (‘theory based as opposed to practice based Mathematics) of the benchmark for Mathematics, Statistics and Operational Research. 19. Programme structure and award requirements (a) numbers of compulsory and optional modules to be taken in each year of the programme Year 1: 120 credit compulsory modules Year 2: 6 x 15 credit compulsory modules, plus 30 optional credits Year 3: 120 optional credits. Students may be permitted to take additional modules up to a maximum value of 30 credits with academic approval. (b) range of credit levels permitted within the programme 4, 5, 6, exceptionally students may be permitted to take a level 7 module (c) maximum number of credits permitted at the lowest level 150 at level 4 (where students have been permitted to take additional credits) (d) minimum number of credits required at the highest level 90 at level 6 (or above) (e) progression and award requirements (if different from the standard) To progress from Year 1 to Year 2 a student must gain an average mark of at least 40% in level 4 mathematics modules, with no mark lower than 33% and 90 credits passed overall. (f) maximum number of credits permitted with a condoned fail (core modules excluded) 45 credits at level 4, 5, 6 or 30 at level 4, 5, 6 plus 15 at level 7. In all cases, the condoning of failed marks will be at the discretion of the programme examination board and in accordance with the College regulations, excepting the above (g) are students permitted to take a substitute module, as per regulation A3, 20.7? no (g) other relevant information to explain the programme structure In year 3 students must include at least 2 modules from the list: 6CCM318A (CM481Z) Fourier Analysis 6CCM321A (CM321A) Real Analysis II 6CCM322A (CM322C) Complex Analysis 6CCM326A (CM326Z) Galois Theory 6CCM327A (CM327Z) Topology 6CCM331A (CM331A) Special Relativity and Electromagnetism 6CCM332A (CM332C) Introductory Quantum Theory 6CCM338A (CM338Z) Mathematical Finance II: Continuous Time 6CCM350A (CM350Z) Rings and Modules 6CCM388A (CM388A) Mathematical Finance I: Discrete Time Students may be permitted to take modules from other Departments within King’s or intercollegiate PAF Originally Approved: 26th June 2007 PAF Modified for 2010/11 by ASQ: 5th May 2010 PAF finalised for 2010/11: 18 October 2010 PAF modified by ASQ for 2011/12: 28th February 2011 PAF finalised for 2011/12: 5 September 2011 PAF modified re exit award title: 29 March 2012 PAF finalised for 2012/13: 20 September 2012 4 Programme Approval 2006/07 mathematics modules with academic approval. Students who transfer between BSc and MSci Mathematics can do so until the end of year 2. Students transferring from BSc to MSci in year three will normally have to conform to compulsory year three modules. Students may not obtain credit from modules based on largely overlapping content (See below for details of modules). Where mathematics modules contain summative coursework, the coursework will only be used in calculating the overall mark at the first attempt. Resit students will be judged solely on their examination performance in level 4, 5 and 6 mathematics modules. PAF Originally Approved: 26th June 2007 PAF Modified for 2010/11 by ASQ: 5th May 2010 PAF finalised for 2010/11: 18 October 2010 PAF modified by ASQ for 2011/12: 28th February 2011 PAF finalised for 2011/12: 5 September 2011 PAF modified re exit award title: 29 March 2012 PAF finalised for 2012/13: 20 September 2012 5 Programme Approval 2006/07 Prohibited module combinations In general PCCMXXXa In particular 4CCM115a 4CCM121a 4CCM122a 4CCM131a 4CCM131a 4CCM141a 5CCM211a 5CCM222a 5CCM223a 5CCM224a 5CCM232a 5CCM241a 5CCM251a 5CCM328b 6CCM320a 6CCM321a 6CCM322a 6CCM326a 6CCM327a 6CCM330a 6CCM334a (CM334Z) 6CCM335a 6CCM338a (CM338Z) 6CCM350a 6CCM352a 6CCM356a 7CCM359b 6CCM436a 6CCM451b 7CCM467a Numbers and Functions (CM115A) Introduction to Abstract Algebra (CM121A) Geometry I (CM122A) Introduction to Dynamical Systems (CM131A) Introduction to Dynamical Systems (CM131A) Probability and Statistics I (CM141A) PDEs and Complex Variable (CM211A) Linear Algebra (CM222A) Geometry of Surfaces (CM223A) Elementary Number Theory (CM224X) Groups and Symmetries (CM232A) Probability and Statistics II (CM241X) Discrete Mathematics (CM251X) Logic Topics in Mathematics (CM320X) Real Analysis II (CM321A) Complex Analysis (CM322C) Galois Theory (CM326Z) Topology (CM327Z) Maths Education and Communication (CM330X) Space-time Geometry & General Relativity Non-Linear Dynamics (CM335Z) Mathematical Finance II: Continuous Time Rings and Modules (CM350Z) Chaotic Dynamics (CM352Y) Linear Systems with Control Theory (CM356Y) Numerical Methods Quantum Mechanics II (CM436Z) Neural Networks (CM451Z) Applied Probability and Stochastics (CM467Z) PAF Originally Approved: 26th June 2007 PAF Modified for 2010/11 by ASQ: 5th May 2010 PAF finalised for 2010/11: 18 October 2010 PAF modified by ASQ for 2011/12: 28th February 2011 PAF finalised for 2011/12: 5 September 2011 PAF modified re exit award title: 29 March 2012 PAF finalised for 2012/13: 20 September 2012 And QCCMXXXb And And And And And And And And And And And And And And And And And And And And 5CCM115b 5CCM121b 5CCM122b 5CCM131b 6CCM357a 5CCM141b 6CCM211b 6CCM222b 6CCM223b 6CCM224b 6CCM232b 6CCM241b 6CCM251b 6CCM328a 7CCM320b 7CCM321b 7CCM322b 7CCM326b 7CCM327b 7CCM330b And And 7CCM334b 7CCM335b And And And And And And And And 7CCM338b 7CCM350b 7CCM352b 6CCM357a 6CCM359a 7CCMMS31 7CCM451b 7CCMFM01 6 Programme Approval 2006/07 Programme Structure Title 4CCM111a Calculus I 4CCM112a Calculus II 4CCM122a Geometry I 4CCM121a Introduction to Abstract Algebra 4CCM131a Introduction to Dynamical Systems 4CCM113a Linear Methods 4CCM115a Numbers and Functions 4CCM141a Probability & Statistics I 5CCM221a Analysis I 5CCM251a Discrete Mathematics 5CCM224a Elementary Number Theory 5CCM223a Geometry of Surfaces 5CCM232a Groups & Symmetries 5CCM231a Intermediate Dynamics 5CCM222a Linear Algebra 5CCM211a Partial Differential Equations & Complex Variable 5CCM241a Probability & Statistics II 6CCM322a Complex Analysis 6CCM251b Discrete Mathematics 6CCM224b Elementary Number Theory 6CCM318A Fourier Analysis 6CCM326a Galois Theory PAF Originally Approved: 26th June 2007 PAF Modified for 2010/11 by ASQ: 5th May 2010 PAF finalised for 2010/11: 18 October 2010 PAF modified by ASQ for 2011/12: 28th February 2011 PAF finalised for 2011/12: 5 September 2011 PAF modified re exit award title: 29 March 2012 PAF finalised for 2012/13: 20 September 2012 Credit level 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 6 6 6 6 6 Credit value 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 Status (I, Cr, Cp, O) for each type of programme Major/ Single Joint minor Cp Cp Cp Cp Cp Cp Cp Cp Cp O O Cp Cp Cp Cp Cp O Cp/O* O O Cp/O* Cp/O* Progression Single NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO Joint Assessment Major/ minor Examination Examination Examination & tests Examination & tests Examination & tests Examination Examination Examination & tests Examination Examination Examination Examination Examination Examination Examination & tests Examination Examination Examination Examination Examination Examination Examination 7 Programme Approval 2006/07 6CCM360a History and Development of Mathematics 6CCM332a Introductory Quantum Theory 6CCM222b Linear Algebra 6CCMCS05 Mathematical Biology 6CCM388a Mathematical Finance I: Discrete Time 6CCM338a Mathematical Finance II: Continuous Time 6CCM314A Mathematical Theory of Collective Behaviour 6CCM330a Mathematics Education and Communication 6CCM241b Probability and Statistics II 6CCM345a The Project Option 6CCM321a Real Analysis II 6CCM351a Representation theory of finite groups 6CCM350a Rings and Modules 6CCM334a Space-time Geometry & General Relativity 6CCM331a Special Relativity and Electromagnetism 6CCMCS02 Theory of Complex Networks 6CCM320a Topics in Mathematics 6CCM327a Topology Other optional modules may be taken where the timetable allows, subject to the approval of the Programme Director * In year 3 students must take at least 4 of the compulsory modules 6 6 6 6 6 6 6 15 15 15 15 15 15 15 O Cp/O* O O Cp/O* Cp/O* O NO NO NO NO NO NO NO 6 6 6 6 6 6 6 6 6 6 6 15 15 15 15 15 15 15 15 15 15 15 O O O Cp/O* O Cp/O* O Cp/O* O O Cp/O* NO NO NO NO NO NO NO NO NO NO NO Examination & coursework Examination Examination Examination Examination Examination Examination Report, assessment & presentation Examination Project Examination Examination Examination Examination Examination Examination Examination Examination O NO Various 5,6 20. Marking criteria The marking scheme for this programme follows the College generic criteria and additionally those in the School of Natural and Mathematical Sciences PAF Originally Approved: 26th June 2007 PAF Modified for 2010/11 by ASQ: 5th May 2010 PAF finalised for 2010/11: 18 October 2010 PAF modified by ASQ for 2011/12: 28th February 2011 PAF finalised for 2011/12: 5 September 2011 PAF modified re exit award title: 29 March 2012 PAF finalised for 2012/13: 20 September 2012 8 Programme Approval 2006/07 PROGRAMME APPROVAL FORM SECTION 2 – SUPPLEMENTARY INFORMATION 1. Programme name BSc Mathematics 2. If the programme is a joint award with an institution outwith the University of London has the necessary approval been sought from Academic Board? Yes No Not applicable X Please attach a copy of the request to Academic Board 3. In cases of joint honours programmes please provide a rationale for the particular subject combination, either educational or academic N/A 4. If the programme involves time outside the College longer than a term, please indicate how the time will be spent, the length of time out and whether it is a compulsory or optional part of the programme N/A Year abroad Year in employment Placement Other (please specify) Time spent ………………………….. Compulsory/optional ………………………. 5. Please provide a rationale for any such time outside the College, other than that which is a requirement of a professional or statutory body N/A 6. Please give details if the programme requires validation or accreditation by a professional or statutory body N/A PAF Originally Approved: 26th June 2007 PAF Modified for 2010/11 by ASQ: 5th May 2010 PAF finalised for 2010/11: 18 October 2010 PAF modified by ASQ for 2011/12: 28th February 2011 PAF finalised for 2011/12: 5 September 2011 PAF modified re exit award title: 29 March 2012 PAF finalised for 2012/13: 20 September 2012 9 Programme Approval 2006/07 7. In cases where parts or all of the programme (other than those in box 4 above) are delivered either away from one of the College campuses and/or by a body or bodies external to the College please provide the following details Name and address of the off-campus location and/or external body There is no requirement for students to take modules at colleges of the University of London outside King’s, but subject to the approval of the relevant Programme Director permission may be granted to students in their Final Year to take modules at: Imperial College University College (University of London) Queen Mary College (University of London) Royal Holloway College (University of London) Percentage/amount of the programme delivered off-campus or by external body The vast majority of students take all their modules at King’s. However, subject to the approval of the relevant Programme Director permission may be granted to students in their Final Year to take modules at other colleges of the University of London (as specified above) or at Imperial College; in practice students exercising this option will take not normally more than 30 credits outside King’s. Nature of the involvement of external body All the colleges listed above are major colleges of London University or of equally high standing and run their own Mathematics programmes. Description of the learning resources available at the off-campus location They offer the same high quality resources as are available at King’s. What mechanisms will be put in place to ensure the ongoing monitoring of the delivery of the programme, to include monitoring of learning resources off-site or by the external body? All the colleges which are listed above have their own procedures for ensuring that a high quality programme is delivered. Additionally, for Undergraduate Ambassador Scheme 6CCM330a (CM330X): Name and address of the off-campus location and/or external body The Undergraduate Ambassador Scheme: London secondary schools Percentage/amount of the programme delivered off-campus or by external body Up to 2% (optional 3rd year 15 credit module) Nature of the involvement of external body Students spend a few hours per week in a Mathematics Department of a London secondary School, supervised by the staff of that school, assisting in the teaching of Mathematics. Description of the learning resources available at the off-campus location Normal secondary school resources What mechanisms will be put in place to ensure the ongoing monitoring of the delivery of the programme, to include monitoring of learning resources off-site or by the external body? All schools are visited by KCL Mathematics Department staff, and an individual teacher is responsible for the student in the school. A member of KCL staff monitors the students while they are in the Undergraduate Ambassador Scheme. PAF Originally Approved: 26th June 2007 PAF Modified for 2010/11 by ASQ: 5th May 2010 PAF finalised for 2010/11: 18 October 2010 PAF modified by ASQ for 2011/12: 28th February 2011 PAF finalised for 2011/12: 5 September 2011 PAF modified re exit award title: 29 March 2012 PAF finalised for 2012/13: 20 September 2012 10