How the System Works 10

Department of Mathematics

How the System Works A Handbook for Undergraduate Students – 2010/11

School of Natural and Mathematical Sciences

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Department of Mathematics How the System Works

2010-2011

A Handbook for Undergraduate Students

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CONTACT DETAILS Department of Mathematics Tel: 020 7848 2828 King’s College London Fax: 020 7848 2017 Strand Email: [email protected] London WC2R 2LS Website: www.mth.kcl.ac.uk

Name Ext No Room No Email Address Prof C Albanese TBA [email protected] Dr A Annibale 2877 S5.26 [email protected] Dr AD Barnard 2245 K4U.19 [email protected] Mrs MJ Bennett-Rees 1071 K4U.21 [email protected] Ms F Benton 2216 S5.01 [email protected] Prof J Berndt 2814 S4.30 [email protected] Prof D Brigo 2855 S5.35 [email protected] Dr C Buescu 2226 S5.37 [email protected] DJ Burns 2863 S4.18 [email protected] Dr PP Cook TBA [email protected] Miss J Cooke 2217 S5.01 [email protected] Prof ACC Coolen 2235 S4.06 [email protected] Prof EB Davies 2698 S4.20 [email protected] Prof F Diamond 1068 S4.21 [email protected] Dr T di Matteo 2223 S5.28 [email protected] Dr B Doyon 2854 S4.12 [email protected] Dr P Emms 2852 S5.30 [email protected] Dr S Fairthorne 2245 K4U.19 [email protected] Dr N Gromov 2149 S5.27 [email protected] Dr WJ Harvey K4U.21 [email protected] Dr LH Hodgkin K4U.21 [email protected] Prof PS Howe TBA [email protected] Dr P Kassaei 2225 S4.07a [email protected] Dr E Katzav 2864 S4.13a [email protected] Dr R Kühn 1035 S4.13 [email protected] Prof N Lambert TBA [email protected] Dr DA Lavis 2240 K4U.24 [email protected] Dr BL Luffman 1071 K4U.21 [email protected] Prof D Makinson 1443 S4.05 [email protected] Dr A Macrina 2633 S5.36 [email protected] Dr D Martelli 2153 S5.29 [email protected] Dr B Noohi 2219 S4.22 [email protected] Prof G Papadopoulos 2227 S4.17 [email protected] Dr I Pérez Castillo 2860 S4.07 [email protected] Dr D Panov 1212 S4.08 [email protected] Prof AN Pressley 2975 S4.19 [email protected] Dr A Pushnitski 1167 S5.32 [email protected] Dr HC Rae 1071 K4U.21 [email protected] Dr A Recknagel 2244 S4.10 [email protected]

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Miss S Rice 2828 S5.01 [email protected] Dr K Rietsch 1443 S4.05 [email protected] Prof DC Robinson 2221 K4U.22 [email protected] Prof FA Rogers 2242 S4.35 [email protected] Prof Y Safarov 2215 S4.17 [email protected] Dr S Schafer-Nameki 2853 S4.08a [email protected] Prof PT Saunders 2218 K4U.19 [email protected] Prof SG Scott 2778 S4.09 [email protected] Prof E Shargorodsky 2676 S4.11 [email protected] Prof W Shaw 1119 S5.24 [email protected] Dr JR Silvester 1071 K4U.21 [email protected] Prof PK Sollich 2875 S5.25 [email protected] Dr DR Solomon 1165 S4.15 [email protected] Prof R Streater 2220 K4U.25 [email protected] Prof JG Taylor 2214 S3.20 [email protected] Dr G Tinaglia 2981 S5.31 [email protected] Dr J Van Baardewijk 1197 Chesham Bldg. [email protected] Dr GMT Watts 1013 S4.14 [email protected] Prof PC West 2224 S4.34 [email protected]

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Preface This handbook is issued to every undergraduate student in the Mathematics Department. The information it contains has been compiled by the Department and is valid for the 2010/11 academic session only. Please note that any rules and regulations outlined in this handbook exist in addition to College Regulations. No information given in this booklet overrides any regulation set by the College. Further information You may find it useful to know the following contact numbers and websites: Mathematics Department Academic Staff Head of Department Professor Jurgen Berndt (020 7848 2814) Director of Studies Professor Alice Rogers (020 7848 2242) Senior Tutor Professor Simon Scott (020 7848 2778) UG Chair of Exam Board Professor Andrew Pressley (020 7848 2975) UG Admissions Tutor Dr David Solomon (020 7848 1165) Chair of Staff/Student Committee Professor Fred Diamond (020 7848 1068) Mathematics Departmental Office Staff Departmental Administrator Ms Frances Benton (020 7848 2216) Student Administrator Miss Joanne Cooke (020 7848 2217) Operations Assistant Miss Stephanie Rice (020 7848 2828) Fax Number for office Fax: 020 7848 2017 Student Registration Office Tel: 020 7848 3410 Fax: 020 7848 3059 www.kcl.ac.uk/about/structure/admin/acservices/reg/ Assessment and Records Centre Tel: 020 7848 2268/1715 Fax: 020 7848 2766 Email: [email protected] The Compass Tel : 020 7848 7070 www.kcl.ac.uk/about/structure/admin/facser/centre/ Email : [email protected] Emergency Tel: 2222 Security Tel: 2874

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Disclaimer The information in this booklet was compiled in August 2010. Whilst every attempt has been made to ensure that details are as accurate as possible, some changes are likely to occur before or during the 2010/11 session. You are advised to check important information either with the Assessment and Records Centre or with your personal tutor. If you notice any errors, please tell your personal tutor. A more recent version of this booklet will be maintained on the website address. If you have doubts or questions please consult the online version.

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Contents Preface.............................................................................................................................5 Further information...........................................................................................................5 Disclaimer ........................................................................................................................6 Contents...........................................................................................................................7

1. INTRODUCTION ...........................................................................................................10 About your Departmental Handbook ..............................................................................10 History of the Department of Mathematics .....................................................................10 Mission Statement..........................................................................................................12 Term dates 2010-11.......................................................................................................12

2. ADMINISTRATIVE MATTERS.......................................................................................13 The Mathematics Departmental Office...........................................................................13 The School of Natural and Mathematical Sciences........................................................13 The Tutor System...........................................................................................................13 The Senior Tutor ............................................................................................................14 The Link-up System .......................................................................................................14 How we contact you .......................................................................................................14 Attendance and absence................................................................................................14

3. ORGANISATIONS FOR STUDENTS ............................................................................15 MathSoc .........................................................................................................................15

4. GENERAL DEPARTMENTAL INFORMATION..............................................................16 Finding your way around the Department ......................................................................16 Local Safety Procedures ................................................................................................19 Staff/Student Liaison Committee....................................................................................19 Prizes for Students 2009/10 ...........................................................................................19

5. STUDYING IN THE DEPARTMENT OF MATHEMATICS.............................................21 Code of Conduct ............................................................................................................21 The Semester System....................................................................................................22 Lectures and Tutorials....................................................................................................22 Walk-in Tutorials ............................................................................................................22 Pop-In Tutorials..............................................................................................................23 Coursework ....................................................................................................................23 Does Coursework Count? ..............................................................................................24 Class Tests in Year 1 .....................................................................................................24 Monitoring of Progress ...................................................................................................25 Student Presentations ....................................................................................................25 Evaluation of Presentations............................................................................................25 Workload ........................................................................................................................26 Submission of Projects and Essays ...............................................................................26

6. EXAMINATION REGULATIONS ...................................................................................27 Registration for and Admission to Examinations ............................................................27 Special Examinations Arrangements..............................................................................28 Attendance at Examinations...........................................................................................28 When are degree examinations held?............................................................................28 Examination Papers .......................................................................................................29 Rubrics ...........................................................................................................................29 Calculators .....................................................................................................................29 Marking Procedures .......................................................................................................30

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Mitigating Circumstances ...............................................................................................30 Appeal against a decision of a Board of Examiners .......................................................32 Degree Titles..................................................................................................................32 Course Units or Credits – How many do I need to pass for a degree? ..........................33 Award of Honours ..........................................................................................................33 Examination Results.......................................................................................................34 College Debtors and Release of Examination Results ...................................................35 August Resits .................................................................................................................35 Progression & Resits......................................................................................................35 Overseas Examinations .................................................................................................37 BSc/MSci transfers.........................................................................................................38 All your own work? .........................................................................................................38 Cheating.........................................................................................................................38 Collusion ........................................................................................................................38 Fabrication .....................................................................................................................38 Plagiarism ......................................................................................................................38

7. PROGRAMMES OF STUDY .........................................................................................40 Single subject honours ...................................................................................................40 Joint honours..................................................................................................................40 Mathematics BSc/MSci ..................................................................................................41 Mathematics with Management and Finance BSc .........................................................46 Graduate Diploma in Mathematics .................................................................................48 Mathematics and Computer Science BSc ......................................................................51 Mathematics and Computer Science MSci.....................................................................54 Mathematics and Physics BSc .......................................................................................56 Mathematics and Physics MSci......................................................................................59 Mathematics and Physics with Astrophysics BSc ..........................................................63 French and Mathematics BA .........................................................................................66 Mathematics and Philosophy BA....................................................................................68 Change of Degree Course .............................................................................................72

8. MODULE/COURSE UNIT LISTING...............................................................................72 4CCM111a (CM111A) Calculus I ...................................................................................73 4CCM112a (CM112A) Calculus II ..................................................................................75 4CCM113a (CM113A) Linear Methods ..........................................................................76 4CCM115a (CM115A) Numbers and Functions.............................................................77 5CCM115b (CM115B) Numbers and Functions for Joint Honours.................................78 4CCM121a (CM121A) Introduction to Abstract Algebra.................................................79 5CCM121b (CM121A) Introduction to Abstract Algebra for Joint Honours.....................80 4CCM122a (CM122A) Geometry I .................................................................................81 5CCM122b (CM122A) Geometry I for Joint Honours.....................................................82 4CCM131a / 5CCM131b (CM131A) Introduction to Dynamical Systems.......................83 4CCM141a / 5CCM141b (CM141A) Probability and Statistics I .....................................85 5CCM211a / 6CCM211b (CM211A) PDEs & Complex Variables ..................................86 5CCM221a (CM221A) Analysis I ...................................................................................88 5CCM222a / 6CCM222b (CM222A) Linear Algebra.......................................................90 5CCM223a / 6CCM223b (CM223A) Geometry of Surfaces ...........................................91 5CCM224A / 6CCM224B (CM224X) Elementary Number Theory .................................92 5CCM231a / 6CCM231b (CM231A) Intermediate Dynamics .........................................93 5CCM232a / 6CCM232b (CM232A) Groups and Symmetries .......................................94 5CCM241a / 6CCM241b (CM241X) Probability and Statistics II ....................................95

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5CCM250a (CM2504) Applied Analytic Methods ...........................................................96 5CCM251a / 6CCM251b (CM251X) Discrete Mathematics ...........................................98 6CCM318a Fourier Analysis ..........................................................................................99 6CCM320a (CM320X) Topics in Mathematics .............................................................100 6CCM321a / 7CCM321b (CM321A) Real Analysis II ...................................................103 6CCM322a / 7CCM322b (CM322C) Complex Analysis ...............................................104 6CCM326a / 7CCM326b (CM326Z) Galois Theory......................................................105 6CCM327a / 7CCM327b (CM327Z) Topology .............................................................106 6CCM328a (CM328X) Logic ........................................................................................107 6CCM330a (CM330X) Mathematics Education & Communication ..............................108 6CCM331a (CM331A) Special Relativity and Electromagnetism .................................110 6CCM332a (CM332C) Introductory Quantum Theory..................................................111 6CCM334a / 7CCM334b (CM334Z) Space-Time Geometry & General Relativity .......112 6CCM338a (CM338Z) Mathematical Finance II: Continuous Time ..............................113 6CCM350a / 7CCM350b (CM350Z) Rings and Modules .............................................115 6CCM351a (CM351A) Representation Theory of Finite Groups ..................................117 6CCM356a (CM356Y) Linear Systems with Control Theory ........................................118 6CCM357a (CM357Y) Introduction to Linear Systems with Control Theory.................119 6CCM359a (CM359X) Numerical Methods ..................................................................120 6CCM360a (CM360X) History and Development of Mathematics ...............................121 6CCM380a (CM380a) Topics in Applied Probability Theory ........................................122 6CCM388a (CM388Z) Mathematical Finance I: Discrete Time ....................................125 6CCMCS02 / 7CCMCS02 Theory of Complex Networks .............................................126 6CCMCS05 / 7CCMCS05 Mathematical Biology .........................................................127 7CCMMS01 (CM424Z) Lie Groups and Lie Algebras ..................................................128 7CCMMS03 (CM422Z) Algebraic Number Theory.......................................................129 7CCMMS08 (CM414Z) Operator Theory .....................................................................130 7CCMMS11 (CM418Z) Fourier Analysis ......................................................................131 7CCMMS18 (CM437Z) Manifolds ................................................................................132 7CCMMS19 (CMMS29) Modular Forms ......................................................................133 7CCMMS20 Algebraic Geometry .................................................................................134 7CCMMS31 (CM436Z) Quantum Mechanics II............................................................135 7CCMMS32 (CM438Z) Quantum Field Theory ............................................................136 7CCMMS34 (CM435Z) String Theory and Branes.......................................................137 7CCMMS38 (CM433Z) Advanced General Relativity...................................................138 7CCMMS41 Supersymmetry and Gauge Theory.........................................................139 Projects ........................................................................................................................140 The BSc Project Option 6CCM345a (CM345C) ...........................................................140 The MSci Project 7CCM461a (CM461C) .....................................................................140 ‘With Management’ programmes .................................................................................142 4CCMY129 - Organisational Behaviour .......................................................................144 4CCMY110 – Economics .............................................................................................145 5CCMY210 - Accounting..............................................................................................146 5CCMY212 - Marketing................................................................................................147 6CCMY325 – Business Strategy and Operations Management...................................148 6CCMY339 – Human Resource Management .............................................................149

9. SAFETY CHECK LIST.................................................................................................150 10. ETHICS IN MATHEMATICS ......................................................................................151 11. INDEX........................................................................................................................153

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1. INTRODUCTION About your Departmental Handbook This handbook is intended as a guide for all undergraduate students in the Department of Mathematics, King’s College London, during the academic session 2010/11. It should be your first point of reference should you need to know anything about the Department. In this booklet you will find information about the Department, details of important procedures which you will need to follow during the session, assessment information and details of programmes and modules available in the Department. We hope you find this handbook a useful accompaniment to your studies at King’s College, and wish you an enjoyable and successful year.

History of the Department of Mathematics Mathematics has been studied at King's throughout its history and the first Professor of Mathematics was appointed in 1830. Since then the Mathematics Department has established a record of accomplishments in central areas of pure mathematics and physical applied mathematics. It achieved very high profiles in both Pure and Applied Mathematics in the 2008 Research Assessment Exercise and was well within the top quartile nationally. The Department provides degree programmes and modules for both undergraduate and postgraduate degrees in mathematics. Its teaching programmes are influenced by the research interests and activities of the staff. The Department is a member of the School of Natural and Mathematical Sciences at King's. The Departments of the School together provide a wide range of degree programmes and modules in mathematics, informatics and physical sciences, from first year to postgraduate level, and in a variety of modes from full- and part-time to continuing education.

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Structure of the Department of Mathematics Head of Department and Professor of Mathematics: Professors: D Brigo, PhD DJ Burns, MA, PhD CJ Bushnell, BSc, PhD, FKC ACC Coolen, MSc, PhD FI Diamond, PhD N Lambert BSc, PhD GP Papadopoulos, PhD AN Pressley, MA, DPhil FA Rogers, BA PhD Y Safarov, BSc, PhD, DSc SG Scott, BSc, DPhil E Shargorodsky, MSc, PhD WT Shaw, MA, DPhil PK Sollich, MPhil, PhD PC West, BSc, PhD, FRS, FKC Readers: T di Matteo PhD R Kϋhn, PhD AH Recknagel, PhD DR Solomon, BA, PhD GMT Watts, BA, PhD Senior Lecturer: AB Pushnitski, PhD Lecturers: A Annibale, PhD C Buescu, PhD PP Cook, PhD B Doyon, PhD P Emms, DPhil N Gromov PL Kassaei, PhD E Katzav, PhD A Macrina, PhD B Noohi, PhD I Pérez Castillo, PhD S Schafer-Nameki, PhD G Tinaglia, PhD EPSRC Advanced Fellows: D Martelli, PhD KC Rietsch, MA, PhD Royal Society University Research Fellow: D Panov, PhD

Professor J Berndt, PhD Emeritus Professors: EB Davies, MA, DPhil, FRS, FKC PS Howe, BSc, PhD DC Robinson, MSc, PhD PT Saunders, BA, PhD RF Streater, BSc, PhD, DIC, LFS, ARCS JG Taylor, BSc, MA, PhD Emeritus Readers: JA Erdos, MSc PhD WJ Harvey, BSc, PhD Research Assistants/Associates: J Gutowski T Koeppe C Papageorgakis, PhD F Riccioni S Sasaki N Shayeghi Visiting Research Fellows: AD Barnard, MA, PhD DA Lavis, BSc, PhD, FInstP, FIMA Visiting Professor: C Albanese, PhD Visiting Lecturers: J Bennett-Rees, MA S Fairthorne, BSc LH Hodgkin, BA, DPhil D Makinson, PhD J Van Baardewijk, PhD Professional Services Staff Departmental Administrator Frances Benton, BA Student Administrator Joanne Cooke, BA Operations Assistant Stephanie Rice, BA IT Support Officer Dan Wade Dennis Hyde

Mission Statement The College’s Mission Statement is:- The College is dedicated to the advancement of knowledge, learning and understanding in the service of society. Since its foundation in 1829, King's has come to occupy a leading position in higher education in the UK and to enjoy a world-wide reputation for teaching and research. The College's objective is to build on this reputation and to have all its research and teaching activities judged excellent by peer review. King's, in line with its founding principles, will continue to foster the highest ethical standards in a compassionate community. This all-embracing pursuit of excellence will touch every part of the College and its constituencies: Staff: The College will continue to appoint outstanding academic and support staff. Training and staff development programmes will help staff to reach their full potential. A continuous programme of improvement of all College facilities will underpin research of the highest standard. Students: King's will continue to encourage applications from students of all backgrounds, selecting only on the grounds of academic merit and potential. Students will study in a research environment which values scholarly enquiry and independence of thought and will enjoy high levels of staff contact, free and open discussion, and flexible course structures. All students will be encouraged to follow an additional course, the Associateship of King's College, which further challenges them to think systematically about their values and beliefs. Location: The College's location in the heart of London brings special advantages and responsibilities. King's will utilise its location to promote the exchange of ideas and skills with government and the business community, the professions, the arts and the world of education. Society: The College, by capitalising on its position, will bring informed influence to bear on national and international decision makers. It will also meet its obligations to society by undertaking and disseminating the results of research, and by producing balanced and well educated graduates. Term dates 2010-11 Monday 27 September 2010 -Friday 17 December 2010 (12 weeks) Monday 10 January 2011 -Friday 1 April 2011 (12 weeks) Monday 26 April 2011 -Friday 3 June 2011 (6 weeks) Departmental Registration Thursday 23 September -Friday 24 September 2010 First Semester Monday 27 September -Friday 17 December 2010 Reading Week Monday 8 November -Friday 12 November 2010 January Exams Monday 10 January -Friday 14 January 2011 Second Semester Monday 17 January -Friday 1 April 2011 Revision/Teaching Weeks Tuesday 26 April -Friday 7 May 2011 Summer Exams Monday 9 May -Friday 3 June 2011 Resits/Replacements Monday 8 August -Friday 19 August 2011 Graduation Dates July 2010

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Students are expected to be available on all of the above dates (a specific graduation date will be given nearer the time). Coursework deadlines will not be extended and neither will other special arrangements be made simply because a student has made travel arrangements which are within these semesters. 2. ADMINISTRATIVE MATTERS The Mathematics Departmental Office The Departmental Office is open to students from 10.00am–12.30pm and 14.30pm– 16.30pm, Monday to Friday, except on Wednesdays when the office is closed for the afternoon. The office is located on the 5th Floor, Strand Building, Room S5.01.

The School of Natural and Mathematical Sciences The School of Natural and Mathematics Sciences comprises the Departments of Informatics, Mathematics, Physics, the Division of Engineering (Electronic and Mechanical) and the Centre for Bioinformatics. The Head of School is Mr Chris Mottershead. Each Department or Division also has its own Head. Examination business is co-ordinated by the Chair of Undergraduate Programme Boards (each Department has its own Programme Board). The business of the Undergraduate Programme Boards is co-ordinated by the School Undergraduate Examination Board, which in turn reports to the College Examination Board. The Tutor System Each student (whether single subject or joint honours) will be assigned a Personal Tutor in the Mathematics Department. Personal Tutors are a primary point of contact between the student and the College and, whenever possible, a student will have the same tutor throughout his or her entire career. They can be consulted about academic, financial or personal matters; where problems are serious, the tutor will help the student find more specialised help. The Department looks to Personal Tutors for information about students, for example, on attendance, examinations performance, other college activities, outside interests and so on. Personal Tutors may speak on behalf of their Tutees on occasions such as examiners meetings. At the end of their college careers students will want their tutors to write testimonials and references supporting applications for employment or further courses. The Department places great importance on the tutorial system; its function depends critically on students keeping in contact with their Personal Tutors. Students are entitled to make appointments with their Personal Tutors, who can be seen at short notice in an emergency. Students must make themselves known to their Personal Tutor on enrolment day, and are strongly urged to keep in regular contact. You should be aware that there are College regulations which state that if a member of College staff knows of any activity which contravenes College regulations (e.g. drug abuse), they should report it to the Academic Registrar. If you wish to discuss matters of a sensitive nature, you may find it more appropriate to visit a College Counsellor, who will maintain confidentiality as far as possible.

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The Senior Tutor The Senior Tutor also plays a pastoral role for all students and may be approached whenever students feel that it would be appropriate to do so. In exceptional circumstances students are permitted to change their tutor by making a request to the Senior Tutor or, if necessary, the Head of Department. The Link-up System Following recommendations from the Staff-Student Committee, a Link-up Scheme has been established between incoming first and second year mathematics students, and between second and third/fourth year students. The aims of the scheme are to make the transition to university as smooth and enjoyable as possible for incoming students, and to provide a network of contacts between first, second and third year students with the purpose of providing academic and social advice. Further information about this scheme will be circulated at the beginning of the academic year.

How we contact you The most important means of communication is the College electronic mail network which is frequently used for the dissemination of information to students and for communication between students and their tutors. Students are required to check their e-mail on a regular basis. The College email system can be accessed at all PAWS machines and via the web. All new students will be automatically registered to use the system. Another method of communication is via the Mathematics departmental notice boards, which are situated near the Departmental Office on the fifth floor of the Strand Building. If you have any correspondence for a member of staff, you should leave it with a member of staff in the Departmental Office. Each student is required to sign a form to indicate that they realise their responsibilities to regularly check email sent to their College email address (which has the standard form [email protected]) and to keep up with College/Departmental information via the relevant web pages. Each student is also required to supply term-time and home addresses. You can make amendments to personal information yourself via OneSpace. A student is responsible for the consequences of not receiving information conveyed by these means. Attendance and absence Students are of course normally expected to attend all lectures, tutorials and other classes for all their modules. Absence is permissible under certain circumstances (such as illness) but students are generally expected to attend as regularly as possible. [Regulation B4 4.1.2 is available via: www.kcl.ac.uk/about/governance/regulations/students.html.

Any student who is absent from College for 7 days or more because of illness, or for some other reason, should keep her or his Personal Tutor informed of the circumstances. Medical certificates should be handed in to the Departmental Office, Room S5.01. Information about medical and other difficulties is important when decisions are made regarding progress to later years and eventually final degree classification. The information is also significant in relation to coursework assignments and assessments which are

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carried out during the course of the year. Overseas students under the new visa requirements should be aware that the college must report any prolonged absences. If the illness or other problem is of a confidential nature, the Personal Tutor, Senior Tutor or some other staff member can keep detailed information privately, and will, on request, give a note to be filed in the office stating the existence of the document, the implications it has for the student's performance, and information as to which member of staff has charge of the document. The actual document will then be seen only by those, such as external examiners and the Chair of the Board of Examiners, who need the information to fully assess a student's performance. 3. ORGANISATIONS FOR STUDENTS MathSoc All Maths students are automatically members of MathSoc, which is a student run society whose main aims are to organise social and academic activities throughout the year. The main events are the summer boat party, Cumberland Lodge and for the first time, a Christmas Party. Other subsidised events such as ice-skating and trips to Pizza Hut take place throughout the year. Cumberland Lodge is a fantastic weekend away, which occurs midway through the second semester; talks on the more appealing side of maths are organised, and there is plenty of leisure time to enjoy Windsor Great Park. Another purpose of MathSoc is to welcome the first years, and a ‘parenting’ system is arranged for the beginning of the year. A link-up party is organised for the last day of registration. Here you will be able to chat informally with your fellow students, as well as enjoy the free food and drink. You will also be given the opportunity to meet your designated ‘parents’ – current students - who will be available to answer any questions and offer advice on life in the Department. Members of the MathSoc committee are usually available in Room S4.37, although they can be contacted via email: the President; Roshni Sakaria ([email protected]) the Treasurer; Hina Varsani ([email protected]) and the Social Secretary; Faris Ahmad ([email protected]).

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4. GENERAL DEPARTMENTAL INFORMATION Finding your way around the Department Departmental staff have rooms spread across several corridors and buildings of the Strand campus. Figure 4.1 shows the central rooms and south side of the 4th floor of the Strand Building. Offices 4th Floor, South Side

Gents' Toilets

Ladies' Toilets Stairs S4.37

To King's Main Building →

LIFTS

S4.36

S4.26 S4.27 S4.35 Alice Rogers

MSc Computer Room S4.25 S4.34 Peter West

MSc Coffee Room

Photocopy Room S4.24 S4.28 S4.32 TBA

Seminar Room

Seminar Room S4.23 S4.29 S4.31

S4.30 Head of Department's Office

Fire Escape

Figure 4.1

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Figure 4.2 shows the offices of academic staff along the north side of the 4th floor of the Strand Building.

Academic Offices - 4th floor, North Side

S4.03 – Gutowski, Koeppe, Papageorgakis

S4.04 – Riccioni, Sasaki, Shayeghi

S4.05 - Konstanze Rietsch

S4.06 - Ton Coolen

S4.07 - Isaac Pérez Castillo

S4.07a - Payman Kassaei

S4.08 - Dmitri Panov

S4.08a - Sakura Schafer-Nameki

S4.09 - Simon Scott

S4.10 - Andreas Recknagel

S4.11 - Eugene Shargorodsky

S4.12 - Benjamin Doyon

S4.13 - Reimer Kühn

S4.13a - Eytan Katzav

S4.14 - Gerard Watts

S4.15 - David Solomon

S4.16 - George Papadopoulos

S4.17 - Yuri Safarov

S4.18 - David Burns

S4.19 - Andrew Pressley

S4.20 - Brian Davies

S4.21 - Fred Diamond

S4.22 - Behrang Noohi

Figure 4.2

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Figure 4.3 shows the offices occupied by academics on the 5th floor Strand Building, north and south side.

5th Floor

S5.01 Departmental Office

Gents' Toilets

Ladies' Toilets Stairs

S5.23 – Dan Wade Lifts

S5.24 – William Shaw

S5.25 – Peter Sollich

S5.26 – Alessia Annibale S5.40 – John Taylor

S5.27 – Nikolay Gromov

S5.28 – Tiziana di Matteo

S5.29 – Dario Martelli

S5.30 – Paul Emms S5.37 – Cristin Buescu

S5.31 – Giuseppe Tinaglia S5.36 – Andrea Macrina

S5.32 –Alexander Pushnitski S5.35 – Damiano Brigo

K4U.19/21/22/24/25

K4U.25 - Ray Streater

K4U.24 - David Lavis

K4U.22-David Robinson

K4U.21 - Luke Hodgkin

/ Bill Harvey

K4U.21 - Bernard Luffman / Jane Bennett-

Rees / Hamish Rae/ John Silvester

Stairs

K4U.19 - Tony Barnard / Simon Fairthorne /

Peter Saunders

Figure 4.4 shows the mezzanine rooms which are occupied by other academic staff.

Figure 4.3

Figure 4.4 18

Local Safety Procedures All students should be aware of basic safety procedures – you will find a basic checklist at the back of this booklet. The Departmental Administrator acts as the Safety Officer. The Department has a Safety Notice Board for the display of relevant notices. A list is displayed of First Aiders who have been trained to give immediate medical help in the event of an accident. Whilst the Health Centre (please see details under Advisory & Welfare Services) can help in these circumstances, it is best to follow the advice of the First Aider and call an ambulance should he/she consider this appropriate. First Aid boxes are located in the Departmental Office as well as in the Undergraduate Common Room, S4.37. When it is necessary to evacuate a building in an emergency, bells will sound and you should leave the building immediately by the nearest marked emergency exit. On emerging from the building it is vital that you move right away from the building to provide access for emergency vehicles and to allow others to leave quickly too. Provide an example to others and follow the instructions of fire marshals. If you are ever concerned about any aspect of safety or have suggestions to make, please direct these to the Departmental Safety Officer on extension 2216. Further information can be found on the College website: www.kcl.ac.uk/about/structure/admin/safety . Staff/Student Liaison Committee The Staff-Student Committee is the principal formal mechanism for feedback from students to staff about all aspects of College life, particularly those directly related to the Department. It also provides a forum for discussion on matters of common concern. It has two calendared meetings every semester, but students can ask for a special meeting at any time. The student membership of the Committee consists of all officers of the undergraduate Mathematics Society, together with a further seven elected representatives, consisting of one single subject student and one joint honours student from each of the three years. The current staff members include the Senior Tutor and the Head of Department.

Prizes for Students 2009/10

The prizes listed below are offered to undergraduate students, and the recipients in 2010 are as indicated. The Award Ceremony this year will take place on 10 November 2010. King’s College London Prizes: Jelf Medal for the most distinguished student (academically, socially and athletically) –

no award Layton Science Research Award – 0613894 Mr SH Benson (MSci Mathematics and

Physics) Sambrooke Joint Honours –0903655 Mr J Baker (BSc Mathematics and Physics with

Astrophysics) The Florence Hughes Prize awarded to female student achieving highest standard in

second year – 0804236 Miss A Kumon (BSc Mathematics)

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Alan Flower Memorial Prize –0613894 Mr SH Benson (MSci Mathematics and Physics) Mathematics Departmental Prizes: Drew Prize and Medal – 0728164 Mr PJK Stapelfeldt (BSc Mathematics with

Management and Finance) Second Drew Prize – 0729496 Mrs AL Houghton (BSc Mathematics) and 0708972 Miss

LJ Elvidge (BSc Mathematics) The George Bell Prize for the most meritorious performance in mathematics by a third

year MSci student – 0719657 Mr NA Malik (MSci Mathematics) 2 IMA Prizes (free graduate membership for one year) – 0701945 Miss CY Ying (BSc

Mathematics) and 0707078 Mr SS Mondair (BSc Mathematics) The J G Semple Prize for the best project by a final-year student – 0844059 Mr S Heise

(Graduate Diploma) The John Tyrrell Prize for the most meritorious performance in mathematics by a first

year student – no award The John Tyrrell Prize for the most meritorious performance in mathematics by a

second year student – 0804236 Miss A Kumon (BSc Mathematics) Prize for Joint Honours Mathematics – 0961452 Mr R Solamides (BA Mathematics and

Philosophy) The Marianne Merts Prize for outstanding contribution to the life of the Department –

0801270 Mr MK Khan (BSc Mathematics with Management and Finance) Prize for Mathematics and Philosophy non-graduating student most worthy of award –

0803195 Mr WDH Hiscock Sambrooke Exhibition in Mathematics for the most meritorious performance in

mathematics by a 1st or 2nd year student – 0900827 Mr V Solanki (MSci Mathematics) Spackman Prize – Joint First Prize: 0958807 Miss A Aneja (MSci Mathematics) and

0728164 Mr P Stapelfeldt (Mathematics with Management and Finance) Mathematics with Management and Finance best graduating student – no award Mathematics with Management and Finance second best graduating student – no

award Prize for the best Mathematics with Management and Finance student (2nd year) –

0803026 Mr S Al Khalifa Prize for the best Mathematics with Management and Finance student (1st year) –

0909819 Mr MP Wolfers Graduate Diploma in Mathematics Prize for best performance by a Graduate Diploma

Student – 0974074 Mr B Gancarz

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5. STUDYING IN THE DEPARTMENT OF MATHEMATICS Code of Conduct

Code of Conduct & Behaviour in Lectures

The way you are taught at university may be very different to what you have experienced before. You may be taught in a very large or very small group. You may be expected to think quickly and follow complicated material at a pace you may find too fast - or too slow. Overall, you will be given greater academic and personal freedom than you have experienced before, and this can be bewildering at first. You will have to learn how to organise your own time so that you get the most from your education. However, there are still certain rules that have to be obeyed. You are required to attend lectures and you will expect these to be well-prepared, logical, audible and correctly paced. You can contribute to the success of lectures by following the guidelines shown below:- Arrive in good time - late arrivals disrupt the rest of the class.

Turn off your mobile phone before the lecture starts. Never make or answer calls during a lecture. Do not receive or send text messages. Do not use any other electronic devices during a lecture without permission of the lecturer.

Sign any attendance register.

Concentrate on the material that is being presented.

Do not talk when the lecturer is talking; only conversations and discussions expressly permitted by the lecturer are allowed.

If you have a question for the lecturer, please attract his/her attention by raising your hand.

Do not eat or drink.

Disruptive behaviour destroys learning and will not be tolerated by teachers. If they are disturbed by disruptive or interfering behaviour, teachers have a right to ask offending students to leave the lecture theatre or teaching room and to enquire of their name. Students who commit misconduct on College premises are liable to the College’s Disciplinary Procedures It is in the interest of the whole class and the lecturer that these guidelines are followed. Please encourage others to follow them. PLEASE THINK OF OTHERS AS WELL AS YOURSELF; HELP MAKE THE LECTURE A SUCCESS FOR EVERYBODY.

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The Semester System Mathematics modules are almost all given either wholly in the first semester or wholly in the second semester. Note, however, that second semester modules continue for the first week of term following the Easter break. All exams for Mathematics modules for single and joint honours Mathematics students are held in the Summer Exam Session in May, with the exception of 4CCM111a (CM111A) which is examined in January. Joint Honours students, in addition to the 4CCM111a (CM111A) examination, may find that they also have examinations in January for some of their non-mathematics first semester modules. The term after Easter (that is, the period from April to June) consists largely of examinations. However, as noted above, the first week is used to complete second semester modules, and the second week is normally devoted to revision, although occasionally new material may be presented during this week – full details will be found on the course information sheet issued during the first lecture of each unit.

Lectures and Tutorials Attendance at lectures and tutorials is compulsory. Listening to an exposition of a subject developed in lectures is an important part of the process of learning mathematics. Copying another student's notes is not a valid substitute. Tutorials are your opportunity to clear up difficulties and consolidate your understanding, as well as to review the assignment work. You cannot expect sympathy if you miss the tutorials and subsequently need individual help for your difficulties. It is recognised that occasional absences may be inevitable. However, in cases of prolonged systematic absences, the students concerned may be excluded from the examination on the grounds that they have not completed the course of study. If you are absent because of illness or some other good cause, you should comply with the procedures concerning such matters (see 'Matters regarding attendance and absence'). Extraneous noise and casual chatter can sometimes be a problem in lectures, particularly if the class is large. It makes difficulties for the vast majority of students and is distracting to the lecturer, resulting in a loss of quality in the lecture. (Conversely, interest and attentiveness of a class can inspire the lecturer to an enhanced performance.) Students are asked to ensure that lectures are not disrupted by extraneous noise. Mobile phones must be switched off during lectures. Walk-in Tutorials These tutorials are for First Year students. The intention is to give students who are at the beginning of their course the opportunity to have their difficulties sorted out in an informal way. They can ask for any topic to be gone over at their own pace, and guidance will be given on how to approach the problems on the weekly exercise sheets (although the actual work set will not be done for you!) You are encouraged to make use of these sessions to sort out anything you are having trouble with.

These tutorials are run by Mrs J Bennett-Rees and will take place on Wednesdays from 14.00–17.00 in room 520 in semester one and two. You should aim to come early in the session but only stay for as long as you wish.

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Pop-In Tutorials In addition to the Walk-in tutorials, the Department offers Pop-in tutorials for First Year students. Usually, there are two such tutorials per week, probably starting in the second week of term and are conducted by a Final Year Mathematics student at King’s. (Students will be notified of the days and times.) These tutorials are informal, and you are free to come and go as you please. You may ask questions about any aspects of your First Year modules which are troubling you, or which you are finding difficult, but please note that these Pop-in tutorials are NOT intended as a forum for solving the problems on next week’s exercise sheet! In the past many students have found these tutorials very helpful and you are encouraged to avail yourself of this opportunity. Students will be advised of times and rooms closer to the time.

Coursework Mathematics is a subject that can only be mastered by relating the theory to applications and examples. The Department of Mathematics attaches great importance to students in all years attending the tutorial classes and handing in weekly assignments as well as going to lectures. For all compulsory and core modules, attendance and assessment marks will be recorded for each tutorial, and for these courses students will be required to attend a minimum of 70% of the tutorials. For all first year students additional coursework requirements are imposed, which are intended to help in making the transition from school to university. Mathematics modules normally taken by first year students have either an element of continuous assessment counting towards the final result for the module, or a coursework requirement based on weekly assignments done in the students' own time. The information sheet for a module will indicate which of these methods is being used. Any coursework requirement for a particular module will be specified on the Course Information Sheet. In cases where the requirement is based on weekly assignments, students are responsible for keeping marked assignments in case of possible appeals concerning their standard, and are asked to make any enquiries about the marking at an early stage. Coursework requirements may be waived for medical or other similar good reason. You should keep your Personal Tutor informed about any problems. The above requirements also apply to joint honours students taking Mathematics modules. Regulations require that a student must complete a proper course of study before being admitted to the summer examinations. The Department of Mathematics rules that, in addition to attendance at lectures and tutorials, meeting a coursework requirement, as appropriate for a module, forms part of the proper course of study. Students who do not meet the coursework requirement will not normally be allowed to sit the Sessional Examination for the module concerned. All coursework tests, which count in the final assessment, are College examinations. The way that they will count in the final assessment will be announced at the beginning of the course and will have been agreed with the Chair of the Board of Examiners. There will be no replacement or resit course tests. Failure to attend a test, except under special circumstances, will normally be penalised. If there are extenuating circumstances,

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medical certificates or other written evidence must be received by the Departmental Office within 48 hours of the test. The condition for a bare pass is a pass on aggregate. Does Coursework Count? All students should read this section carefully ⎯ especially First Year students. It is important that all students, particularly First Year students, be aware of the fundamental importance of sitting and performing well in all the Class Tests which will contribute to the final mark for the module; these are discussed in more detail below.

Please note that Second Year students do not receive a coursework mark in 5CCM1xxxB modules; they are graded solely on the basis of the written examination. Class Test marks relate to First Year students taking Level 4 modules (4CCM1xxxA) only. Lecturers teaching First or Second Year modules set homework exercises week by week. At Third and Fourth Year level exercises will also be set as a module progresses, but not necessarily on a weekly basis. Making a serious attempt to do the set questions is a crucial ingredient in developing your understanding of Mathematics; Mathematics is a subject where one learns by ‘doing’. Although studying lecture notes is an important and valuable activity you will never really discover whether or not you understand a topic until you try to solve the weekly exercise problems. A sensible approach involves studying the lecture, thinking about the definitions and theorems, trying to understand the proofs, and so on. Then attempt some questions from the weekly exercise; at that point you may have to return to your lecture notes, you may have to read the relevant part of a textbook, and perhaps think more deeply about a definition or a theorem which you had previously thought you understood. For First and Second Year students your attempts at the exercises will be graded week by week, and the results recorded; in a few modules these marks may contribute to your final mark. For precise information you should study the Course Information sheet, distributed by lecturers at the start of a module; the Course Information sheet is also available on the module web-site. The primary factor in determining your mark for most modules will be the mark you obtain in the written examination in May/June (but that in turn may be heavily influenced by your attitude to exercise work throughout the year!).

However, many modules do have a ‘coursework element’ and a ‘coursework mark’ which does contribute to your final mark. This is assigned on the basis of your performance in class tests, or by some other method of assessment. In every case the mode of assessment is described in the Course Information sheet; in particular, this will make clear whether or not there are class tests, and the extent to which these contribute towards the final mark for the module.

You should note that coursework marks only have relevance the ‘first time round’; if you fail to pass a module at the first attempt and have to resit an examination, your mark in the resit examination will be determined solely on the basis of the written paper and any coursework mark will not be taken into account. Class Tests in Year 1 In 2009/10 there will be a coursework mark for each First Year module, contributing 20% towards the final mark for the course, the remaining 80% being secured on the basis of the written examination which will be held in May/June. In the First Semester there will be four

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Class Tests in each course (except for 4CCM111a/CM11A), conducted under examination conditions; three of these tests will be held during the period in which the course is actually taught, and a fourth test will be held in January 2009 during Examination Week. In the Second Semester there will be three Class Tests, all being held during the period in which the course is taught. It is crucial that you sit all these tests; there will be no ‘re-sit’ tests. Information about the Class Tests, including the dates the tests will take place, can be found on the web: http://www.kcl.ac.uk/schools/nms/maths/curr/ug/tests.html The importance of working hard throughout the module, and sitting and performing well in all the Class Tests, cannot be overestimated. The tests will be designed to gauge whether or not you have mastered the basic concepts; although the questions will not be trivial, neither will they be ‘difficult’. A student who works diligently should be able to approach the January and May/June examinations secure in the knowledge that she/he is well on the way to reaching the 40% pass mark. Please note that if you fail an examination in January and/or May/June your mark in any re-sit examination (taken in August or subsequent years) will be determined solely on the basis of the written paper; coursework marks will not count. Marks obtained in August re-sit examinations are capped at 40%. Monitoring of Progress Your performance in class tests and homework will be monitored on a continuous basis. Students whose progress is unsatisfactory will be required to attend a meeting with the Senior Tutor. Student Presentations All Single Honours Mathematics students in Years 1, 2 and 3 will be required to give a short presentation, once a year, on a mathematical topic. First Year presentations, relating to a topic prescribed by the lecturer responsible, will normally take place in a tutorial class, unless the lecturer decides that it is appropriate for the presentation to take place at the start or end of his/her lecture, for example. In most cases students will be asked to present their solution to a simple problem, to be assigned in advance by the relevant lecturer. The presentation should last five minutes or a little longer.

Second and Third Year students will be invited to ‘sign up’ to give a presentation in a module of their choice ⎯ although there will be a limit as to how many presentations may take place in any one module; the sooner you sign up, the more likely you will be to be able to give your presentation on your favourite subject! Evaluation of Presentations Your presentation will be graded as Excellent, Good, Satisfactory or Fail. These grades will be recorded in your student file, and although they have no bearing on the class of degree that you will receive, they could be important if you ask a member of the Department to write a job reference on your behalf. The ability to express oneself clearly is highly valued in today’s world, and it is important to obtain some practice in the art of verbal communication before you graduate from King’s. Presentations are a small step in helping you to develop your skills in this area.

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Workload During term time you should expect to spend at least 40 hours per week on your studies. Lectures and tutorials will normally take up 16 hours of your time, but you cannot expect to follow your course successfully without several hours a week of additional work on each module. It is particularly important that after each lecturing session you go through your notes making sure that you understand the material, and that your notes are sufficiently clear for you to be able to follow them when the lecture is no longer fresh in your memory. If you are not on top of the material from the preceding lectures you will find subsequent lectures hard to follow. It is also essential that you complete the assignments which are set as the module progresses. If you do this you will find you have digested a useful proportion of the material. Most of the time, when one is learning mathematics, one is struggling to cope with material that seems difficult. If you really are struggling, you will be learning more than you realise, but if you are stuck, do not give up – there are sources of help: Other students on the course. While you must not copy assessed coursework whose

mark contributes towards the mark for the module, most assignments are set as practice and collaboration is encouraged. Students helping each other is a two-way benefit; the student who needs help is assisted while the giver of help usually discovers that she/he understands the work better from having had to put it in her/his/ own words.

Tutorials, including the walk-in tutorials for first year students, provide an opportunity to ask questions about any aspect of the course.

The course lecturers and helpers will have office hours when they are available for consultation.

Submission of Projects and Essays All project or essay work must be handed in to the Office by 4pm on the date which will be specified at the beginning of the module. Normally two copies will be required and receipts will be provided by the Office. Late work will not be accepted except under special circumstances and it will normally receive a mark of zero. If the deadline is not met written evidence of extenuating circumstances, such as medical certificates or other written evidence, must be received by the Departmental Office within 48 hours of the deadline.

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6. EXAMINATION REGULATIONS These instructions supplement the College Regulations. They do not replace the College’s Academic Regulations, Regulations Concerning Students & General Regulations and the School’s Programme Specifications and Marking Scheme, which cover all aspects of your degree programme in detail. You can find the College Regulations in the College Libraries and on the web at:

www.kcl.ac.uk/about/governance/regulations Our aim here is simply to help you to understand the way in which our exams are organised, the options available to you, and the procedures that you must follow for various eventualities. Please read this material carefully (and the College Academic Regulations, Regulations Concerning Students & General Regulations if you have concern on matters not covered here) and remember: Ignorance is no excuse for failure to comply. The School for Natural and Mathematical Sciences has produced a handbook for students available at

www.kcl.ac.uk/schools/nms/current/handbook.html It should be consulted for further information about several of the issues addressed below, in particular those not specific to the Mathematics Department.

Registration for and Admission to Examinations Registration for examinations has to be made online via OneSpace within the first two weeks of the session for all subjects (whether taught in the first or second terms or both) so that your entries can be registered in the College records. You will be notified of the detailed arrangements near to the time. Compulsory subjects will be entered automatically on your record but you must enter all optional subjects and resit examinations, even if you are only to resubmit coursework. You will then receive a list of your examination entries via OneSpace. It is YOUR responsibility to check your entry, to inform the Assessment and Records Centre (ARC) if there are any errors or omissions, and to meet all the relevant deadlines. The importance of doing this carefully cannot be overstated. In this context it is of the utmost importance that you regularly study the ‘Urgent Notices Board’ opposite the Departmental office and read your e-mail on a daily basis. It may be possible to amend your registration list at a later date if you wish to change your choice of subjects, but (except in the case of a withdrawal under exceptional circumstances, see below) this will not be possible after a prescribed date to be announced early in the session. Any amendments should be approved by your Senior Tutor and must be submitted in writing by completing a form available from ARC. Students should be aware, that if, come the examination, it is found that they are not registered for an examination there is no guarantee that they will be allowed to sit it and/or gain credit for it. It should also be noted that admissions to an examination may be refused if, because

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your attendance is deemed inadequate, the authorities are unable to complete the certificate of attendance for the relevant subject. Special Examinations Arrangements If you have a learning or physical disability/condition (including pregnancy), and have not already received concessions for the whole of your programme, you can apply to the College's Special Examination Arrangements Committee (SEAC) for special examination provisions in respect of written examinations. Please note that if you are dyslexic (or believe you may be), you must provide a full dyslexia assessment. This assessment must be conducted by a chartered educational psychologist and show all your test results. It should also be dated within three years of the date of your application to the SEAC. If you have a physical disability/condition, the medical evidence must be detailed and recent - preferably written by a consultant. Alternatively, an additional section of the application form can be completed. Information regarding the closing dates for the submission of completed application forms and supporting documentation, are available on the web. No arrangements will be considered where the appropriate deadline has not been met, except in the case of accidental injury or acute illness. An application form is available from the School Office or on the web at: www.kcl.ac.uk/about/structure/admin/acservices/examinations/sea/ and must be returned to the Examinations Office. If special provision is granted, then it will apply to one examination period only, and you will need to reapply for subsequent examination periods if the disability persists. Please note that special examination arrangements are do not automatically carry over to class tests, which you may need to sit during the semester.

Attendance at Examinations You must make every effort to attend your examinations. It is YOUR responsibility to ascertain the time and place of all the examinations which you are sitting. Be sure to check the FINAL timetable which is available via: www.kcl.ac.uk/about/structure/admin/acservices/examinations/students Absence from an examination, will count as a failed attempt, you will receive a mark of zero. (See the section on Mitigating Circumstances below on what to do, if you fall seriously ill.) You must take a printout of your Examination Passport to all your examinations. It lists all examinations for which you are registered and will be obtainable from OneSpace. Note that you will normally not be permitted entry to any examinations for which you are not registered. When are degree examinations held? All Mathematics examinations are examined at the end of the teaching year (with the exception of 4CCM111a (CM111A) and 7CCMMS30 (CMMS30) and one or two ancillary modules with degree or midsessional exams in January). The examination period itself lasts for about a month and in the current session runs from Mon 9 May to Fri 3 June 2011.

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Joint Honours students need to bear in mind that some departments (e.g. Computer Science and Management Studies) examine their First Semester modules in January. Examination Papers At the end of each session, students are examined in the modules which they have taken during that session. The common format is a two or three hour written exam. The precise format of an examination paper is described in a so-called rubric which appears on the front cover of the examination paper in question. The rubrics in most common use are described below. Rubrics The Department's `standard rubric' for first-year examination papers in the Mathematics Department runs as follows:

This paper consists of two sections, Section A and Section B. Section A contributes half the total marks for the paper. All questions in Section B carry equal marks. Answer all questions.

For second- and third-year exams the standard version is: This paper consists of two sections, Section A and Section B. Section A contributes half the total marks for the paper. Answer all questions in Section A. All questions in Section B carry equal marks, but if more than two are attempted, then only the best two will count.

In such an exam students are advised to concentrate first on completing Section A. This consists mainly of easier questions which should generally resemble exercises and/or examples from the lecture. In order to obtain a high grade (as opposed to a pass) students will also need to provide answers that are as full as possible to two questions from Section B. These may require a little more thought and the rubric clearly encourages you to focus your energy on at most two such questions. Some exams may employ other, `non-standard' rubrics (because of the nature of the material of the module, for example, or because the paper has several sections). In third- and fourth-year exams this is particularly common. For instance, there may be a `non-standard' rubric of the following form (with some value of N, which is often less than the total number of questions on the paper):

Full marks will be awarded for complete answers to N questions. Only the best N questions will count towards grades A or B, but credit will be given for all work done for lower grades.

In all modules the lecturer will inform you of which rubric is to be used. If coursework marks are included in the assessment of a module, then normally the provisions of the rubric are applied before these are added in. Calculators For examinations in which the use of calculators is permitted, students are expected to bring their own calculators. However, these calculators must be one of the two following approved models – CASIO-FX83xx, or CASIO-FX85xx. In these specifications,

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xx stands for an arbitrary two-letter model specification (e.g. xx=ES). All such specifications are allowed. Bringing a non-approved calculator to an exam will be regarded as an examination offence! Marking Procedures All examination scripts are marked by a first examiner, who is normally the lecturer for the module, and then by a second examiner. This is formally Model 2 as described in the College Marking Framework The script may also be considered by an external examiner. This will always happen, if the script turns out to be a borderline case. The criteria for judging the quality of a script or project report are summarised in a set of mark schemes which will be available, when finalised, on the NMS website at: http://www.kcl.ac.uk/schools/nms/internal/pol/mark.html Marking of BSc and MSci/MSc projects on the other hand basically follows Model 1 of the College Marking Framework, in that two copies of the project report are marked separately and independently by two examiners. Mitigating Circumstances Withdrawal from Examinations or Extension of Deadlines The following notes are for guidance only. They address the question of what to do when circumstances beyond your control would seriously affect your performance in one or more examinations or prevent you from submitting an assessment by the deadline. Such `mitigating circumstances' might include significant illnesses or accidents, or the death of a close relative.

For details concerning rules governing mitigating circumstances, students are urged to consult the student guidance supplied with the mitigating circumstances form (MCF). The MCF is available by following the appropriate link on www.kcl.ac.uk/about/governance/regulations/acregs.html An overarching principle of the College’s assessment policy is that if you present yourself for an examination or submit an assessment, then by doing so you are declaring yourself fit to take that examination or to undertake that assessment, and therefore whatever mark you are awarded will stand. Only in very exceptional circumstances will a mark awarded be annulled if you have sat the examination or submitted the assessment.

For mitigating circumstances to be taken into account, you must complete a Mitigating Circumstances Form (MCF) or an Extension Request Form (ERF). You may use these forms to request (possibly retroactive) withdrawal from the examination(s) in question or an extension to the deadline for the submission of an assessment. Alternatively, if you do not wish to withdraw from the exams, you may ask for consideration (of the mitigating circumstances). Please note however, that as of September 2005 it is no longer possible for individual examination marks to be altered as a result of any such consideration, even if granted by the board. It follows that consideration is only relevant (if granted at all) to the board's decision in assigning the overall degree class, and this only in cases in which the class as predicted by the C-Score or I-indicator (`Award of Honours' below) is very close indeed to the borderline between classes. Consideration is therefore mostly of concern to finalists (although in some circumstances it may, if granted, be carried over to the final year).

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MCF and ERF forms are available from ARC or the Examinations Office, and may also be downloaded from the College Policy Zone: http://www.kcl.ac.uk/college/policyzone/ (search term ‘MCF’) They must be completed in full (incomplete forms will not be accepted) and submitted directly to your Department along with all supporting documentary evidence. Until supporting documentary evidence is provided, your form will not be passed to the relevant board chair for consideration. The case you need to make for withdrawal/extension must satisfy very strict criteria. These criteria then depend crucially on when the MCF and complete documentation are submitted: • If submitted at least 7 days before the start of the first examination from which you wish

to withdraw/the deadline for which you require extension, you must have serious reasons beyond your control (not simply lack of preparation, or a minor ailment or condition, or illness several months before the exam) which would either prevent you from sitting the exam or which would make you unfit to sit it (or prevent you from submitting the assessment in time). You must include full documentary evidence (e.g. doctor's certificate) to prove that your mitigating circumstances are true. In this case, it should be possible for you to receive a decision before the exam.

• If less than 7 days before the first exam/the deadline (or after the exam/deadline) your MCF1 will in addition need to show that you were unable, or for good reasons unwilling, to request a withdrawal/extension before the 7-day deadline prior to the examination. ‘Good reasons’ would include the circumstances arising less than 7 days before the examination, or if you were ill and in hospital up until 7 days before the examination or deadline and therefore unable to submit your MCF. The circumstances must also be severe enough to prevent you from attending and completing the exam (even under special arrangements, see above). Your MCF must be submitted within 7 days of the missed examination. In this case, because of the lack of time, a decision will only be reached after the exam(s) at the next meeting of the relevant Board of Examiners. The Board also reserves the right to offer you an alternative form of assessment. Only in exceptional circumstances may you request to be retroactively withdrawn from an exam from which you have actually sat. In this case, your MCF and accompanying evidence must be submitted in advance of the meeting of the Board of Examiners at which the results of your examination or assessment will be discussed. It must satisfy the next meeting of the Board of Examiners not only of serious mitigating circumstances which made you unfit to sit the exam but also why you were, for good reason, unable at the time of the exam to recognise that you were unfit to sit it (e.g. due to the nature of an illness).

If your withdrawal request is accepted, you will be withdrawn from the exam (if retroactively, your mark will be ignored) and it will not count as an attempt. Except under special conditions in which it is not appropriate (for example, if you are interrupting your studies) you will be offered a replacement examination which you must normally take at the first available opportunity. This might mean an August replacement (if a finalist, this would normally mean that you would not graduate until the following January). However, it

1

Late extension requests must be submitted on a MCF not on an ERF.

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might also mean that you are required to take the replacement the following year instead. If an extension request is accepted, a new deadline for the submission of the assessment in question will be set, or you will be permitted to negotiate a new deadline with the assessment organiser. If your withdrawal/extension request is rejected, you will not be allowed to withdraw/submit the assessment after the deadline. In particular, if you do not attend (or have not attended) the examination in question or submit the assessment after the deadline, a mark of zero will be recorded. Finally, you should note that relatively few requests for withdrawal and replacement are granted. Only well-documented, serious circumstances are considered and they must be unlikely to persist until the date of the replacement. You should read carefully the criteria supplied with the MCF. You should also ensure that you inform the Senior Tutor, your Personal Tutor or Programme Board Chair of your situation as soon as possible. Appeal against a decision of a Board of Examiners If you wish to appeal against a decision of the Mathematics or School Board of Examiners you are advised first of all to contact the Chair of the UG Mathematics Board to discuss the situation. You should note in particular:

• That you may not challenge a decision of the board on academic grounds (e.g. because your assessment of your performance is different from theirs). In particular, you may not simply ask for a `re-mark': Contrary to some students' belief, College exam papers are never re-marked simply at a student's request.

• That an appeal must meet very strict criteria before it is even considered. If, for instance, it is based on mitigating circumstances, then you will need to show that there is new information that, for good reason, could not be brought to the attention of the board (e.g. via an MCF) before the Board made its original decision.

• That any appeal and all relevant documentation must normally be submitted within 14 days of the publication of progression or degree results on the departmental notice board or of the notification of individual exam results on OneSpace, whichever is relevant

You should realise that few appeals are granted because of the strict criteria. However, if after discussion and serious consideration you decide to submit an appeal, you will find full details of the procedure at: www.kcl.ac.uk/about/governance/regulations/acregs.html

Degree Titles The title of your degree will normally be that of your field of study. Single subject students may take some modules in (say) theoretical physics or computer science but provided that at least 3/4 of the modules passed are in mathematics then the degree title will be "Mathematics". For the precise rules concerning degree titles in single honours and in joint honours (“and” or “with” degrees) please see College’s Academic Regulations, Regulations Concerning Students & General Regulations, under “Field of Study”

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Course Units or Credits – How many do I need to pass for a degree? Pre-2007 Course Unit System: King’s College requires that for the award of a three-year degree based on course units, a student should complete, and satisfy the examiners in courses to the value of 9 units. For the four-year MSci degree, a minimum of 14 course units is normally required. For further details see previous versions of this handbook, available from the Departmental web site Post-2007 Credit Framework System: For students starting their programme in 2007 or later the minimum requirement is: • for a three-year BSc Degree: 360 credits, of which (i) at least 90 at level 6 or above, (ii)

at most 150 at level 4, and (iii) at most 45 credits are condoned fails. • for a four-year MSci Degree: 480 credits, of which (i) at least 120 at level 7, (ii) at most

150 at level 4, and (iii) at most 45 credits are condoned fails. • for the Graduate Diploma: 120 credits, of which (i) at least 90 at level 6 or above, at

most 30 at level 4, and (iii) at most 30 credits are condoned fails. Condoned credits: For the BSc at most 45 at levels 4, 5, or 6. For the MSc at most 45 at levels 4, 5, or 6, or 30 at levels 4, 5, or 6 plus 15 at level 7. In general, condoned fail marks are between 33-39%, or 40-49% for level 7; for Mathematics modules, fails can be condoned irrespectively of the mark obtained.) Note that condoned fails cannot contribute to the minimum number of credits required at the highest level, nor to the minimum number of credits required for progression. Award of Honours Assuming that these minimum requirements are met, you will be considered for award of honours in one of the categories: First Class (1), Second Class Upper Division (2A), Second Class Lower Division (2B), Third Class (3). The award of honours is a College matter with procedures laid down in the College Regulations and the final decision on an award rests with the College. Recommendations to the School Boards for award of honours are made by the Board of Examiners in Mathematics for single subject students and the appropriate BSc or BA Joint Honours Board for joint honours students. As noted above (see ‘Examination papers’) visiting examiners from other London Colleges and other Universities are appointed to membership of the Boards to monitor the standard. The visiting examiners can see all the examination scripts, comment on the level of difficulty of the papers and act as arbitrators in borderline cases. The Boards make recommendations for award of honours on the basis of a full record of all course-unit examinations taken by the student. A preliminary indicator is calculated from the marks, but the Board decides each case on the basis of the student’s total performance and may take special circumstances into account. All marks for course-unit examinations (including coursework marks, if appropriate) are used in the calculation of the guiding indicator.

Pre-2007 Course Unit System: For three year BSc degrees the first, second and third year marks are weighted in the ratio 1:3:5. For four year MSci degrees, the marks for each year are weighted in the ratio 1:3:5:5. Values of the indicator I in the ranges 100 ≥ I ≥ 70, 70 > I ≥ 60, 60 > I ≥ 50, and 50 > I ≥ 40 correspond to the classes 1, 2A, 2B and 3 respectively. However, in addition, a candidate for a first or upper second class degree

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must pass relevant modules to the value of 1.5 units in the final year at or above the level of honours being awarded. In this context language modules are not ‘relevant’. A brief description as to how the indicator is calculated including a link to an online calculator which allows you to perform these calculations automatically using a complete set of real or hypothetical marks can be found at: www.mth.kcl.ac.uk/~database/Database/Award.html. The indicator formula will apply to almost all students of Mathematics, single and joint honours, in the School of Physical Science and Engineering. Other formulae apply, for instance to students who entered the College in their second or third year. Students reading for the BA in Mathematics and Philosophy or the BA in Mathematics and French are assessed for Honours in the School of Humanities Full details of the scheme for the award of honours are to be found in the College Academic Regulations. Post-2007 Credit Framework System: For students starting their program in 2007 or later a so called C-score is calculated as a weighted average as follows

C = ∑ [mark x relevant credit volume x weight]/∑ [relevant credit volume x weight]

where for BSc degrees The marks of the best 90 credits at level 6 (and/or level 7 where taken) have weight 5 The mark for any remaining level 6 credits and any level 5 credits have weight 3 The mark for all level 4 credits have weight 1.

for MSci degrees The marks of the best 120 credits at level 7 have weight of 71 The marks for any remaining level 7 credits and all level 6 credits have weight 5 The marks of all level 5 credits have weight 3 The marks for all level 4 credits have weight 1.

and for the Graduate Diploma the weights are independent of level (meaning that a plain average of your results is taken).

Values of the indicator C in the ranges 100 ≥ C ≥ 70, 70 > C ≥ 60, 60 > C ≥ 50, and 50 > C ≥ 40 correspond to the classes 1, 2A, 2B and 3 respectively. It is important to understand that in either case the indicator is merely a guide to the classification and the decisions are not made mechanically. The Boards have discretion which is exercised with great care to recommend just awards. However, for a student below but close to a degree boundary to be raised to the next higher degree level, a minimum requirement is that at least 45 credits in the final year have been obtained at or above the higher level. Examination Results Final degree classifications and progression lists will be displayed on OneSpace as soon as possible after the meetings of the Programme and School Boards of Examiners. In the 2010/11 session this should be around July 7, 2011 or soon thereafter. Staff are precluded by College rules from disclosing marks or literal grades. Complete details of your results will normally be mailed to you in late July by the School Office, so please do

1 For students starting their programme 2009/10 or later; for those starting their programme prior to 2009/10 the weight of the best 120 credits at level 7 is 5 instead of 7.

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NOT contact the College asking to be told your results over the telephone; Data Protection restrictions do not permit staff to tell you your results in this way. College Debtors and Release of Examination Results The College is dependent on all students meeting their obligations in respect of fees at the proper time, i.e. on receipt of an invoice from the Accounts Department. Under no circumstances will students have their results released (nor will they be able to obtain references from members of staff) if they have unpaid debts in respect of tuition or hall fees, or if they have any library books still on loan. Be warned: every year some finalists have the upsetting experience of discovering that their names have been omitted from the Honours List because they have defaulted in this area. A student who is in debt to the College should note that even after a debt has been discharged, several weeks may elapse before the necessary administrative procedures can be completed and the student’s results finally disclosed. August Resits Pre-2007 Course Unit System: Please refer to previous versions of this handbook, available from the Departmental website at:

www.kcl.ac.uk/schools/nms/maths/curr/ug/ Post-2007 Credit Framework System: For students starting their programme in 2007 or later, all examinations failed in January or May/June must be resat at the earliest available opportunity, which is the August examination period of the same year. Resit examinations under the New Credit Framework System are always capped at the pass mark (40% at levels 4, 5, and 6, and 50% at level 7), irrespectively of whether they are taken as 2nd attempt in August or (as possibly 3rd attempt) in the following year; they are normally based entirely on the exam excluding any existing coursework.

Progression & Resits Progression Criteria (BSc and MSci)

Year 1 - Year 2 - Must have passed all 4. c.u. (SH), or at least 3 c.u., all maths modules and any requirements of sister department (JH), if starting course after Sept 2004 & prior to Sept 2007. - Must gain an average mark of at least 40% in level 4 mathematics modules, with no mark lower than 33% and 90 credits (excluding condoned fails) passed overall (SH), and any requirements of sister department (JH and Math with ... programmes), if starting course after Sept 2007. Year 2 - Year 3

- Must have passed a minimum of 3 2nd year c.u. (SH), a total of 6 c.u (JH), if starting course after Sept 2004 & prior to Sept 2007. - Must have obtained 210 credits (excluding condoned fails), if starting course after Sept 2007. - Must have passed a minimum of 7 c.u. (MSci), and overall performance in 2nd year with average mark > 59%

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- Must have obtained 210 credits (excluding condoned fails) and “good second class performance in Year 2” (MSci) [guideline: an average of at least 65 % on the best 105 credits at level 5].

Otherwise demote to BSc, and progress if possible. Year 3 - Year 4 (MSci.)

- Must have passed a minimum of 10 c.u. (MSci) and overall performance in first 3 years giving I > 59%, and not on significant downward trend. - Must have obtained 330 credits (excluding condoned fails) and “an overall performance approaching IIa level” [guideline: 3-year C > 59 and trend not significantly downwards]. For JH, other departments opinion should also be sought. Otherwise demote to BSc. and consider for honours.

Progression (Graduate Diploma, PT) Year 1 - Year 2

- Part time students should normally obtain 60 credits (excluding condoned fails), i.e. passes in all 4 modules for which they are registered in their first year.

- Part time students may, at the discretion of the Board of Examiners, be allowed to progress to second year also if they fall short of the normal requirement. This will normally require students to obtain at least 45 credits (excluding condoned fails), i.e. passes in 3 modules, and the Board will base its decision on whether the candidate has a reasonable chance of successfully completing the programme. If in September, students have failed to meet the progression criteria, they will be required to retake, in the following year, all papers which they have failed.

Under the pre-2007 Course Unit System, examinations sat the following year are uncapped (unlike August resits), whereas under the new post-2007 Credit Framework System all resits, whether August resits or exams sat the following year, will be capped. In Mathematics all resit marks are based on the written paper alone, discounting any existing coursework mark.

However, even if students do meet the progression criteria, the College Regulations allow them to resit failed examinations. First year modules and compulsory modules in the second year are important constituents of the degree and students are normally expected to resit any such modules which they fail; students may also resit other failed modules and this is usually advisable. The College Regulations require that all resits must be taken at the first available opportunity, otherwise the right to a resit may be forfeited. Consequently re-entry for a failed examination must be made in the following year. Moreover, students may be allowed to re-sit a particular examination at most twice (making 3 attempts in all, including any August re-sits) but this is subject to the approval of the Chair of the School Board of Examiners, acting on the recommendations of the Board of Examiners in Mathematics, and it should not be assumed that a total of three attempts is ‘guaranteed’. If students have an un-condonable fail in a module after their third attempt, their degree programme will have to be terminated (despite the fact that they may still formally satisfy normal progression criteria). Students who contemplate withdrawing from a degree programme before its completion, because they feel they might not be up for it, should note that the timing of their withdrawal

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could affect their eligibility for funding of another degree programme. Further information is available from King's compass (Tel: 020 7848 7070, www.kcl.ac.uk/thecompass.

What should I do if I cannot progress? If, following the May/June or August examinations, you find that you have not qualified for admission to the next year of the course, you are strongly advised to contact your Personal Tutor or the Senior Tutor as soon as possible in order to discuss your position and talk over future plans. Far too few students come to discuss their failure with members of staff, all of whom are ready and willing to help where they can, and some students probably give up quite unnecessarily for want of freely available advice at the right time.

Please note the following: If you are resitting exams from outside College, it is your responsibility to register for resit examinations with ARC (see “Registration for Examinations” above). It is also your responsibility, in the case of a re-sit, to contact the current lecturer to check for any change either in content or the style of the examination. If you have passed an examination, you are NOT allowed to retake it to improve your mark. If you fail both an exam and all the resits for a particular module, the highest mark will be the one entered into the indicator calculation (see above). Overseas Examinations Resits and replacement examinations may be sat at a British Council (or similar approved institution) office overseas. If you wish to sit these examinations overseas then you should complete an ‘Application for Special Examination Arrangements for Written Examinations’ available from the Examinations Office, email: [email protected] or on the web at www.kcl.ac.uk/about/structure/admin/acservices/examinations/sea/ Deadlines for applications are published on this site, and must be adhered to.

Special rules pertaining to MSci students Students registered for the MSci in Mathematics will be assessed at the end of their Second Year of study. Those who have passed modules to the value of 210 credits (7 course units in pre-2007 currency) and whose overall performance in the second year is of good second-class standard (normally interpreted as meaning an average mark of at least 60%) may continue in the MSci programme if they wish to do so. Students who do not continue in the MSci programme transfer to the BSc programme, complete their studies, and are assessed for Honours after one more year. In order to progress from the third to the final year of the MSci programme, a student must have passed at least 330 credits (10 course-units), and an overall performance approaching the Upper Second Class level is normally required. This is understood to imply that the student has an indicator I (based on the marks for the first three years) in excess of 59, and that the ‘trend’ of the student’s marks in the third year is not significantly downward. Similar considerations apply to Joint Honours MSci Students whose progression will be determined in consultation with the other department. Students who do not meet these requirements will be automatically transferred to the BSc programme and considered for Honours and graduation, by the Board of Examiners, at the end of their third year.

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BSc/MSci transfers Transferring `up': Transfer from the BSc to the MSci will, with the approval of the Programme Director for the Fourth Year MSci Programme and the School of Natural and Mathematical Sciences, be possible up to 31 March of the third year of full time study (or its part time equivalent), subject to respective curricula, provided they reach the required standard at the end of their second and/or third year (see MSci progression above). You should bear in mind that you must keep your Local Education Authority / Student Loan Company informed of any changes in your degree programme, or your funding may be terminated. Transferring `down': Transfer from the MSci to the BSc may, with the approval of the Senior Tutor and the School of Natural and Mathematical Sciences, be possible at any time up to the end of the third year of full time study, or its part time equivalent, again subject to respective curricula. All your own work? The College regards the following types of behaviour as serious disciplinary offences for which severe penalties can be applied. It is important that, as a student, you understand that cheating, collusion, fabrication and plagiarism, as defined below, are unacceptable; furthermore, they will not help your learning in the long term. Cheating Includes:- • communicating with any other student in an examination • copying from any other student in an examination • bringing any unauthorised material into the examination room with the intention of using

it during the examination • copying coursework Collusion Includes:- • collaborating with other students in preparing a piece of work and the submitting it in an

identical or similar form and claiming it to be your own • obtaining unauthorised co-operation of any other person when preparing work which

you present as being your own • allowing someone to copy your work which they then present as being their own Fabrication Refers to research or experimental work, when unjustifiable claims are made to have obtained certain results. Plagiarism Includes:-

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• creating the impression that someone else’s work is your own • quoting someone word for word or summarising what they say without acknowledging

them in a reference. You are reminded that all work submitted as part of the requirements for any examination of the University of London (of which King’s College is a part) must be expressed in your own words and incorporate your own ideas and judgements. Plagiarism must be avoided in examination scripts but particular care should also be taken in coursework, essays and reports. Direct quotations from published or unpublished works of others (including lecture hand-outs) must always be clearly identified as such by being placed inside quotation marks and a full reference to their source must be provided in the proper form. A series of short quotations from several different sources, if not clearly identified as such, constitutes plagiarism just as much as does a single unacknowledged long quotation from a general source. Paraphrasing – expressing another person’s ideas or judgements in other words – can be plagiarism if the origin of the text is not acknowledged or the work paraphrased is not included in the bibliography. Also counted as plagiarism is the repetition of your own work, if the fact that the work has been or is to be presented elsewhere (especially if it has already been presented for assessment) is not clearly stated.

Plagiarism is a serious examination offence. An allegation of plagiarism or any other form of cheating can result in action being taken under the College’s Misconduct regulations available from www.kcl.ac.uk/about/governance/regulations/students.html. A substantiated charge of plagiarism will result in a penalty being ordered ranging from a mark of zero for the assessed work to expulsion from the College. You will be asked to sign the College Plagiarism Statement saying that you understand what plagiarism is.

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7. PROGRAMMES OF STUDY Students in the Department of Mathematics are classified as either single subject or joint honours students. The following fields of study are available. Single subject honours Mathematics Mathematics with Management and Finance

Graduate Diploma

Joint honours In the School of Natural and Mathematical Sciences: Mathematics and Computer Science Mathematics and Physics Mathematics and Physics with Astrophysics

In the School of Humanities: Mathematics and Philosophy

Changing from one field of study to another may be possible but only with the approval of all departments involved. Set out below are the normal programmes for each year of each field of study. The aim of the Department is to provide as much flexibility as possible in the choice of modules, but it has been found in practice that this can only be achieved in the later years by restricting the first year choice. There is a Programme Director for each year of each field of study. Students should discuss their programme with the appropriate Programme Director, who must approve the programme and any subsequent changes. Some modules have prerequisites, which should be discussed with the Programme Director. As a general rule, students who fail a compulsory module are required to resit the examination. Information on programme regulations is found in programme specifications which are available here: http://www.kcl.ac.uk/about/structure/admin/acservices/asq/prog/spec/pse/math09a.html Please note: As of 2005/06 the word `core', as applied to all Mathematics modules, is used in this handbook to mean `has to be taken AND has to be passed' In the same context, `compulsory' will be used to mean only that the module `has to be taken'. For ‘core’ modules in other disciplines, students are advised to refer to the appropriate department for clarification.

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Mathematics BSc/MSci BSc programme: UCAS Code: G100 Route Code: UBSH3CSMM; MSci programme: UCAS Code: G103 Route Code: UMSH4CSMM Single subject Mathematics students are registered either for the BSc degree or the MSci degree. The BSc in Mathematics is a three-year programme, whilst the MSci in Mathematics is a four-year programme. All students take official examinations, mostly at the end of each year. The BSc and MSci programmes are the same for the first two years. All information in this booklet about first and second year single subject Mathematics applies to both programmes. Please note that the module codes in parentheses are those applying to students who entered the College prior to 2007. First Year Programme Director: Professor PK Sollich

First semester Compulsory modules:

4CCM111a (CM111A) Calculus I 4CCM113a (CM113A) Linear Methods 4CCM115a (CM115A) Numbers & Functions 4CCM122a (CM122A) Geometry I

Second semester Compulsory modules:

4CCM112a (CM112A) Calculus II 4CCM121a (CM121A) Introduction to Abstract Algebra 4CCM131a (CM131A) Introduction to Dynamical Systems 4CCM141a (CM141A) Probability and Statistics I

NOTE: in order 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. Second Year Programme Director: Professor AN Pressley There is a group of compulsory modules which all students must take, and a choice of optional modules. It is advisable to try all of the modules for the first two weeks before finally selecting the eight which you will continue with.


5CCM211a (CM211A) PDEs and Complex Variable 5CCM221a (CM221A) Analysis 1 5CCM222a (CM222A) Linear Algebra

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5CCM231a (CM231A) Intermediate Dynamics


5CCM223a (CM223A) Geometry of Surfaces 5CCM232a (CM232A) Groups and Symmetries

Standard options: 5CCM224a (CM224X) Elementary Number Theory 5CCM241a (CM241X) Probability and Statistics II 5CCM251a (CM251X) Discrete Mathematics 5CCM328b (CM328X) Logic

Third Year (BSc) Programme Director: Dr E Katzav

There are ten selected options of which students are required to take at least two, and a choice of standard optional modules. First semester Selected options:

6CCM321a (CM321A) Real Analysis II 6CCM322a (CM322C) Complex Analysis 6CCM327a (CM327Z) Topology 6CCM331a (CM331A) Special Relativity and Electromagnetism 6CCM332a (CM332C) Introductory Quantum Theory 6CCM350a (CM350Z) Rings and Modules 6CCM388a (CM388Z) Mathematical Finance I: Discrete Time

Standard options: 6CCM320a (CM320X) Topics in Mathematics1

6CCM356a (CM356Y) Linear Systems with Control Theory 6CCM359a (CM359X) Numerical Methods 6CCM380a (CM380A) Topics in Applied Probability 6CCMCS02 Theory of Complex Networks

Second semester Selected options: 6CCM318a (CM418Z) Fourier Analysis

6CCM326a (CM326Z) Galois Theory 6CCM338a (CM338Z) Mathematical Finance II: Continuous Time

Standard options: 6CCM224b (CM224X) Elementary Number Theory 6CCM241b (CM241X) Probability and Statistics II 6CCM251b (CM251X) Discrete Mathematics 6CCM320a (CM320X) Topics in Mathematics 6CCM328a (CM328X) Logic 6CCM330a (CM330X) Mathematics Education and Communication 6CCM334a (CM334Z) Space-Time Geometry and General Relativity 6CCM351a (CM351A) Representation Theory of Finite Groups 6CCM360a (CM360X) History and Development of Mathematics

1 6CCM320a (CM320X) and 6CCM380a (CM380A) cannot be taken together

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6CCM380a (CM380A) Topics in Applied Probability 6CCMCS05 Mathematical Biology

Third year BSc students may elect to do a project 6CCM345a (CM345C). They may also choose to take a language module at credit level 5 or higher, normally

from the KCL language unit, subject to the approval of the Programme Director. Note however, that under the course unit system, a pass in a language module, although counting towards your indicator, does not contribute to satisfying the requirement that in order to obtain a First or Upper Second class degree a candidate must pass at least 3 modules at the level at which the degree is awarded.

Students may, subject to the approval of the Programme Director, also take up to two modules at other colleges of the University of London or at Imperial College.

Third Year (MSci) Programme Director: Dr E Katzav

There are ten selected options of which students must take at least four. Optional units are subject to the agreement of the Programme Director and timetable issues. First semester Selected options:

6CCM321a (CM321A) Real Analysis II 6CCM322a (CM322C) Complex Analysis 6CCM327a (CM327Z) Topology 6CCM331a (CM331A) Special Relativity and Electromagnetism 6CCM332a (CM332C) Introductory Quantum Theory 6CCM350a (CM350Z) Rings and Modules 6CCM388a (CM388Z) Mathematical Finance I: Discrete Time

Standard options: 6CCM320a (CM320X) Topics in Mathematics 6CCM356a (CM356Y) Linear Systems with Control Theory

6CCM359a (CM359X) Numerical Methods 6CCM380a (CM380A) Topics in Applied Probability 6CCMCS02 Theory of Complex Networks

Second semester Selected options: 6CCM318a (CM418Z) Fourier Analysis

6CCM326a (CM326Z) Galois Theory 6CCM338a (CM338Z) Mathematical Finance II: Continuous Time

Standard options: 6CCM224b (CM224X) Elementary Number Theory 6CCM241b (CM241X) Probability and Statistics II 6CCM251b (CM251X) Discrete Mathematics

6CCM320a (CM320X) Topics in Mathematics 6CCM328a (CM328X) Logic 6CCM330a (CM330X) Mathematics Education and Communication 6CCM334a (CM334Z) Space-time Geometry and General Relativity 6CCM351a (CM351A) Representation Theory of Finite Groups

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6CCM360a (CM360X) History and Development of Mathematics 6CCM380a (CM380A) Topics in Applied Probability 6CCMCS05 Mathematical Biology

Third year MSci students may elect to do a project 6CCM345a (CM345C).

Fourth Year (MSci) Programme Director: Professor Y Safarov There is a compulsory Project Option 7CCM461a (CM461C), which all students are required to take, and a choice of optional modules. In addition to the optional modules given below, students may also take suitable third year modules subject to the approval of the Programme Director. All fourth year MSci students are required to complete a project on a mathematical topic. This involves writing a report of between 5,000 and 10,000 words, giving an informal seminar to staff and fellow students and producing a poster. The project counts as 30 credits (a full unit), which makes it a very important part of the final year. Each student will have a supervisor; their task is to advise not direct the project, but students are advised to show them a draft of the report at an early stage. Students must complete a form stating the topic and provisional title of the project which must be signed by the supervisor and returned to the projects co-ordinator, Dr Nikolay Gromov, by Monday 11 October 2010. The deadline for submission of projects is Wednesday 23 March 2011. Note: 6CCM320a (CM320X), 6CCM356a (CM356Y), 6CCM360a (CM360X) cannot be taken in the fourth year. First semester Compulsory module:

7CCM461a (CM461C) Project Standard options:

7CCM321b (CM321A) Real Analysis II 7CCM322b (CM322C) Complex Analysis 7CCM327a (CM327Z) Topology 7CCM350a (CM350Z) Rings and Modules 7CCMMS01 (CM424Z) Lie Groups & Lie Algebras 7CCMMS08 (CM414Z) Operator Theory 7CCMMS18 (CM437Z) Manifolds 7CCMMS31 (CM436Z) Quantum Mechanics II 7CCMMS32 (CM438Z) Quantum Field Theory 7CCMFM01 (CM467Z) Applied Probability and Stochastics

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Second semester Standard options:

7CCM326a (CM326Z) Galois Theory 7CCM334a (CM334Z) Space-time Geometry and General Relativity 7CCM351b (CM351A) Representation Theory of Finite Groups 7CCMMS03 (CM422Z) Algebraic Number Theory 7CCMMS11 (CM418Z) Fourier Analysis 7CCMMS20 (CMMS20) Algebraic Geometry 7CCMMS34 (CM435Z) String Theory and Branes 7CCMMS38 (CM433Z) Advanced General Relativity 7CCMMS41 (CMMS41) Supersymmetry and Gauge Theory

Final year students may, subject to the approval of the Programme Director, also take up to two modules at other colleges of the University of London or at Imperial College.

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Mathematics with Management and Finance BSc UCAS Code: BSc programme – G1N2 / Route Code: UBSH3CMMMMF Programme Director: Dr PL Kassaei Please note that the module codes in parentheses are those applying to students who entered the College prior to 2007.

First Year First semester Compulsory modules:

4CCM111a (CM111A) Calculus I 4CCM113a (CM113A) Linear Methods 4CCM115a (CM115A) Numbers & Functions 4CCYM129 Organisational Behaviour


4CCM112a (CM112A) Calculus II 4CCM121a (CM121A) Introduction to Abstract Algebra 4CCM141a (CM141A) Probability and Statistics I 4CCYM110 Economics

NOTE: in order to progress to the second year students must: • gain an average mark of at least 40% in level 4 mathematics modules, with no mark

lower than 33% • pass at least one of Economics or Organisation Behaviour • 90 credits passed Second Year First semester Compulsory modules:

5CCM211a (CM211A) PDEs and Complex Variable Either 5CCM221a (CM221A) Analysis I Or 5CCM250a (CM2504) Applied Analytic Methods

5CCM222a (CM222A) Linear Algebra 5CCYM212 Marketing NOTE: students are strongly advised to take 5CCM221a (CM221A), which is a prerequisite for many third year modules. Second semester Compulsory modules:

5CCM232a (CM232A) Groups & Symmetries

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5CCM241a (CM241X) Probability and Statistics II 5CCM251a (CM251X) Discrete Mathematics

5CCYM210 Accounting

NOTE: students must pass either Marketing or Accounting to progress to the third year. Third Year Students must take five compulsory modules in the third year and choose three optional modules from the list below.


6CCM380a (CM380A) Topics in Applied Probability 6CCM388a (CM388Z) Mathematical Finance I: Discrete Time 6CCYM325 Business Strategy

Standard options:

6CCM321a (CM321A) Real Analysis II 6CCM322a (CM322C) Complex Analysis 6CCM350a (CM350Z) Rings and Modules

6CCM357a (CM357Y) Introduction to Linear Systems with Control Theory 6CCM359a (CM359X) Numerical Methods 6CCMCS02 Theory of Complex Networks

Second Semester Compulsory modules:

6CCM338a (CM338Z) Mathematical Finance II: Continuous Time 6CCM380a (CM380A) Topics in Applied Probability 6CCYM339 Human Resource Management

Standard options: 6CCM223b (CM223A) Geometry of Surfaces 6CCM224b (CM224X) Elementary Number Theory

6CCM326a (CM326Z) Galois Theory 6CCM328a (CM328X) Logic

6CCM330a (CM330X) Mathematics Education and Communication 6CCM351a (CM351A) Representation Theory of Finite Groups 6CCM360a (CM360X) History and Development of Mathematics 6CCMCS05 Mathematical Biology Third year students may elect to do a project 6CCM345a (CM345C).

Other options may also be permitted subject to the agreement of the Programme Director and timetable issues. You may also choose to take a language module at credit level 5 or higher, normally from the KCL language unit, subject to the approval of the Programme Director. Students may, subject to the approval of the Programme Director, also take up to two modules at other colleges of the University of London or at Imperial College.

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Graduate Diploma in Mathematics Route codes: CUGD1MATGDD, CUGD2MATGDD Programme Director: Professor E Shargorodsky

The Graduate Diploma programme consists of a one-year full- time study programme or a two-year part- time study programme. Students must take eight modules which may include an individual project on a subject of their choice. All students take official examinations, mostly in May/June.

Students must select eight of the following options including at least six third year modules, subject to the approval of the Programme Director. The list of permitted options includes second and third year modules which can be taken by Single Honours BSc/MSci students of Mathematics. Exceptionally students may be permitted to take fourth year modules and up to two first year modules. First semester Second year modules:

5CCM211a (CM211A) PDEs and Complex Variable 5CCM221a (CM221A) Analysis 1 5CCM222a (CM222A) Linear Algebra 5CCM231a (CM231A) Intermediate Dynamics 5CCM250a (CM2504) Applied Analytic Methods

Third year modules:

6CCM211b (CM211A) PDEs and Complex Variable 6CCM222b (CM222A) Linear Algebra 6CCM231b (CM231A) Intermediate Dynamics 6CCM320a (CM320X) Topics in Mathematics

6CCM321a (CM321A) Real Analysis II 6CCM322a (CM322C) Complex Analysis 6CCM327a (CM327Z) Topology 6CCM331a (CM331A) Special Relativity and Electromagnetism 6CCM332a (CM332C) Introductory Quantum Theory 6CCM350a (CM350Z) Rings and Modules 6CCM356a (CM356Y) Linear Systems with Control Theory1

6CCM359a (CM359X) Numerical Methods 6CCM380a (CM380A) Topics in Applied Probability2

6CCM388a (CM388Z) Mathematical Finance I: Discrete Time 6CCMCS02 Theory of Complex Networks

1 Or 6CCM357a (CM357Y) Introduction to Linear systems with Control Theory (according to the advice of your Programme Director) 2 6CCM320a (CM320X) and 6CCM380a (CM380A) cannot be taken together

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Second semester Second year modules:

5CCM223a (CM223A) Geometry of Surfaces 5CCM224a (CM224X) Elementary Number Theory 5CCM232a (CM232A) Groups and Symmetries 5CCM241a (CM241X) Probability and Statistics II 5CCM251a (CM251X) Discrete Mathematics

Third year modules:

6CCM223b (CM223A) Geometry of Surfaces 6CCM224b (CM224X) Elementary Number Theory 5CCM232a (CM232A) Groups and Symmetries 6CCM232b (CM232A) Groups and Symmetries 6CCM241b (CM241X) Probability and Statistics II 6CCM251b (CM251X) Discrete Mathematics 6CCM318a (CM418Z) Fourier Analysis 6CCM320a (CM320X) Topics in Mathematics 6CCM326a (CM326Z) Galois Theory 6CCM328a (CM328X) Logic 6CCM334a (CM334Z) Space-Time Geometry and General Relativity 6CCM338a (CM338Z) Mathematical Finance II: Continuous Time 6CCM351a (CM351A) Representation Theory of Finite Groups 6CCM360a (CM360X) History and Development of Mathematics 6CCM380a (CM380A) Topics in Applied Probability 6CCMCS05 Mathematical Biology

Students may choose to do a project 6CCM345a (CM345C). Students may, subject to the approval of the Programme Director, also take up to two modules at other colleges of the University of London or at Imperial College. NOTE: a student may not enrol on a module that the student has already taken and passed at either undergraduate or postgraduate level. Neither may a student enrol for a module that overlaps with another module that the student has already taken and passed. Modules will be deemed to overlap if both the content and the level of complexity are similar.

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Joint Honours Modules In a joint honours course the student's time is divided more or less equally between the two main subjects. Nevertheless, there is scope for flexibility to take account of individual preferences and developing interests and abilities. There is in fact the opportunity in later years to adjust the distribution of modules so that more time is devoted to one subject than the other. Constraints of the timetable must obviously be borne in mind and, in any case, it is crucial that the appropriate Programme Director be consulted. The majority of Mathematics modules taken by Joint Honours students are the same as the ones taken by Single Subject mathematicians. However, some modules have been devised with the special needs of the Joint Honours student in mind.

The responsibility for non-mathematics modules rests with the relevant department. They may make changes which are not reflected in this booklet, and you must consult their booklet and/or programme director for definitive information.

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Mathematics and Computer Science BSc UCAS code: GG14 / Route Code: UBSH3CJMMCS Programme Director: Dr AB Pushnitski Please note that the module codes in parentheses are those applying to students who entered the College prior to 2007. First Year First semester Compulsory modules:

4CCM111a (CM111A) Calculus I 4CCM113a (CM113A) Linear Methods 4CCS1PRP (CS1PRP) Programming Practice 4CCS1CS1 (CS1CS1) Computer Systems I


4CCM112a (CM112A) Calculus II 4CCM141a (CM141A) Probability and Statistics I 4CCS1PRA (CS1PRA) Programming Applications 4CCS1DST (CS1DST) Data Structures

NOTE: Mathematics modules: in order 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. Computer Science modules: students must pass at least one of 4CCS1PRP and 4CCS1PRA in order to progress to Year 2. Second Year First semester Compulsory modules:

5CCM115b (CM115A) Numbers and Functions 5CCM250a (CM2504) Applied Analytic Methods

5CCS2OSD (CS2OSD) Object-Oriented Specification and Design 5CCS02DB (CS02DB) Database Systems


5CCM121b (CM121A) Introduction to Abstract Algebra 5CCM328b (CM328X) Logic

5CCS2PLD (CS2PLD) Programming Language Design Paradigms 5CCS2OSC (CS2OSC) Operating Systems and Concurrency

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Third Year Students will normally take four of the following mathematics modules and four of the computer science modules: Standard options: First semester

6CCM211b (CM211A) PDEs and Complex Variable 6CCM222b (CM222A Linear Algebra 6CCM231b (CM231A) Intermediate Dynamics

6CCM320a (CM320X) Topics in Mathematics 6CCM357a (CM357Y) Introduction to Linear Systems with Control Theory1



6CCS3AIN (CS3AIN) Artificial Intelligence 6CCS3CIS (CS3CIS) Cryptography and Information Security 6CCS3GRS (CS3GRS) Computer Graphics Systems 6CCS3SMT (CS3SMT) Software Measurement and Testing 6CCS3INS (CS3INS) Internet Systems 6CCS3PAL (CS3PAL) Parallel Algorithms 6CCS3PRJ (CS3PRJ) Computer Science Project

Second semester

6CCM223b (CM223A) Geometry of Surfaces 6CCM224b (CM224X) Elementary Number Theory 6CCM232b (CM232A) Groups and Symmetries

6CCM241b (CM241X) Probability and Statistics II 6CCM251b (CM251X) Discrete Mathematics

6CCM320a (CM320X) Topics in Mathematics 6CCM330a (CM330X) Mathematics Education and Communication 6CCM338a (CM338Z) Mathematical Finance II: Continuous Time 6CCM351a (CM351A) Representation Theory of Finite Groups

6CCM360a (CM360X) History and Development of Mathematics 6CCM380a (CM380A) Topics in Applied Probability 6CCMCS05 Mathematical Biology 6CCS3SIA Software Engineering of Internet Applications 6CCS3DSM Distributed Systems 6CCS3SAD Software Architecture and Design 6CCS3PRJ Computer Science Project 6CCS3OME Optimisation Methods 6CCS3TSP Text Searching and Processing 6CCS3AST Advanced Security Topics

1 This course is not an option for students who have previously taken CM131A, Introduction to Dynamical Systems. 2 6CCM320a (CM320X) and 6CCM380a (CM380A) cannot be taken together

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Other options available to 3rd year single honours students may be taken where the timetable allows, subject to approval by the Programme Director.


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Mathematics and Computer Science MSci UCAS code: GGD4 / Route Code: UMSH4CJMMCS Programme Director: Dr AB Pushnitski Please note that the module codes in parentheses are those applying to students who entered the College prior to 2007. As of September 2009 there is no first, second or third year on this programme. Fourth Year Core module: CS4PRJ1/2 Computer Science Project Standard options - A choice of 6 options from the following list, of which 4 should be Mathematics. One Computer Science option is to be taken in each semester.

First semester 7CCM321b (CM321A) Real Analysis II 7CCM322b (CM322C) Complex Analysis 7CCM327b (CM327Z) Topology 7CCM350b (CM350Z) Rings and Modules 7CCMMS01 (CM424Z) Lie Groups and Lie Algebras 7CCMMS08 (CM414Z) Operator Theory

7CCMMS18 (CM437Z) Manifolds 7CCSMAMS (CSMAMS) Agents and Multi-agent Systems 7CCSMDBT (CSMDBT) Database Technology 7CCSMAIN (CSMAIN) Artificial Intelligence 7CCSMART (CSMART) Advanced Research Topics

Second semester

7CCM326b (CM326Z) Galois Theory 7CCM334b (CM334Z) Space-time Geometry and General Relativity 7CCM351b (CM351A) Representation Theory of Finite Groups 7CCMMS03 (CM422Z) Algebraic Number Theory 7CCMMS11 (CM418Z0 Fourier Analysis 7CCMMS20 (CMMS20) Algebraic Geometry 7CCSMTSP (CSMTSP) Text Searching and Processing 7CCSMCMB (CSACMB) Algorithms for Computational Molecular Biology 7CCSMCFC (CS4CFC) Computer Forensics and Cybercrime 7CCSMCOM (CSMCOM) Computational Models 7CCSMOME (CSMOME) Optimisation Methods

Fourth year students may elect to do a project 7CCM461a (CM461C45C) which has 30 credits (one full unit). Other options may also be permitted subject to the agreement of the Programme Director and timetable issues. Students may, subject to the approval of the Programme Director, also take up to two modules at other colleges of the University of London or at Imperial College.

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Mathematics and Physics BSc UCAS code: FG31 / Route Code:UBSH3CJMMPH Programme Director: Dr N Gromov Please note that the module codes in parentheses are those applying to students who entered the College prior to 2007. First Year First semester Core module:

4CCP111A First Year Laboratory Physics A Compulsory modules:

4CCM111a (CM111A) Calculus I 4CCM113a (CM113A) Linear Methods 4CCM115a (CM115A) Numbers and Functions

*(Students must take either 4CCM115a or 4CCM141a) 4CCP1471 Thermal Physics 4CCP1500 Fields, Waves and Matter

Second semester Core module:


4CCM112a (CM112A) Calculus II 4CCM141a (CM141A) Probability and Statistics I *(Students must take either 4CCM141a or 4CCM115a)

4CCP1500 Fields, Waves and Matter Optionally, students may take 4CCP1600 Astrophysics I (2nd semester) in addition to the modules listed above. NOTE: in order 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.

Second Year First semester Core modules:

5CCP211A Second Year Laboratory Physics A Compulsory modules:

5CCM211a (CM211A) PDEs and Complex Variable Either

5CCM221a (CM221A) Analysis I Or 5CCM250a (CM2504) Applied Analytic Methods

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5CCM231a (CM231A) Intermediate Dynamics 5CCP2240 Modern Physics



5CCM121b (CM121A) Introduction to Abstract Algebra 5CCP2240 Modern Physics 5CCP2380 (CP2380) Electromagnetism*

* Exceptionally, students may be permitted to omit 5CCP2380 and take 6CCM331a in the third year instead. In that case they may chose a further module from 4CCP1600, 5CCP211B, 5CCM122b, 5CCM328b or other Maths or Physics modules recommended by the Programme Director. Students should attend the Physics laboratory classes 6CCP211A in the first or the second semester. Please contact the Physics Department at the beginning of the year to make detailed arrangements. Third Year Students must choose one of the following:

6CCP3131 (CP3131) 3rd Year Project in Physics (Semester 2) 6CCP3132 Third Year Literature Review (Semester 1 or 2) 6CCP3133 University Ambassador Scheme (Semester 1) †

First Semester Compulsory modules: 6CCM331a (CM331A) Special Relativity & Electromagnetism*

6CCM436a (CM436Z) Quantum Mechanics II** 6CCP3212 (CP3212) Statistical Mechanics

Standard options: Students will take four of the following options, of which two will normally be Mathematics, subject to the approval of the Programme Director:

6CCM222b (CM222A) Linear Algebra 6CCM321a (CM321A) Real Analysis II 6CCM322a (CM322C) Complex Analysis 6CCM327a (CM327Z) Topology 6CCM350a (CM350Z) Rings and Modules 6CCM356a (CM356Y) Linear Systems with Control Theory

6CCM359a (CM359X) Numerical Methods 6CCM380a (CM380A) Topics in Applied Probability 6CCM388a (CM388Z) Mathematical Finance I: Discrete Time 6CCMCS02 Theory of Complex Networks

6CCP3241 (CP3241) Theoretical Particle Physics 6CCP3380 (CP3380) Optics

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6CCP3221 (CP3221) Spectroscopy and Quantum Mechanics** Standard options:

6CCM223b (CM223A) Geometry of Surfaces 6CCM224b (CM224X) Elementary Number Theory

6CCM232b (CM232A) Groups and Symmetries 6CCM251b (CM251X) Discrete Mathematics 6CCM326a (CM326Z) Galois Theory

6CCM328a (CM328X) Logic 6CCM330a (CM330X) Mathematics Education & Communication † 6CCM334a (CM334Z) Space-time Geometry and General Relativity*** 6CCM338a (CM338Z) Mathematical Finance II: Continuous Time 6CCM351a (CM351A) Representation Theory of Finite Groups 6CCM380a (CM380A) Topics in Applied Probability 6CCMCS05 Mathematical Biology

6CCP3402 (CP3402) Solid State Physics 6CCP3630 (CP3630) General Relativity and Cosmology***

6CCPMP36 (CPMP36) Medical Imaging and Measurement * Not if 5CCP2380 Electromagnetism was taken in the second year. ** Students must take one of 6CCP3221 (CP3221) and 6CCM436a (CM436Z) but not both. *** 6CCP3630 (CP3630) General Relativity and Cosmology and 6CCM334a (CM334Z) Space-time Geometry and General Relativity cannot be taken together. † 6CCP3133 University Ambassador Scheme and 6CCM330a (CM330X) Mathematics Education and Communication cannot be taken together. Other options available to 3rd year single honours students may be taken where the timetable allows, subject to approval by the Programme Director. The responsibility for non-mathematics modules rests with the relevant department. They may make changes which are not reflected in this booklet, and you must consult their booklet and/or programme director for definitive information.

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Mathematics and Physics MSci UCAS code: FGH1 / Route Code: UMSH4CJMMPH Programme Director: Dr N Gromov Please note that the module codes in parentheses are those applying to students who entered the College prior to 2007. First Year First semester Core module:


4CCM111a (CM111A) Calculus I 4CCM113a (CM113A) Linear Methods 4CCM115a (CM115A) Numbers and Functions

*(Students must take either 4CCM115a or 4CCM141a) 4CCP1471 Thermal Physics 4CCP1500 Fields, Waves and Matter


4CCP111A First Year Laboratory Physics A Compulsory module:

4CCM112a (CM112A) Calculus II 4CCM141a (CM141A) Probability and Statistics I

*(Students must take either 4CCM141a or 4CCM115a) 4CCP1500 Fields, Waves and Matter Optionally, students may take 6CCP1600 Astrophysics I (2nd semester) in addition to the modules listed above. NOTE: in order 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.

Second Year First semester Core modules:


5CCM211a (CM211A) PDEs and Complex Variable Either

5CCM221a (CM221A) Analysis I Or 5CCM250a (CM2504) Applied Analytic Methods 5CCM231a (CM231A) Intermediate Dynamics

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5CCP2240 Modern Physics



5CCM121b (CM121A) Introduction to Abstract Algebra 5CCP2240 Modern Physics 5CCP2380 (CP2380) Electromagnetism*

* Exceptionally, students may be permitted to omit 5CCP2380 and take 6CCM331a in the third year instead. In that case they may chose a further module from 4CCP1600, 5CCP211B, 5CCM122b, 5CCM328b or other Maths or Physics modules recommended by the Programme Director. Students should attend the Physics laboratory classes 5CCP211A in the first or the second semester. Please contact the Physics Department at the beginning of the year, to make detailed arrangements. NOTE: students take either 5CCM221a (CM221A) or 5CCM250a (CM2504). Students reading for the MSci are strongly advised to take 5CCM221a (CM221A) which is a prerequisite for many third and fourth year modules.

Third Year Students must choose one of the following:


First Semester Compulsory modules:

6CCM331a (CM331A) Special Relativity and Electromagnetism* 6CCM436a (CM436Z) Quantum Mechanics II** 6CCP3212 (CP3212) Statistical Mechanics

Standard options: Students will take four of the following options, of which two will normally be Mathematics, subject to agreement with the Programme Director:

6CCM222b (CM222A) Linear Algebra 6CCM321a (CM321A) Real Analysis II

6CCM322a (CM322C) Complex Analysis 6CCM327a (CM327Z) Topology 6CCM350a (CM350Z) Rings and Modules 6CCM356a (CM356Y) Linear Systems with Control Theory

6CCM359a (CM359X) Numerical Methods 6CCM380a (CM380A) Topics in Applied Probability 6CCM388a (CM388Z) Mathematical Finance I: Discrete Time 6CCMCS02 Theory of Complex Networks

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6CCP3241 (CP3241) Theoretical Particle Physics 6CCP3380 (CP3380) Optics

Second Semester Compulsory module:

6CCP3221 (CP3221) Spectroscopy and Quantum Mechanics**

Standard modules: 6CCM223b (CM223A) Geometry of Surfaces 6CCM224b (CM224X) Elementary Number Theory

6CCM232b (CM232A) Groups and Symmetries 6CCM251b (CM251X) Discrete Mathematics

6CCM326a (CM326Z) Galois Theory 6CCM328a (CM328X) Logic 6CCM330a (CM330X) Mathematics Education and Communication †

6CCM334a (CM334Z) Space-time Geometry and General Relativity*** 6CCM338a (CM338Z) Mathematical Finance II: Continuous Time 6CCM351a (CM351A) Representation Theory of Finite Groups 6CCM380a (CM380A) Topics in Applied Probability 6CCMCS05 Mathematical Biology

6CCP3402 (CP3402) Solid State Physics 6CCP3630 (CP3630) General Relativity and Cosmology*** 6CCPMP36 (CPMP36) Medical Imaging and Measurement * Not if 5CCP2380 Electromagnetism was taken in the second year. ** Students must take one of 6CCP3221 (CP3221) and 6CCM436a (CM436Z) but not both. *** 6CCP3630 (CP3630) General Relativity and Cosmology and 6CCM334a (CM334Z) Space-time Geometry and General Relativity cannot be taken together. † 6CCP3133 University Ambassador Scheme and 6CCM330a (CM330X) Mathematics Education and Communication cannot be taken together. Other options available to 3rd year single honours students may be taken where the timetable allows, subject to approval by the Programme Director. Fourth Year Core module:

7CCM461a (CM461C) or 7CCP4100 (CP4100) 30 credits (one unit) Project

Standard options: First Semester

7CCM321b (CM321A) Real Analysis II 7CCM322b (CM322C) Complex Analysis 7CCM327b (CM327Z) Topology 7CCM350b (CM350Z) Rings and Modules 7CCMMS08 (CM414Z) Operator Theory 7CCMMS01 (CM424Z) Lie Groups and Lie Algebras

7CCMMS31 (CM436Z) Quantum Mechanics II 7CCMMS18 (CM437Z) Manifolds 7CCMMS32 (CM438Z) Quantum Field Theory

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7CCMFM01 (CM467Z) Applied Probability and Stochastics Second Semester

7CCM326b (CM327Z) Galois Theory 7CCM334b (CM334Z) Space-time Geometry and General Relativity 7CCM351b (CM351A) Representation Theory of Finite Groups 7CCMMS03 (CM422Z) Algebraic Number Theory 7CCMMS11 (CM418Z) Fourier Analysis

7CCMMS20 (CMMS20) Algebraic Geometry 7CCMMS34 (CM435Z) String Theory and Branes 7CCMMS38 (CM433Z) Advanced General Relativity 7CCMMS41 (CMMS41) Supersymmetry and Gauge Theory Other options may be taken where the timetable allows, after discussion with the programme director. Students may, subject to the approval of the Programme Director, also take up to two modules at other colleges of the University of London or at Imperial College. The physics component consists of a choice of intercollegiate modules, a list of which can be found in the Physics Department’s Undergraduate Handbook.


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Mathematics and Physics with Astrophysics BSc UCAS code: FGJ1 / Route Code: UBSH3CJMMPA Programme Director: Dr N Gromov Please note that the module codes in parentheses are those applying to students who entered the College prior to 2007. First Year First semester Core module:


4CCM111a (CM111A) Calculus I 4CCM113a (CM113A) Linear Methods 4CCP1471 Thermal Physics 4CCP1500 Fields, Waves and Matter



4CCM112a (CM112A) Calculus II 4CCP1500 Fields, Waves and Matter 4CCP1600 Astrophysics I

NOTE: in order 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. Second Year First semester Core module:


5CCM211a (CM211A) PDEs and Complex Variable 5CCM231a (CM231A) Intermediate Dynamics 5CCP2240 Modern Physics 5CCP2621 (CP2621) Astrophysics 2



5CCP2240 Modern Physics

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Standard options:

5CCM121b (CM121A) Introduction to Abstract Algebra 5CCM328b (CM328X) Logic 5CCP2380 (CP2380) Electromagnetism*

* Exceptionally, students may be permitted to omit 5CCP2380 and take 6CCM331a in the third year instead. In that case they may chose a further module from 4CCP1600, 5CCP211B, 5CCM122b, 5CCM328b or other Maths or Physics modules recommended by the Programme Director. Third Year Student must choose one of the following:


First Semester Compulsory module:

6CCM331a (CM331A) Special Relativity & Electromagnetism* 6CCM436a (CM436Z) Quantum Mechanics II** 6CCP3212 (CP3212) Statistical Mechanics

Standard options: 6CCM321a (CM321A) Real Analysis II 6CCM322a (CM332C) Complex Analysis 6CCM327a (CM327Z) Topology 6CCM350a (CM350Z) Rings and Modules 6CCM357a (CM357Y) Linear Systems with Control Theory 6CCM359a (CM359X) Numerical Methods 6CCM380a (CM380A) Topics in Applied Probability 6CCM388a (CM388Z) Mathematical Finance I: Discrete Time 6CCMCS02 Theory of Complex Networks 6CCP3241 (CP3241) Theoretical Particle Physics


Either 6CCM334a (CM334Z) Space-time Geometry & General Relativity Or 6CCP3630 (CP3630) General Relativity and Cosmology 6CCP3221 (CP3221) Spectroscopy and Quantum Mechanics**

Standard options:

6CCM223b (CM223A) Geometry of Surfaces 6CCM224b (CM224X) Elementary Number Theory 6CCM232b (CM232A) Groups and Symmetries 6CCM251b (CM251X) Discrete Mathematics 6CCM326a (CM326Z) Galois Theory 6CCM328a (CM328X) Logic 6CCM330a (CM330X) Mathematics Education and Communication †

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6CCM338a (CM338Z) Mathematical Finance II: Continuous time 6CCM351a (CM351A) Representation Theory of Finite Groups 6CCM380a (CM380A) Topics in Applied Probability 6CCMCS05 Mathematical Biology 6CCP3201 (CP3201) Mathematical Methods in Physics III 6CCP3402 (CP3402) Solid State Physics 6CCPMP36 (CPMP36) Medical Imaging and Measurement

* Not if 5CCP2380 Electromagnetism was taken in the second year. ** Students must take one of 6CCP3221 and 6CCM436a (CM436Z) but not both. † 6CCP3133 University Ambassador Scheme and 6CCM330a (CM330X) Mathematics Education and Communication cannot be taken together. Note: 6CCP3630 (CP3630) General Relativity and Cosmology and 6CCM334a (CM334Z) Space-time Geometry and General Relativity cannot be taken together. The responsibility for non-mathematics modules rests with the relevant department. They may make changes which are not reflected in this booklet, and you must consult their booklet and/or programme director for definitive information.

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French and Mathematics BA UCAS code: RG11 / Route Code: UBAH4AJFRMM Programme Director: Prof FA Rogers Please note that the module codes in parentheses are those applying to students who entered the College prior to 2007. As of September 2009 there is no first, second or third year on this programme. Fourth Year Students should choose four modules from the following list of Mathematical modules:

First Semester Standard options:

6CCM320a (CM320X) Topics in Mathematics 6CCM321a (CM321A) Real Analysis II 6CCM322a (CM322C) Complex Analysis 6CCM327a (CM327Z) Topology

6CCM331a (CM331A) Special Relativity and Electromagnetism 6CCM332a (CM332C) Introductory Quantum Theory

6CCM350a (CM350Z) Rings and Modules 6CCM356a (CM356Y) Linear Systems with Control Theory

6CCM380a (CM380A) Topics in Applied Probability1

6CCM388a (CM388Z) Mathematical Finance I: Discrete Time Second Semester Standard options:

6CCM224b (CM224X) Elementary Number Theory 6CCM320a (CM320X) Topics in Mathematics 6CCM326a (CM326Z) Galois Theory 6CCM330a (CM330X) Mathematics Education and Communication

6CCM334a (CM334Z) Space-time Geometry and General Relativity 6CCM338a (CM338Z) Mathematical Finance II: Continuous Time

6CCM351a (CM351A) Representation Theory of Finite Groups 6CCM380a (CM380A) Topics in Applied Probability

Or any other Third Year Single-Honours optional module which is compatible with the timetable, subject to the approval of the Programme Director. The French component comprises AF/F300 Core Language – final year (0.5 cu) which is compulsory and a choice to the value of 1.5 cu from the following modules AF/F332 The Stylistics of Translation (0.5 cu), AF/F336 Use of Spoken French*(0.5 cu), AF/F334 Citizenship and Exclusion (1 cu). In Semester 1: AF/F338 Medieval Occitan Literature (0.5 cu), AF/F340 The City in the Literature of Seventeenth- and Eighteenth-century France (0.5 cu), AF/F349 Shadows of Enlightenment (0.5 cu), AF/F348 French Literature under the Second Empire (0.5 cu), AF/F317 Proust (0.5 cu), AF/F347 1 6CCM320a (CM320X) and 6CCM380a (CM380A) cannot be taken together.

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Contemporary Algerian Literature (0.5 cu), AF/F350 Topics in French Film II (0.5 cu), In Semester 2: AF/F339 The Debate about Women in the Middle Ages (0.5 cu), AF/F309 The Literary Perception of the honnete homme (0.5 cu), AF/F341 Gender and Discourse in Eighteenth-century France (0.5 cu), AF/F344 Contemporary Women’s Writing in French (0.5 cu), AF/F351 Troubling Desires (0.5 cu), AF/F320 Recent French Thought (0.5 cu), AF/F330 (0.5 cu) Dissertation may be offered in place of one of the options by students who may wish to go on to do research after their degree. *Only students who have not done year-abroad units in French may do AF/F336; it is not open to francophones.

The responsibility for non-mathematics modules rests with the relevant department. They may make changes which are not reflected in this booklet, and you must consult their booklet and/or programme director for definitive information. Students may also wish to consult the French Department website: www.kcl.ac.uk/french.

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Mathematics and Philosophy BA UCAS code: GV15 / Route Code: UBAH3AJMMPL Programme Director: Professor FI Diamond Please note that the module codes in parentheses are those applying to students who entered the College prior to 2007. First Year Mathematics Modules


4CCM111a (CM111A) Calculus I 4CCM113a (CM113A) Linear Methods

5CCM115b (CM115A) Numbers and Functions


4CCM112a (CM112A) Calculus II 4CCM121a (CM121A) Introduction to Abstract Algebra

Philosophy modules: First and Second semesters: Students must choose three modules, one from each of the three categories: 1) 4AANA001 Greek Philosophy I (semester 1) 4AANB005 Modern Philosophy (semester 2) 2) 4AANA002 Ethics I (semester 1) 4AANB006 Political Philosophy I (semester 2) 3) 4AANA003 Elementary Logic (semester 1) 4AANA004 Metaphysics (semester 1) 4AANB007 Epistemology I (semester 2) 4AANB008 Methodology I (semester 2)

: NOTE: in order 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. Second Year Mathematics Students take one 15 credit compulsory mathematics module and three 15 credit optional modules.

First Semester Compulsory module:

5CCM221a (CM221A) Analysis I

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Standard options: 5CCM122b (CM122A) Geometry i 5CCM211a (CM211A) PDEs and Complex Variable 5CCM222a (CM222A) Linear Algebra 5CCM231a (CM231A) Intermediate Dynamics

Second Semester Standard options:

5CCM131b (CM131A) Introduction to Dynamical Systems for Joint Honours 5CCM141b (CM141A) Probability and Statistics I 5CCM223a (CM223A) Geometry of Surfaces 5CCM224a (CM224X) Elementary Number Theory 5CCM232a (CM232A) Groups and Symmetries 5CCM241a (CM241X) Probability and Statistics II 5CCM251a (CM251X) Discrete Mathematics

Second Year Philosophy Students must choose three modules from at least two of the following categories: A) 5AANA001 Greek Philosophy II: Plato (sem 1)

5AANB002 Greek Philosophy II: Aristotle (Sem 2) 5AANA003 Modern Philosophy II: Locke & Berkley (sem 1) 5AANB004 Modern Philosophy II: Spinoza & Leibniz (sem 2)

B) 5AANA005 Ethics II: history of ethical philosophy (sem 1) 5AAMB006 Ethics II: contemporary ethical Philosophy (sem 2) 5AANB007 Political Philosophy II: theories of justice (sem 2)

5AANB008 Political Philosophy II: history of political philosophy (s1) C) 5AANA009 Epistemology II (sem 1) 5AANA010 Metaphysics II (sem 1) 5AANB011 Philosophy of Logic & Language (sem 2) 5AANB012 Philosophy of Mind (sem 2) Students must choose one module from the lists above and the following list: 6AANA028 First-order Logic (sem 1)

6CCNB031 Modal Logic (sem 2) 6AANB017 Indian Philosophy: the Heterodox Schools (sem 2) 6AANB023 Medieval Philosophy (sem 2)

6AANA022 Philosophy of Mathematics (sem 1) 6AANA024 Philosophy of Psychology (sem 1) 6AANB0025 Philosophy of religion (sem 2) 6AANA018 Kant’s Epistemology & Metaphysics (sem 1)

Note: • All modules are worth 15 credits and taught for one semester only.

• All the modules require one hour’s lecture per week plus one hour of seminars/exercise class per week.

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• Some modules require the submission of coursework instead of sitting an exam (you can find the module descriptions and requirements in http://www.kcl.ac.uk/schools/humanities/depts/philosophy/current/ug/modules.html

• If you are unsure about which modules to choose, please make an appointment via email with your Philosophy personal tutor or with the senior tutor, Dr Mark Textor, to discuss your potential choices.

• We generally suggest that in the second year, you take all credits at level 5 (these are the modules whose codes start with 5), unless you have a particular interest in one of the level 6 modules (whose codes start with 6).

Note: students, who choose to take level 6 Philosophy options in the second year, if allowable by the Programme Director, may experience timetable clashes which cannot be resolved. Third Year Students should choose three mathematics modules from the following: Mathematics Modules

First Semester Standard options:

6CCM211b (CM211A) PDEs and Complex 6CCM222b (CM222A) Linear Algebra 6CCM231b (CM231A) Intermediate Dynamics 6CCM320a (CM320X) Topics in Mathematics 6CCM321a (CM321A) Real Analysis II

6CCM322a (CM322C) Complex Analysis 6CCM327a (CM327Z) Topology 6CCM331a (CM331A) Special Relativity & Electromagnetism 6CCM332a (CM332C) Introductory Quantum Theory 6CCM350a (CM350Z) Rings and Modules 6CCM356a (CM356Y) Linear Systems with Control Theory1

6CCM357a (CM357Y) Introduction to Linear Systems with Control Theory2



Second Semester Standard options:

6CCM223b (CM223A) Geometry of Surfaces 6CCM224b (CM224X) Elementary Number Theory 6CCM232b (CM232A) Groups and Symmetries

1 This course is an option for students who have previously taken 4CCM131a, Introduction to Dynamical Systems. 2 This is not an option for students who have previously taken 4CCM131a. 3 6CCM380a (CM380A) and 6CCM320a (CM320X) cannot be taken together.

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6CCM241b (CM241X) Probability and Statistics II 6CCM251b (CM251X) Discrete Mathematics 6CCM320a (CM320X) Topics in Mathematics

6CCM326a (CM326Z) Galois Theory 6CCM328a (CM328X) Logic 6CCM330a (CM330X Mathematics Education and Communication 6CCM334a (CM334Z) Space-time Geometry & General Relativity 6CCM338a (CM338Z) Mathematical Finance II: Continuous Time 6CCM351a (CM351A) Representation Theory of Finite Groups

6CCM380a (CM380A) Topics in Applied Probability 6CCMCS05 Mathematical Biology

Third Year Philosophy Modules First and Second semester: Students must take 4 modules (or 60 credits) from the following list:

Dissertation (30 credits) Arabic Philosophy Hellenistic Philosophy

Indian Philosophy Kant Mediaeval Philosophy

Logic and Set Theory Neoplatonism

Philosophy of Psychology Philosophy of Religion Philosophy of Science

Pre-Socratics Reading in Aristotle Reading in Plato Topics in Philosophy of Language

Topics in Philosophy of Mind

And other modules in Philosophy, subject to the approval of the relevant Programme Director in the Philosophy Department. The responsibility for non-mathematics modules rests with the relevant department. They may make changes which are not reflected in this booklet, and you must consult their booklet and/or programme director for definitive information.

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Change of Degree Course Students arrive at King's College having given much thought to their choice of course. Likewise, in admitting students to a particular course, the College goes to some considerable lengths to ensure that they are suitably qualified. There is, therefore, a high degree of commitment on both sides. However, we do realise that inclinations and interests sometimes change, and if you feel that you would be better suited to a different course you should not delay in seeking advice and finding out if a change is allowable. As a rule, note that changes of courses are the more difficult the more material you have missed from your new programme. In the Department of Mathematics, first year students in their first term should see the Admissions Tutor (Dr D Solomon). After the first term, the appropriate person is the Programme Director for the proposed course. Your personal tutor should in any case be consulted. A change of degree course requires written permission from all departments involved and is not automatic. A Change of Registration Status form is available online. The form will be signed on behalf of the Mathematics Department by the Senior Tutor, and should then be returned to the Compass. Similar arrangements apply to temporary interruption or permanent withdrawal. The College will inform your Local Education Authority about any change in your course of study, but you are also required to write to your LEA. 8. MODULE/COURSE UNIT LISTING This part of the handbook gives a provisional list of modules, which may be modified before the session begins. Be reminded that you should always consult your Programme Director about prerequisites for the modules and your intended programme. Please remember that you may and should consult members of staff; this includes consultation by students who are not attending the particular staff member's module. The names of staff members willing to help with each module will be publicised on departmental notice boards and given on the information sheet for the course. At the start of each module, the lecturer will hand out a Course Information Sheet, which includes more detailed information about the module.

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4CCM111a (CM111A) Calculus I

Lecturer: Professor PK Sollich Web page: via links from King's Maths home page Semester: First Teaching arrangements: Three hours of lectures each week, one tutorial per week, throughout the term; one hour of maple tutorial for half the term. Prerequisites: A-level mathematics Assessment: The module is assessed by several 30-minute class tests held at intervals during the First Semester, together with a two-hour written examination in January; there are NO resit class tests. The class tests together contribute 20% towards the final mark and the written examination in January generates the remaining 80%; the overall pass mark is 40%. Assignments: Exercises will be given out and questions set each week to be handed in the following week. These problems will be discussed in the tutorials and solutions will be available on the web. In addition, the Maple tutorials will proceed via a series of computer-based exercises; these are assessed for satisfactory completion directly in the Maple tutorials. A full statement of the regulations for tests and assignments will be handed out in lectures at the start of term. Aims and objectives: The aim of the module is to review and enhance aspects of pre-university mathematics in order to foster genuine confidence and fluency with the material. This will help provide a firm grasp of basic ideas thus allowing concentration on the many new and often abstract concepts that will be introduced in various modules throughout the academic programme. Syllabus: Complex numbers; trigonometric functions; the logarithm and exponential functions; limits; review of differentiation; integration; series; Taylor's theorem; use of Maple. Books: This module does not follow any particular book but printed “skeleton” notes will be made available. These will need to be filled in during lectures with proofs, examples etc. In addition, there are many books which you might find helpful for the module-to provide background, alternative explanations, and generally supplement the lectures. The typical US-style introductory Calculus book has on the order of 1000 pages, is rather heavy to carry around, and goes a long way beyond this module (but will not necessarily cover all the material either). Having said that, such books can be very well written and also useful for Calculus II next semester, and also possibly for Analysis I or Joint Honours Analysis. There are any number to choose from, mostly located in section QA303 in the library - not a bad example being

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Calculus (one and several variables) by Salas, Hille and Etgen, Wiley (10th edition, 2007, or earlier editions). Less typical is: Maths - A Student's Survival Guide, Jenny Olive, CUP which is written in a very `chatty' style. It is intended for `science' students, rather than mathematics students, and so in parts it is rather basic, as well as missing out some of the more advanced topics, but it has well written sections on most of the material covered in this module. Finally, a book which might also prove useful is: Engineering Mathematics by K.A. Stroud, Palgrave 2001 Again this is not intended for mathematics students, but covers almost all the topics in the module in a very straightforward and clear way with many worked examples, and might prove useful if you find the other books too technical or need to see more examples. Maple: Maple is a very versatile and powerful computer package for performing mathematical calculations, from the simplest all the way to research level. As part of this module students must attend compulsory laboratory sessions designed to introduce them to aspects of Maple. The times of the various sessions will be displayed on the notice board and the module web page.

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4CCM112a (CM112A) Calculus II Lecturer: Dr S Schafer-Nameki Web page: See departmental web pages Semester: Second Teaching arrangements: Three hours of lectures each week, together with a one-hour tutorial. Prerequisites: 4CCM111a (CM111A) Calculus I, or equivalent. Assessment: There are three assessments during the semester, which count for 20% of the final mark. The remaining 80% of the course marks are assessed by a two-hour written examination at the end of the academic year. Assignments: There are exercises included in the course notes and you will be set a selection of questions each week. Some of these are for group work in a tutorial, some for homework. All students are expected to hand in their homework by a set date for marking and discussion at a subsequent tutorial. Aims and objectives: The course aims to extend the methods of calculus of one variable to calculus for functions of many variables, that is, calculus on higher dimensional spaces. This involves concepts such as multiple integrals and partial derivatives, which enable us to make sense of the idea of length of a curve, area of a surface, and maxima and minima of functions of many variables. The final part of the course presents the great integral theorems: Green’s Theorem, Stokes’ theorem and the Divergence Theorem which form a cornerstone of mathematics. Syllabus: Surface sketching, partial derivatives, multiple integrals, geometry of curves, vector fields, geometry of surfaces, maxima and minima, generalised derivatives, Stokes’ Theorem, the Divergence Theorem. Books: The Course Notes will be available at the start of the semester. There are many texts on this subject, and you might take a look at the following: R Adams, Calculus, a complete course (6th Edition) – this includes sections on calculus using Maple J Marsden, A Tromba, Vector Calculus (4th Edition) Salas and Hille, Calculus: one and several variables (6th Edition) McCallum et al., Multivariable Calculus W Cox, Vector Calculus You may also want to look at the worked problems in the following Schaum outline books by Murray Spiegel: Schaum's Outline of Theory and Problems of Advanced Calculus Schaum's Outline of Theory and Problems of Vector Analysis

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4CCM113a (CM113A) Linear Methods Lecturer: Dr PL Kassaei Web page: http://www.mth.kcl.ac.uk/courses/cm113 Semester: First Teaching arrangements: Three one-hour lectures each week. In addition, a one-hour tutorial each week (beginning Week 2) to discuss Homework exercises from the previous week. Pre-requisites: A-level Mathematics (algebra, trigonometry, geometry and calculus). Assessment: There are three tests during the semester, with the fourth one in January, all of which comprise 20% of the final mark. The remaining 80% of the course marks are assessed by a two-hour written examination at the end of the academic year. Assignments: There will be a weekly sheet of Homework exercises. You must attempt these to keep up with the course. Solutions are later posted on the web page. Aims and objectives: Linear algebra provides basic ideas and tools for much of the work we do in mathematics, particularly the aspects which concern geometry in 3D Euclidean space. The course introduces the general notion of linearity, a principle which illuminates wide areas of Mathematics. In pursuit of this, we cover a range of topics and provide a unifying framework for them. Syllabus: 1. Algebra and geometry of vectors in R2, R3 and Rn. Lines and planes, linear

independence and bases. 2. Matrices, systems of linear equations and linear maps, inverse matrices. 3. Determinants; the cross product for vectors in R3. 4. Eigenvalues & eigenvectors; similarity; complex matrices; canonical forms for rank 2

matrices. 5. Linear ordinary differential equations; solutions, principle of linearity, linear systems. Coursework: Homework exercises and occasional class tests. Course Notes: There is a set of lecture notes for this course, containing all the material to be covered in lectures. They will be available from the departmental office. Other Reference Texts. In addition, many textbooks in the library cover some or all of the course, including: [1] H. Anton and C. Rorres, Elementary Linear Algebra with Applications (J.Wiley). [2] F. Ayres, Linear Algebra, Schaum Outline Series (McGraw-Hill). Many worked problems.

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4CCM115a (CM115A) Numbers and Functions

Lecturer: Dr AB Pushnitski Web page: http://www.mth.kcl.ac.uk/courses/cm115 (or via links from the King’s web page) Semester: First Teaching arrangements: Three hours of lectures each week, together with a one-hour tutorial. Aims and objectives: To introduce the ideas and methods of university level pure mathematics. In particular, the module aims to show the need for proofs, to encourage logical arguments and to convey the power of abstract methods. This will be done by example and illustration within the context of a connected development of the following topics: real numbers, sequences, limits, series. Brief outline of syllabus: Sets and functions. Real numbers. Sequences: boundedness, convergence, subsequences, Cauchy sequences. Assessment: There are three tests during the semester, and a fourth test in January, which count for 20% of the final mark. The remaining 80% of the marks are assessed by a three- hour written examination at the end of the academic year. Assignments: Exercise sheets are handed out on a weekly basis and written answers must be given in by the due date. Books: There is no set book for the module. However, there are a variety of books that are useful for certain sections: K.E.Hirst, Numbers, Sequences and Series. (Edward Arnold, 1995) V.Bryant, Yet Another Introduction to Analysis (Cambridge University Press, 1990) R.Haggarty, Fundamentals of Mathematical Analysis. (Addison-Wesley, 1992)

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5CCM115b (CM115B) Numbers and Functions for Joint Honours

Lecturer: Dr AB Pushnitski Web page: http://www.mth.kcl.ac.uk/courses/cm115 (or via links from the King’s web page) Semester: First Teaching arrangements: Three hours of lectures each week, together with a one-hour tutorial. Aims and objectives: To introduce the ideas and methods of university level pure mathematics. In particular, the module aims to show the need for proofs, to encourage logical arguments and to convey the power of abstract methods. This will be done by example and illustration within the context of a connected development of the following topics: real numbers, sequences, limits, series. Brief outline of syllabus: Sets and functions. Real numbers Sequences: boundedness, convergence, subsequences, Cauchy sequences. Assessment: The module is assessed by a three-hour written examination at the end of the academic year. Assignments: Exercise sheets are handed out on a weekly basis and written answers must be given in by the due date. Books: There is no set book for the module. However, there are a variety of books that are useful for certain sections: K.E.Hirst, Numbers, Sequences and Series. (Edward Arnold, 1995) V.Bryant, Yet Another Introduction to Analysis (Cambridge University Press, 1990) R.Haggarty, Fundamentals of Mathematical Analysis. (Addison-Wesley, 1992)

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4CCM121a (CM121A) Introduction to Abstract Algebra Lecturer: Professor DJ Burns

Web page: http://www.mth.kcl.ac.uk/courses/ (or via links from the King’s web page)

Semester: Second Teaching arrangements: Three hours of lectures and a one-hour tutorial each week. Assessment: There are three tests during the semester, which count for 20% of the final mark. The remaining 80% of the course marks are assessed by a three-hour written examination at the end of the academic year. Assignments: Problem sheets are given out at the end of each week. All students are expected to hand in their work on these sheets the following week so that this can be marked, returned and discussed at the subsequent tutorial. Aims of the course: The main aim of the course is to introduce students to basic concepts from abstract algebra, especially the notion of a group. The course will help prepare students for further study in abstract algebra as well as familiarize them with tools essential in many other areas of mathematics. The course is also intended to help students in the transitions from concrete to abstract mathematical thinking and from a purely descriptive view of mathematics to one of definition and deduction. Syllabus: The integers: Principle of induction, Division Algorithm, greatest common divisor.

Linear diophantine equations. Prime numbers, unique factorisation. Groups: Examples - roots of unity, rotations, symmetries, dihedral groups, matrices,

permutations. Group axioms and elementary properties. The order of an element and the orders of its powers. Subgroups, cosets, Lagrange’s theorem. Cyclic groups, subgroups of cyclic groups. Homomorphisms, Kernels, isomorphisms, isomorphism classes of cyclic groups.

Rings: Axioms, examples and elementary properties. Group of units of a ring, units of the ring Z of residue classes of integers modulo n. Integral domains, fields. Homomorphism and isomorphism of rings.

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Congruences: Solution of linear congruences. Simultaneous linear congruences, Chinese Remainder Theorem. Properties of the Euler function. Theorems of Euler and Fermat.

Polynomials: Degree. Euclidean Algorithm, greatest common divisor. Unique factorisation theorem for polynomials over a field. Number of zeros of a polynomial over a field. Polynomials over the rationals - Gauss’s lemma, Eisenstein’s criterion.

Books: A set of lecture notes for the course is available from the Mathematics Office.

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5CCM121b (CM121A) Introduction to Abstract Algebra for Joint Honours Lecturer: Professor DJ Burns

Web page: http://www.mth.kcl.ac.uk/courses/ (or via links from the King’s web page)

Semester: Second Teaching arrangements: Three hours of lectures and a one-hour tutorial each week. Assessment: The course will be assessed by a three-hour written examination at the end of the academic year. Assignments: Problem sheets are given out at the end of each week. All students are expected to hand in their work on these sheets the following week so that this can be marked, returned and discussed at the subsequent tutorial. Aims of the course: The main aim of the course is to introduce students to basic concepts from abstract algebra, especially the notion of a group. The course will help prepare students for further study in abstract algebra as well as familiarize them with tools essential in many other areas of mathematics. The course is also intended to help students in the transitions from concrete to abstract mathematical thinking and from a purely descriptive view of mathematics to one of definition and deduction. Syllabus: The integers: Principle of induction, Division Algorithm, greatest common divisor.

Linear diophantine equations. Prime numbers, unique factorisation. Groups: Examples - roots of unity, rotations, symmetries, dihedral groups, matrices,

permutations. Group axioms and elementary properties. The order of an element and the orders of its powers. Subgroups, cosets, Lagrange’s theorem. Cyclic groups, subgroups of cyclic groups. Homomorphisms, Kernels, isomorphisms, isomorphism classes of cyclic groups.

Rings: Axioms, examples and elementary properties. Group of units of a ring, units of the ring Z of residue classes of integers modulo n. Integral domains, fields. Homomorphism and isomorphism of rings.

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Congruences: Solution of linear congruences. Simultaneous linear congruences, Chinese Remainder Theorem. Properties of the Euler function. Theorems of Euler and Fermat.

Polynomials: Degree. Euclidean Algorithm, greatest common divisor. Unique factorisation theorem for polynomials over a field. Number of zeros of a polynomial over a field. Polynomials over the rationals - Gauss’s lemma, Eisenstein’s criterion.

Books: A set of lecture notes for the course is available from the Mathematics Office.

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4CCM122a (CM122A) Geometry I Lecturer: Dr G Tinaglia Web page: Follow links from King’s Maths home page Semester: First Teaching arrangements: Three hours of lectures each week, together with a one-hour tutorial. Aims and objectives: Geometrical ideas are central to several of modern mathematics. This module aims to describe and link various rather different approaches to geometry, and in doing so encourage logical argument and convey the power of abstract methods. At the end of the module a student should understand the key basic ideas in the topics listed below and have developed abilities to construct mathematical arguments and tackle challenging problems using a range of techniques. Brief outline of syllabus Euclidean geometry, the plane R2, transformations, Non-Euclidean geometries, a brief introduction to projective geometry. Assessment: Class tests held during the semester and in January together count for 20% of the final mark. The remaining 80% of the marks are assessed by a three-hour written examination in May. Assignments: Exercise sheets are handed out on a weekly basis and written answers must be given in by the due date. Course notes It is an important part of studying this module that each student takes notes during lectures and edits these into a good set of notes on the material. Books: G. D. Birkhoff and R. Beatley, Basic Geometry (AMS Chelsea Publishing) J. R. Silvester, Geometry Ancient and Modern (Oxford, 2001) D. A. Brannan, M. F. Esplen and J. J. Gray, Geometry, (Cambridge University Press) M. J. Greenberg, Euclidean and Non-Euclidean Geometries: Development and History (W. H. Freeman and Company)

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5CCM122b (CM122A) Geometry I for Joint Honours Lecturer: Dr G Tinaglia Web page: Follow links from King’s Maths home page Semester: First Teaching arrangements: Three hours of lectures each week, together with a one-hour tutorial. Aims and objectives: Geometrical ideas are central to several of modern mathematics. This module aims to describe and link various rather different approaches to geometry, and in doing so encourage logical argument and convey the power of abstract methods. At the end of the module a student should understand the key basic ideas in the topics listed below and have developed abilities to construct mathematical arguments and tackle challenging problems using a range of techniques. Brief outline of syllabus Euclidean geometry, the plane R2, transformations, Non-Euclidean geometries, a brief introduction to projective geometry. Assessment: The module is assessed by a three-hour written examination in May. Assignments: Exercise sheets are handed out on a weekly basis and written answers must be given in by the due date. Course notes It is an important part of studying this module that each student takes notes during lectures and edits these into a good set of notes on the material. Books: G. D. Birkhoff and R. Beatley, Basic Geometry (AMS Chelsea Publishing) J. R. Silvester, Geometry Ancient and Modern (Oxford, 2001) D. A. Brannan, M. F. Esplen and J. J. Gray, Geometry, (Cambridge University Press) M. J. Greenberg, Euclidean and Non-Euclidean Geometries: Development and History (W. H. Freeman and Company)

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4CCM131a / 5CCM131b (CM131A) Introduction to Dynamical Systems Lecturer: Dr A Annibale Web page: http://www.mth.kcl.ac.uk/courses/ (or via links from King's Maths home page) Semester: Second Teaching arrangements: Three hours of lectures will be held each week. The classes will be divided in five for tutorials. Tutorial groups will be allocated in the first week of term and the lists will be posted on the course web page. Prerequisites: Normally CM111A Calculus I, and CM113A Linear Methods Assessment: 4CCM131A: There are three tests during the semester, which count for 20% of the final mark. The remaining 80% of the course marks are assessed by a two-hour written examination at the end of the academic year. 5CCM131B: There is a two-hour written examination at the end of the academic year, which represents 100% of the final grade of this module. Assignments: Exercise sheets will be given out. Solutions handed in will be marked and difficulties discussed during tutorials and in class. Assignments are regarded as an essential element of the course as they provide the necessary opportunity for active training and for sharpening ideas about the material presented in the course. Aims and objectives: The course aims to introduce students to the analysis of simple dynamical systems described in terms of first or second order differential equations, emphasising concepts such as phase flow, fixed points, and stability of fixed points. The ideas introduced have applications in biology and economics, as well as in Newtonian mechanics. Newtonian mechanics is taught with emphasis on motion in one spatial dimension, and in that case furnishes examples of so-called second order dynamical systems. Elements of the Hamiltonian approach to Newtonian mechanics are also introduced. Syllabus: Differential equations; first-order dynamical systems, autonomous systems, phase flow and fixed points; second-order dynamical systems, phase flow, classification of fixed points; kinematics of particle motion, Newton's laws; conservation of energy, conservative forces, motion on a straight line; Hamiltonian systems; elements of Hamiltonian mechanics.

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Books: (i) Introduction to dynamics, by I. Percival and D. Richards (Cambridge University Press), (ii) Differential equations, maps and chaotic behaviour, by D.K. Arrowsmith and C.M. Place (Chapman Hall), (iii) Mechanics, by P.C. Smith and R.C. Smith (Wiley), (iv) Differential Equations and Their Applications, by M. Braun (Springer) Notes: A set of lecture notes will be available on the course web page. These notes cover virtually all material of the course, but the course will not follow the notes strictly.

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4CCM141a / 5CCM141b (CM141A) Probability and Statistics I Lecturer: Dr E Katzav

Web page: http:/ http://www.mth.kcl.ac.uk/courses/ (or via links from King’s Maths home page)

Semester: Second Teaching arrangements: Three hours of lectures each week, and a weekly tutorial of one hour. Prerequisites: None, but the module is a prerequisite for more advanced probability and statistics modules such as Probability and Statistics II. Aim: The aim of the module is to introduce the basic concepts and computations of probability theory as well as the statistical analysis of data and the main statistical tests. Syllabus: Elementary combinatorial analysis, Definition of probability, Unions and intersections - Statistical Independence, Exclusivity and exhaustibility, Conditional probability, Bayes’ theorem, Random variables discrete and continuous, The binomial distribution, the Poisson distribution, the normal distribution, Descriptive Statistics, Correlation and regression, Hypothesis tests, confidence intervals, Normal, Students t, Chi squared, Sign, Mann Whitney and Wilcoxon tests Reading: A good textbook that covers all the material of the module, and which is also used in the more advanced Probability and Statistics II is Wackerley, Mendenhall & Scheaffer, Mathematical Statistics with Applications. One highly recommended collection of tables which you will find useful in this module D.V. Lindley and W.F. Scott, New Cambridge Statistical Table, Second Edition (Cambridge University Press.) Assessment: The current arrangement is 3 class tests (together contributing 20%) and a 2 hour examination in May for the remaining 80%. You should make every effort to attend all the class tests. (There are no resits.) Do prepare for the tests so that you will be able to maximize the 20% coursework component. The exam paper is also the answer booklet. You must write your answer at the appropriate places on the question paper. Rough work, which will not be marked, can be done on the reverse sides of the question paper, or in additional booklets. During the examination you will have access to the New Cambridge Statistical Tables. You may bring a college approved calculator.

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5CCM211a / 6CCM211b (CM211A) PDEs & Complex Variables Lecturer: Professor SG Scott Web page: http://www.mth.kcl.ac.uk/courses Semester: First Teaching arrangements: Three hours of lectures each week, together with a one-hour tutorial class. Prerequisites: A thorough knowledge of 4CCM112a (CM112A) Calculus II. It will be helpful to attend 5CCM221a (CM221A) Analysis I, possibly concurrently, or to have attended 5CCM250a (CM2504) Applied Analytic Methods, but neither of these is essential. Assessment: The module will by assessed by a two-hour written examination at the end of the academic year. Assignments: Exercises will be given out on a weekly basis, starting in the first week of the module; it is essential that you make a serious attempt to do these. Solutions handed in will be marked and difficulties discussed in the tutorial class. In addition, it is essential that students work through the lectures as the module progresses. Aims and Objectives: The theory of Partial Differential Equations (PDEs) forms the basis for many fundamental areas of mathematics. Apart from their fundamental role in physics and mechanics, such as in describing how electromagnetic-waves propagate through space, PDEs also provide the tools for many areas of pure mathematics. In ‘geometric analysis’, for instance, the way in which a given space is curved (e.g a surface such as a sphere) is studied by associating to it a geometric evolution equation ---- the idea is this, different spaces sound differently when you tap them, as for example we know from tapping drums of different shapes and sizes; the question, then, is “can you hear the shape of a drum”? An important technique in solving PDEs is provided by functions of a complex variable, which constitutes one of the most elegant branches of pure mathematics. The second part of the module will be devoted to the implementation of those techniques. The module will be taught in a manner akin to Calculus II, That is, this is a ‘methods course’ and so will not deal with the many abstractions that a more rigorous exposition would entail. Nevertheless, a student who has mastered this module will be in a strong position to appreciate the subtleties of a rigorous module on Complex Analysis such as CM322C, or one of the many third and fourth year modules dealing with various aspects of PDEs.

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Syllabus: Partial Differential Equations Basic ideas: linear equations, homogeneous equations, superposition principle. Laplace’s equation in two variables, simple boundary value problems. Separation of variables. Fourier series. Introduction to Fourier transforms with applications. Complex Variable Revision of complex numbers. Basic definitions: open sets, domain, curves, trace of a curve. Definitions of continuity, differentiability, analyticity. Cauchy-Riemann equations. Integration along a smooth curve; integration along a contour; Cauchy’s theorem. Cauchy’s integral formula, Laurent’s theorem, Taylor’s theorem. Calculus of residues. Contour integration.

Books:

Many books serve to give further information on the topics covered --- visit the Chancery Lane library! – or visit Foyles bookshop in Charing Cross Road. The following are a few suggestions --- but are fairly arbitrary choices:

For a good quite rigorous text on PDEs:

W A Strauss, Partial Differential Equations An Introduction (Wiley)

Less theory based, possibilities are (for example)

P. Drabek, G. Holubova, Elements of Partial Differential Equations, (de Gruyter) Y. Pichover, J. Rubinstein, An Introduction to Partial Differential Equations, (CUP) N. Asmar, Partial Differential Equations with Fourier Series and Boundary Value Problems, (Pearson, Prentice-Hall) H F Weinberger, Partial Differential Equations with Complex Variables and Transform Methods (Dover 1995)

For complex variable theory:

H A Priestley, Introduction to Complex Analysis (2nd Edition) (OUP)

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5CCM221a (CM221A) Analysis I Lecturer: Professor Y Safarov

Web page: http://www.mth.kcl.ac.uk/courses/ or via links from King’s Maths home page Semester: First Teaching arrangements: Three hours of lectures each week, together with a one hour tutorial. Prerequisites: 4CCM115a Numbers and Functions (or equivalent background). Assessment: The module will be assessed by a two hour written examination at the end of the academic year. There will be three class tests during the module, each of which will carry 5% of the final grade. The dates will be announced in advance. There will be no duplicate class tests for absentees. Students who miss class tests without good reason will get zero marks. Students who miss class tests for good reason (e.g. can supply doctors’ certificates) will be given an appropriately higher weighting for the final examination. Assignments: Exercise sheets will be given out. Solutions handed in will be marked. Students must realise that for successful progress in the module, the coursework has to be done regularly, as it is handed out. Aims and objectives: Real Analysis is one of the core subjects in every reputable Mathematics degree programme. It enables us to explain why results require proof and that statements are only true in a context of some precise technical conditions. It also provides the knowledge needed to make sense of a variety of other topics in the syllabus, such as complex analysis, dynamical systems and differential equations, all of which have immense importance within the subject. It is expected that students will understand and be able to reproduce the proofs of the major theorems of the subject. They should also appreciate the logical relationships between the different parts of the subject and be able to use the ideas of the module in a variety of situations. Syllabus: The module builds upon the material in 4CCM115a Numbers and Functions, which you are expected to know. It emphasises the difference between school level calculus and a rigorous treatment of the same topics. The material starts with definitions of limits of sequences and series, and simple criteria for convergence, with many examples of the kind you should learn how to handle. This part of the module includes the Cauchy criterion, absolute convergence of series and a study of power series. Real variable theorems include definitions of continuity and differentiation with proofs of well established theorems for functions of a single real variable up to Taylor's theorem. Properties of an elementary integral in one space dimension will be studied briefly, starting from a list of axioms for the integral. Proofs will be given of the fundamental theorem of calculus and of the rules for evaluating integrals.

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Books: You are advised to acquire and use one of the following books (all available in the library): ▪ K G Binmore: Mathematical Analysis, a straightforward approach, Cambridge University Press. ▪ R Haggarty: Fundamentals of Mathematical Analysis. Addison Wesley. ▪ David S. Stirling : Mathematical Analysis and Proof, Albion. ▪ David Brannan: A First Course in Mathematical Analysis, Cambridge University Not all the books adopt the same approach to integration and some notes will be distributed on this topic.

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5CCM222a / 6CCM222b (CM222A) Linear Algebra Lecturer: Professor FI Diamond

Web page: http://www.mth.kcl.ac.uk/courses/ (or via links from King’s Maths home page)

Semester: First

Teaching arrangements: Three hours of lectures plus a 1hr. tutorial each week.

Prerequisites: 4CCM113a (CM113A) or similar course giving familiarity with basic vectors and matrices in Rn (especially R2 and R3); 4CCM121a (CM121A) or some course containing abstract algebraic ideas.

Assessment: For 5CCM222A, a 2hr. written examination at the end of the academic year will count for 85% of total mark. In addition there will be 3 class tests during the semester, time-tabled separately from the lectures (each counting for 5% of the total mark). For 6CCM222B, there are no class tests and the exam counts for 100% of total mark

Assignments: Regular exercise work is essential for success in this course. Exercises will be set and marked weekly and the performance of each student will be recorded for later reference.

Aims and objectives: This course sets concepts from the ‘methods' course 4CCM113a (CM113A) (e.g. determinant and dimension) in the more general framework of abstract vector spaces. It also gives the precise definitions and proofs that are essential for much of higher mathematics, both pure and applied. Further concepts and methods are also introduced in the same manner. Examples from Rn and Cn will be given where possible to illustrate the geometrical meaning behind the algebraic ideas. The course will emphasize the interplay between abstract and more concrete ideas.

Syllabus: General definition and properties of vector spaces, subspaces and linear maps. Linear independence, basis and dimension. Rank and nullity for linear maps. The relation between linear maps and matrices. Change of basis and similarity of matrices. Inverse matrices. Eigenvectors, eigenvalues and diagonalisation of matrices. Inner product spaces and orthogonal diagonalisation.

Books: The course will not follow one particular textbook. There is a vast array of books on linear algebra that contain the material of the course (often also covering the preliminary material from linear methods). Here is a small sample, listed in roughly increasing order of sophistication:

1. ‘Elementary Linear Algebra’, Howard Anton, 8th ed., Wiley, 2000. 2 ‘Linear Algebra with Applications', W. Keith Nicholson, 3rd ed. PWS 1995. 3 ‘Linear Algebra', RBJT Allenby, Edward Arnold Modular Mathematics, 1995. 4 ‘Elementary Linear Algebra' W. Keith Nicholson,1st ed., McGraw-Hill, 2001. 5. ‘Basic Linear Algebra’ T.S. Blyth and E.F. Robertson, Springer 1998. 6. ‘Linear Algebra’ S. Lang, Addison-Wesley, 1966. 7. ‘Introduction to Linear Algebra’ Thomas A. Whitelaw, Blackie 1991. 8. ‘Linear Algebra’ A. Mary Tropper, Nelson 1969.

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5CCM223a / 6CCM223b (CM223A) Geometry of Surfaces Lecturer: Dr G Tinaglia Web page: Follow links from King’s Maths home page Semester: Second Teaching arrangements: Three hours of lectures each week, together with a one-hour tutorial Prerequisites: 4CCM111a (CM111A) Calculus I, 4CCM112a (CM112A) Calculus II, 4CCM113a (CM113A) Linear Methods Assessment: The module will be assessed by a two-hour written examination at the end of the academic year. There will be two versions of the final exam paper, a version for second year students and a slightly more difficult version for third year students. Assignments: Exercise sheets will be given out each week. Solutions handed in will be marked and difficulties discussed in the tutorial. Aims and objectives: This module will apply the methods of calculus to the geometry of curves and surfaces in three-dimensional space. The most important idea is that of the curvature of a curve or a surface. The module should prepare you for more advanced modules in geometry, as well as courses in mathematical physics such as relativity. Syllabus: Definition of a curve, arc length, curvature and torsion of a curve, Frenet-Serret equations. Definition of a surface patch, first fundamental form, isometries, conformal maps, area of a surface. Second fundamental form of a surface, gaussian, mean and principal curvatures. Gauss map. Theorema Egregium. Geodesics. Gauss-Bonnet theorem. Books: M. P. Do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, 1976 A. Pressley, Elementary Differential Geometry, Springer, 2001 A Gray, Modern Differential Geometry of Curves and Surfaces, CRC Press, 1993 S. Montiel and A. Ros, Curves and Surfaces, American Mathematical Society

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5CCM224A / 6CCM224B (CM224X) Elementary Number Theory Lecturer: Dr B Noohi Web page: http://www.mth.kcl.ac.uk/courses/ Semester: Second Teaching arrangements: Three hours of lectures and a one-hour tutorial each week. Prerequisites: Introduction to Abstract Algebra (4CCM121A or 5CCM121B) Assessment: The module will be assessed by a class test during the semester (counting for 10% of the final mark) and a two-hour written exam at the end of the academic year (counting for 90% of the final mark). There will be two versions of the final exam paper, a version for second year students and a slightly more difficult version for third year students. Assignments: Problem sheets will be given out every week, and work handed in will be marked and returned to the student. Solutions will be posted on the course web page. Aims and objectives: The aim of this module is to give an introduction to elementary number theory and to further develop the algebraic techniques met in ‘Introduction to Abstract Algebra’. By introducing several new concepts in the concrete setting of rational integers, this module is a good preparation for more demanding modules in number theory and algebra. Syllabus: Review of divisibility, prime numbers and congruences. Residue class rings, Euler’s φ-function, primitive roots. Quadratic residues and quadratic reciprocity law. Irrational and transcendental numbers. Sums of squares. Some Diophantine equations. Books: The module is not based on any particular book, but the following books may be useful: D. M. Burton, Elementary Number Theory, McGraw-Hill Education, 5th ed., 2001. J. H. Silverman, A Friendly Introduction to Number Theory, Prentice Hall, 3rd ed., 2005. G. A. Jones and J. M. Jones, Elementary Number Theory, Springer, 1998.

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5CCM231a / 6CCM231b (CM231A) Intermediate Dynamics

Lecturer: Dr PP Cook

Web page: http://www.mth.kcl.ac.uk/courses/ (or via links from King's Maths home page)

Semester: First

Teaching arrangements: Three hours of lectures plus a one-hour tutorial each week. Prerequisites: Normally 4CCM131a (CM131A) Introduction to Dynamical Systems. Assessment: The module will be assessed by a two-hour written examination at the end of the academic year. The examination will closely follow the material covered in lectures and homework assignments. You may bring a College approved calculator. Aims: The aim of the module is to develop the basic concepts and mathematical techniques of classical analytical mechanics, including Newtonian, Lagrangian, and Hamiltonian methods, and to lay the foundation for studies of quantum theory, statistical mechanics, and chaos. Syllabus: Newton's Laws; Conservation Laws; Kepler's Laws; Lagrangian Dynamics; Hamiltonian Dynamics; Poisson Brackets; Noether's Theorem; Liouville's Theorem and the Poincare Recurrence Theorem. If there is sufficient time the Action Principle and modes of vibration will also be studied. Books: Any of the many books you can find in the library on classical mechanics or dynamics can be consulted including: 1. H. Goldstein, C. Poole and J. Safko, Classical Mechanics 2. T. W. Kibble and F. H. Berkshire, Classical Mechanics 3. A. P. French and M. Ebison, Introduction to Classical Mechanics However, the lectures will cover precisely those things you will need to know. Therefore, you are advised to attend all lectures, and take time to read through and think about the notes.

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5CCM232a / 6CCM232b (CM232A) Groups and Symmetries Lecturer: Dr B Doyon Web page: http://www.mth.kcl.ac.uk/courses/ (or via links from King’s Mathematics Dept. home page) Semester: Second Teaching arrangements: Three hours a week and one hour tutorials, four tutorial groups Assessment: The module will be assessed by a two-hour written examination at the end of the academic year. Assignment: Weekly homework will be given out. Solutions handed in will be marked. Difficulties with the material will be explained during the tutorials. The solutions to the tutorial questions and homework will be posted on the internet about a week after distribution of the problems. Aims and objectives: To provide an understanding of group theory and its applications in geometry and theoretical physics. Syllabus: General group theory: Definitions of a group, cyclic groups, coset spaces, conjugacy classes, normal subgroups, quotient groups, dihedral groups, isomorphism theorems, group of automorphisms. Classical groups: GL(n,R), U(n), SU(n), 0(n), S0(n) and the various relations between them; centres of classical groups; 0(n) = Z2 x S0(n), n odd; scalar product and 0(n), U(n); parametrization of S0(2) and S0(3), rotations in R2 and R3; S0(3) = SU(2)/Z2; Euclidean group, Lorentz group. Lattice groups; lattices, lattice translations and rotations; crystallographic restriction; two-dimensional lattice symmetry groups. Books: J F Humphreys: A course in Group Theory, Oxford Science Publications C Isham: Lectures on Groups and Vector Spaces for Physicists, World Scientific E Wigner: Group Theory, Academic Press

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5CCM241a / 6CCM241b (CM241X) Probability and Statistics II

Lecturer: Professor PT Saunders

Web page: http://www.mth.kcl.ac.uk/courses/ Semester: Second Teaching arrangements: Three lectures and one tutorial per week Prerequisites: 4CCM141a (CM141A) Probability and Statistics I Assessment: One two-hour examination in May Assignments: Exercise sheets will be handed out weekly and work handed in within a week will be marked and returned to the student. Solutions will be posted on the web and any remaining difficulties can be discussed in the tutorial. Aims and objectives: This course should make you familiar with the standard techniques of elementary statistics and, by introducing such fundamental concepts as hypothesis testing, estimation and analysis of variance, prepare you for further study in both theoretical and practical statistics. Syllabus: Bivariate probability, continuous densities, generating functions. The exponential densities, including normal, t-, χ2 and F. Simple parametric and nonparametric tests. Further topics include the consistency, efficiency and sufficiency of estimates, maximum likelihood estimation; the central limit theorem, the Neyman-Pearson lemma and the likelihood ratio test; regression, analysis of variance. Books: Wackerly, Mendenhall & Scheaffer: Mathematical Statistics with Applications (7th edition), Duxbury. (This text is strongly recommended but it is not compulsory.) Notes: Not provided, as there are many books that cover the material.

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5CCM250a (CM2504) Applied Analytic Methods Lecturer: Professor E Shargorodsky

Web page: http://www.mth.kcl.ac.uk/courses/ (or via links from King’s Maths home page) Semester: First Teaching arrangements: Three hours of lectures each week, together with a one-hour tutorial. Prerequisites: 4CCM112a (CM112A) Calculus II and 4CCM115a (CM115A) Numbers and Functions. Assessment: There will be three class tests during the semester, each counting for 5% of the final grade, and a two-hour written examination at the end of the academic year, counting for 85% of the final grade. There will be no duplicate class tests for absentees. Students who miss class tests without good reason will get zero marks. Students who miss class tests for good reason (e.g. can supply doctors’ certificates) will be given an appropriately higher weighting for the final examination. Assignments: Exercise sheets will be given out. Solutions handed in will be marked and difficulties discussed in the tutorials. In addition, it is essential that students work through the theory as the course progresses. Aims and objectives: This module will introduce you to various mathematical problems that can be solved by analytical means. The goal is to demonstrate in an explicit and non-abstract way the importance of Analysis and the need to justify formal methods and arguments. The module prepares you for applying analytical methods to `real world’ problems. Syllabus: About five topics will be selected from the following list: 1) evaluation of integrals from known results by differentiation under the integral, including some work on improper integrals; 2) Laplace transforms; 3) solution of ordinary differential equations by power series; 4) Fourier series – possibly used to solve the one-dimensional wave equation; 5) rudimentary calculus of variations; 6) generating functions; 7) Green’s functions for ordinary differential equations with two point boundary conditions; 8) the Dirichlet problem in the unit disc; 9) other topics at a similar level. Books: The module will be self-contained and there are no required texts. Many books serve to give further information on the topics covered. A few suggestions are given below.

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1. W. Ledermann, Integral calculus, Library of Mathematics. London: Routledge and Kegan Paul, 1964. 2. V.I. Smirnov, A course of higher mathematics. Vol. II: Advanced calculus, International Series of Monographs in Pure and Applied Mathematics. Oxford-London-Edinburgh: Pergamon Press, 1964. 3. C.H. Edwards and D.E. Penney, Differential equations and boundary value problems, Pearson Education, 2004. 4. R.K. Nagle, E.B. Saff, and A.D. Snider, Fundamentals of differential equations and boundary value problems, Pearson Education, 2004. 5. I.N. Sneddon, Fourier series, Library of Mathematics. London: Routledge and Kegan Paul, 1961. 6. G.P. Tolstov, Fourier series, New York: Dover Publications, 1976. 7. I.M. Gelfand and S.V. Fomin, Calculus of variations, Mineola, NY: Dover Publications, 2000. 8. D.I.A. Cohen, Basic techniques of combinatorial theory, New York- Chichester-Brisbane: John Wiley & Sons, 1978. 9. N. Biggs, Discrete mathematics, Oxford Science Publications, New York: The Clarendon Press, Oxford University Press, 1989.

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5CCM251a / 6CCM251b (CM251X) Discrete Mathematics Lecturer: Mr S Fairthorne Web page: http://www.mth.kcl.ac.uk/courses/ (or via links from King’s Mathematics home page Semester: Second Teaching arrangements: Three hours of lectures each week, together with a one hour tutorial. Prerequisites: Although originally designed for joint-honours Mathematics-Computer Science students, the module is also suitable for other second year single and third year joint-honours students. There are no formal prerequisites. Pre-knowledge is minimal - a little linear algebra helps. Any tools needed will be presented in the course, which can be taken by Computer Science students who have a reasonable pass in CS1MC1 or CS1FC1 and permission from their Programme Director. Assessment: The module will be assessed by a two-hour written examination at the end of the academic year. Assignments: Weekly problems are set which are for learning not assessment. In previous years there has been a strong correlation between attempting the weekly problems and passing / doing well in the exam. Aims and objectives: To give students an understanding of the nature of an algorithmic solution to problems, to illustrate the idea by applications to problems in discrete mathematics and to promote an algorithmic viewpoint in subsequent mathematical work. Syllabus: Elementary properties of Integers. Functions and their behaviour. Introduction to Recursion. Algorithms and complexity. Graphs including Euler’s Theorem, shortest path algorithm and vertex colouring. Trees - applications include problem solving and spanning trees. Directed Graphs including networks. Dynamic programming. Codes and Cyphers - with Hamming codes and RSA. Books. The module was designed as a combination of useful and interesting (hopefully both) topics and so is not based on any particular book. Books you may like to look at are (do not buy but use for background reading): Introduction to Graph Theory, Robin J Wilson Discrete Mathematics and Its Applications, Kenneth H Rosen Discrete and Combinatorial Mathematics, Ralph P Grimaldi Elementary number theory and its Applications, K H Rosen (for RSA) Notes: All the problems, solutions and prepared material shown on the OHP (with two exceptions) will appear on the module web page and can be downloaded. The web page will be updated weekly and will carry any news or announcements.

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6CCM318a Fourier Analysis

Lecturer: Dr. Behrang Noohi Web page: via links from King’s Maths home page Semester: 2 Teaching arrangements: Two hours of lectures each week.

Prerequisites: Both of CM221A and CM321A, or similar analysis courses using normed spaces.

Assessment: The course will be assessed by a two hour written examination at the end of the academic year. Assignments: Exercise sheets will be given out. Aims and objectives: The purpose of the module is to introduce the notions of Fourier series and Fourier transform and to study their basic properties. The main part of the module will be devoted to the one dimensional case in order to simplify the definitions and proofs. Many multidimensional results are obtained in the same manner, and those results may also be stated. The Fourier technique is important in various fields, in particular, in the theory of (partial) differential equations. It will be explained how one can solve some integral and differential equations and study the properties of their solutions using this technique.

Syllabus: Series expansions. Definition of Fourier series. Related expansions. Bessel's inequality. Pointwise and uniform convergence of Fourier series. Periodic solutions of differential equations. The vibrating string. Convolution equations. Mean square convergence. Schwartz space S. Fourier transform in S. Inverse Fourier transform. Parseval's formula. Solutions of differential equations with constant coefficients. Books: A book covering most of the module is: H. Dym and P. McKean, Fourier series and integrals, Academic Press, 1972.

Notes: http://www.mth.kcl.ac.uk/~ysafarov/Lectures/Past

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6CCM320a (CM320X) Topics in Mathematics This module will consist of four ‘mini-modules’ of 10-12 hours duration, and will thus enable students to gain a satisfactory understanding of the key concepts and applications of a selection of important topics in both pure and applicable mathematics. Students need only attend any selection of THREE of these four mini-modules. Web page: http://www.mth.kcl.ac.uk/courses/ (or via links from King's Maths home page) Semester: First and Second Teaching arrangements: Two hours of lectures per week Assessment: This is solely by means of a single two-hour examination at the end of the academic year, consisting of one selection for each of the mini-modules. Each of the four selections will have equal weight and students may answer questions from any selection of at most three of the sections. The mini-modules which will be offered this year are listed below. In each case, there are few pre-requisites beyond the material which is covered in the relevant core modules from the first and second year.

Game Theory Lecturer: Professor AN Pressley Prerequisites: Linear methods Assignments: Exercise sheet handed out each week. Solutions will be provided. Aims and objectives: The module aims to give an introduction to the theory of two-person zero-sum games. It should enable you to go on to more advanced topics involving linear programming, as well as applications in the theory of financial markets and economics. Syllabus: Two-person zero sum games, game trees, pure strategies, mixed strategies, optimal strategies, minimax theorems, Shapley-Snow algorithm. Books: Most books are either too advanced or depend on knowledge of other fields such as economics. I have prepared a set of printed notes to accompany the module which are available from the departmental office.

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Markov Chains Lecturer: Dr I Pérez Castillo Prerequisites: 4CCM113a (CM113A) Linear methods, 4CCM111a (CM111A) Calculus I and 4CCM112a (CM112A) Calculus II, 4CCM141a (CM141A) Probability and Statistics Assignments: Problems will be set each week. Aims and objectives: The module aims to introduce the basic concepts of finite-state, discrete-time Markov chains and to illustrate these with applications to a range of problems such as random walks and simple statistical mechanical models. Outline Syllabus: Definition of Markov chains, forward and backward equations, positive matrices, ergodicity, stationary states, Perron-Frobenius theorem. Random walks with absorbing and reflective boundaries. Interacting walkers, detailed balance, Boltzmann distributions. Possible extensions: Reaction-diffusion systems, kinetic constraints. Books: G R Grimmett and D R Stirzaker, Probability and Random Processes, OUP, 3rd edition, 2001. W Feller, An Introduction to Probability Theory and Its Applications, Wiley, 3rd edition, 1968. Notes: To be confirmed; skeletal lecture notes may be made available. Introduction to Information Theory Lecturer: Dr R Kühn

Prerequisites: Mainly 4CCM111a (CM111A) Calculus I, 4CCM112a (CM112A) Calculus II, 4CCM141a (CM141A) Probability and Statistics Assignments: Problem sheets will be made available via the course web page.

Aims and objectives: The course aims to give an introduction to concepts and methods for quantifying information, and analysing the transmission of informaion and various forms of information processing, including coding and data analysis

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Syllabus: The concept of information; introduction to Shannon's information theory: definitions and properties, with proofs, of the main tools for quantifying information, e.g. Shannon entropy, relative entropy, conditional entropy, differential entropy, mutual information; coding theory.

Books: TM Cover and JA Thomas, `Elements of Information Theory', Wiley 1991 Notes: A set of self-contained lecture notes prepared by ACC Coolen will be available at the departmental office. Distribution of Prime Numbers Lecturer: Dr DR Solomon Prerequisites: 4CCM111a Calculus I, 4CCM121a/5CCM121b Introduction to Abstract Algebra Assignments: Problem sheets will be handed out each week. Aims and objectives: The aim of this module is to discuss several important results about the distribution of prime numbers, and to give an understanding of some of the techniques used to prove these results. Syllabus: Divisibility theory of the integers, basic distribution issues, the prime number theorem, the Riemann zeta function, arithmetic functions and Dirichlet series, primes and arithmetic progressions. Books: A set of lecture notes will be available. In addition, the following books may be useful. D. M. Burton, Elementary Number Theory, McGraw-Hill Education, 5th ed., 2001. G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Oxford University Press, 5th ed., 1980. G. J. O. Jameson, The prime number theorem, Cambridge University Press, 2003.

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6CCM321a / 7CCM321b (CM321A) Real Analysis II Lecturer: Professor SG Scott Web page: http://www.mth.kcl.ac.uk/~ysafarov/Lectures/CM321A/ (or via links from King’s Maths home page) Semester: First Teaching arrangements: Two hours of lectures each week and 3-4 informal tutorials during the revision week and the last week of the term. Prerequisites: 5CCM221a (CM221A) Assessment: The module will be assessed by a two-hour written examination at the end of the academic year. Assignments: Exercise sheets will be given out. Aims and objectives: The main aims of the module are: (i) to extend your knowledge and appreciation of analysis to a wider range of situations and introduce you to the important concepts that are applicable in these more general cases; (ii) to establish the central results on continuity in this more general context; (iii) to demonstrate some applications of the theory to other parts of mathematics. Syllabus: Metrics and norms. Open and closed sets. Continuity. Bounded linear maps. Cauchy sequences. Completeness. Absolutely convergent series in complete normed spaces. Contraction mapping theorem. Connectedness and path connectedness. Totally disconnected metric spaces. Compactness. Compact and sequentially compact sets. Uniformly continuous functions. Stone--Weierstrass theorem. Integration (rigorous definition via uniform approximation by step functions). Integrals depending on a parameter. Picard's existence theorem for first order differential equations. Books: The following books contain a substantial portion of the module: J.C. & H. Burkill, A second course in mathematical analysis W.A. Light, An introduction to abstract analysis W.A. Sutherland, Introduction to metric and topological spaces A. Kolmogorov & S. Fomin, Introductory real analysis Notes: http://www.mth.kcl.ac.uk/~ysafarov/Lectures/CM321A/

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6CCM322a / 7CCM322b (CM322C) Complex Analysis

Lecturer: Professor Y Safarov

Web page: http://www.mth.kcl.ac.uk/courses/ (or via links from King’s Maths home page)

Semester: First Teaching arrangements: Three hours of lectures each week.

Prerequisites: 5CCM211a (CM211A) and 5CCM221a (CM221A)

Assessment: The module will be assessed by a two hour written examination at the end of the academic year. There will be two class tests during the module, each of which will carry 5% of the final grade. The dates will be announced in advance. There will be no duplicate class tests for absentees. Students who miss class tests without good reason will get zero marks. Students who miss class tests for good reason (e.g. can supply doctors’ certificates) will be given an appropriately higher weighting for the final examination.

Assignments: Exercise sheets will be given out. Solutions handed in will be marked. In addition, it is essential that students work through the theory as the module progresses.

Aims and objectives: This module will provide a detailed introduction to complex function theory which interrelates the geometric and analytic aspects. A principal goal is Cauchy’s famous integral theorem and its many intriguing consequences.

Syllabus: Möbius transformations, analytic functions, Cauchy-Riemann equations, complex trigonometric and exponential functions, complex logarithm, contour integration, Cauchy’s Theorem, Cauchy’s Integral Formulae, Taylor series, Identity Theorem, Liouville’s Theorem, Laurent Expansion, singularities, residues, winding number, Cauchy’s Residue Theorem, Argument Principle, Maximum Modulus Principle.

Books: Books covering most of the course are ▪ I. Stewart & D. Tall, Complex Analysis, Cambridge 1993 ▪ J. Bak & D. Newman, Complex Analysis, Springer, 1997 ▪ H A Priestley, Introduction to Complex Analysis, OUP 2003

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6CCM326a / 7CCM326b (CM326Z) Galois Theory

Lecturer: Professor D J Burns Web page: http://www.mth.kcl.ac.uk/courses/ (or via links from King's Maths home page)

Semester: Second

Teaching arrangements: Three hours of lectures each week plus occasional one-hour tutorials that will be announced in advance.

Prerequisites: 5CCM222a (CM222A) (or 4CCM113a (CM113A) with some extra preparation) and 4CCM121a (CM121A) (or CM2501 with some extra preparation).

Assessment: Assessment is by a two-hour written examination at the end of the academic year.

Assignments: Exercise sheets will be distributed in lectures. Solutions handed in the following week will be marked and returned. Solution sheets will be handed out. Particular points will be discussed in the occasional tutorials.

Aims and objectives: To develop the theory of finite extensions of fields, culminating in an understanding of the Galois Correspondence. To demonstrate the power of this theory by applying it to the solution of historically significant questions. For instance: for which polynomials can all the roots be written as `radical expressions' (i.e. expressions involving the usual operations of arithmetic together with roots of any degree)? To provide an important tool for further studies in Algebra e.g. Number Theory.

Syllabus: Review of the basic theory of rings, polynomials and fields; Eisenstein's Criterion; first properties of finite extensions of fields and their degrees; algebraicity and transcendence; field embeddings and automorphisms; normal extensions; separable extensions; the Galois Correspondence; examples of practical calculation; soluble groups and extensions; (in)solubility of polynomial equations by radical expressions. Further topics may include finite fields, constructibility by straightedge and compass, etc. as time allows.

Books: The two following are highly recommended:

(1) I. Stewart, `Galois Theory ', Chapman and Hall: 2nd ed. 1989, 3rd ed. 2004.

(2) J. Rotman, `Galois Theory ', Universitext, Springer, 2nd ed. 1998. The course most closely follows the level and order of exposition of the 2nd edition of (1). (The 3rd, expanded, edition starts at too elementary a level but contains interesting extra detail). Rotman's book (2) lacks some of the colour and historical detail of (1). On the other hand, it has useful sections on groups and rings. Further background material on groups may be found in:

(3) T. Barnard and H. Neill,`Teach Yourself Mathematical Groups', Hodder and Stoughton, 1996.

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6CCM327a / 7CCM327b (CM327Z) Topology Lecturer: Professor AN Pressley Web page: http://www.mth.kcl.ac.uk/courses/

Semester: First Teaching arrangements: Three hours of lectures each week, together with a weekly tutorial. Prerequisites: 6CCM321a (CM321A) Real Analysis II, or equivalent. However, this may in some circumstances be waived if there is a willingness to read up on the material. Assessment: The module will be assessed on a two-hour written examination at the end of the academic year Assignments: Exercises are set each week. The solutions to the homework exercises and any other difficulties will be discussed in the tutorial. It is essential that students work through the theory and homework sheets as the module progresses. Aims and objectives: The aims of the module are to introduce the basic notions of general topology and algebraic topology. The concepts of homology and/or homotopy will be introduced and methods developed for computing the resulting topological invariants. Syllabus: Topological spaces, compactness and connectedness, quotient and product topologies, topological groups, homotopy of maps, fundamental groups, covering spaces, homology. Books: JR Munkres: Topology (2nd edition), Prentice Hall, 2000 MA Armstrong: Basic Topology, Springer, 1990 DW Blackett: Elementary Topology, Academic Press, 1982 S Carlson: Topology of surfaces, Knots, and Manifolds, Wiley, 2001 ND Gilbert and T Porter: Knots and Surfaces, OUP, 1994 WS Sutherland, Introduction to Metric and Topological Spaces, OUP, 1988

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6CCM328a (CM328X) Logic

Lecturer: Professor D Makinson. Email: [email protected] or [email protected] Personal webpage: http://sites.google.com/site/davidcmakinson

Web page: http:/ http://www.mth.kcl.ac.uk/courses/ (or via links from King’s Maths home page)

Semester: Second

Prerequisites: Working knowledge of sets, relations and functions, as well as some appreciation of mathematical induction.

Aims: To introduce the student to the basic ideas of mathematical logic.

Syllabus: Classical propositional and predicate logic.

Textbooks and reading: David Makinson Sets, Logic and Maths for Computing (Springer, 2008) chapter 8 and 9 and additional notes on the module webpage.

Teaching arrangements: Three hours of lectures each week, plus a one hour ‘tutorial’ session to go through homework and exercises together. Tutorials may sometimes also introduce new lecture material.

Homework: Taken from exercises in the textbook, additional notes or assigned in class. They are not collected, but are reviewed in the tutorials.

Assessment: By a two-hour final examination at the end of the semester. The examination follows the ‘standard undergraduate’ format. Past exams: Examination papers for 2008-10 are placed on the module webpage. Papers from years earlier than that are not a good guide, as the content and angle of approach differ. Remark: The module is not difficult, but to be successful the student should attend the lectures and tutorials, read the textbook and additional notes, conscientiously attempt the exercises, and do any further homework assigned in class.

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6CCM330a (CM330X) Mathematics Education & Communication Lecturers: Mrs MJ Bennett-Rees and Professor FA Rogers Web page: http://www.mth.kcl.ac.uk/courses/cm330.html (or via links from the King’s web page) Semester: Second Important note: If you wish to take this module then you must inform Stephanie Rice in writing before the end of September 2010 by sending an email to [email protected] with the subject "6CCM330A: registration request". This does not commit you to taking the module. Numbers are limited and selection of eligible students will be by means of a short interview in early October. You should also decide which alternative module you will take in case your application to join 6CCM330A is unsuccessful and initially register for this alternative module. Please DO NOT register for 6CCM330A until you have been selected to take this module. Short Description: This module provides an opportunity for final year students to gain first hand experience of mathematics education, through a mentoring scheme with mathematics teachers in local schools. Each student will work with the same class(es) for half a day every week throughout the Spring Term (Second Semester). Students will be selected for their commitment and suitability for working in schools and will be given a range of responsibilities from classroom assistance to self-originated special projects. Aims: To help the student gain confidence in communicating their subject and develop strong organisational and interpersonal skills that will be of benefit to them in employment and in life. To enable the student to understand how to address the needs of individuals and devise and develop mathematics projects and teaching methods appropriate to engage the relevant age group they are working with. To allow the student to act as an enthusiastic role model for pupils interested in mathematics and to offer them a positive experience of working with pupils and teachers. Training and basic skills: The student will be given an initial introduction to relevant elements of the National Mathematics Curriculum and its associated terminology. They will receive basic training in working with children and conduct in the school environment and also will normally be given a chance to visit the school they will be working in before the start of the module.

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Classroom observation and assistance: Initial contact with the teacher and pupils will be as a classroom assistant, watching how the teacher handles the class, observing the level of mathematics taught and the structure of the lesson and offering practical support to the teacher. Teaching assistance: The teacher will assign the student actual teaching tasks, which will vary according to specific needs. This could include offering problem-solving coaching to a smaller group of higher or lower ability pupils or taking the last ten minutes of the lesson for the whole class. The student will have to demonstrate that the teaching they give is appropriate for the level of mathematics knowledge and understanding of the pupils they are teaching. The teacher will offer guidance to the student during their weekly interaction and also through feedback and liaison with the Departmental Module Coordinator will individually determine the level of responsibility and special project given to the student. Special project: Each student will devise a special project on the basis of his/her own assessment of what will interest the particular pupils they are working with. The student will have to show that he/she can analyse a specific teaching problem and devise and prepare appropriately targeted teaching materials (including plans for coverage of topic items, integrating structured activities for pupils and possibly basic tests). Written reports: Each student will keep a journal of her/his own progress in working in the classroom environment and will be asked to prepare a written report on the special project he/she has run, with an assessment of how well it worked and how it might be improved. Assessment Methods:

o Student’s end of module report (40%); o Teacher’s end of module report including assessment of student’s planning and

delivery of special projects (40%); o Student’s oral presentation (20%).

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6CCM331a (CM331A) Special Relativity and Electromagnetism Lecturer: Dr N Gromov Web page: http://www.mth.kcl.ac.uk/courses/ Semester: First Teaching arrangements: Three hours of lectures per week (in the first semester); some lectures can be used as tutorials and question sessions. Prerequisites: Linear methods and vector calculus; Newtonian mechanics; elements of groups and symmetries. An interest for physical applications of mathematics helps. Assignments: There will be weekly assignments which all students should complete as far as possible. Solutions will be distributed the week after. Assessment: The module will be assessed by an examination in the summer examination period. Aims and objectives: The first part of the module aims at understanding electromagnetism, both in its unified description in terms of Maxwell's equations and at the level of simple phenomena from electrostatics, magnetostatics and wave propagation. The aim of the second part is to give an introduction to Einstein's concept of space-time and to discuss Lorentz transformations and their far-reaching consequences. Syllabus: Electric and magnetic fields; charge; Lorentz force. Maxwell's equations (in various forms). Electrostatics; magnetostatics; wave equation. Inertial frames, Newtonian space and time, Galilei transformations. Propagation of light and principle of relativity. Derivation of Lorentz transformations. Consequences: simultaneity, time dilation, length contraction, etc. Lorentz group; three- and four-vectors and -tensors. Relativistic mechanics: energy and momentum, E=mc2. Relativistic formulation of electrodynamics. Books, course material: Typed course notes, problem sheets and past exam papers are available on the course homepage. In addition, the following textbooks may be useful: J.D. Jackson, Classical Electrodynamics W. Rindler, Essential Relativity R. Feynman, Lectures on Physics, vols. I and II

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6CCM332a (CM332C) Introductory Quantum Theory

Lecturer: Professor FA Rogers Web Page: http://www.mth.kcl.ac.uk/courses/ Semester: First Teaching Arrangements: Three hours of lectures each week, and one of tutorials. Prerequisites: Normally 5CCM231a Intermediate Dynamics, 5CCM222a Linear Algebra and 5CCM211a Partial Differential Equations and Complex Variable. Assessment: The module will be assessed by a two-hour written examination at the end of the academic year. Aims and Objectives: This module provides a self-contained introduction to the theory of quantum mechanics, describing the basic formalism, where states are vectors in an infinite-dimensional space and observables such as position and momentum are operators on this space, and considers the dynamics of various simple quantum systems. It is shown how two of the key features of quantum mechanics—Heisenberg's uncertainty principle and the surprising discreteness of certain quantities—flow naturally from the formalism. Syllabus: The module starts with a historical account of the problems with classical physics which led to the development of quantum physics. The remainder of the module includes a development of the basic formalism of quantum mechanics and its probabilistic interpretation, examples of simple systems, the particular case of a particle in one dimension in a variety of potentials, the Dirac delta function, Heisenberg's and Schrödinger's equations of motion and the relationship between these two approaches, a derivation of Heisenberg's uncertainty principle for two observables which do not commute and a discussion of symmetry. Books: R Shankar: Principles of Quantum Mechanics, Springer (1994) (paperback ISBN: 0306447908 hardback ISBN 0306447908) K Hannabuss, An Introduction to Quantum Theory, Oxford University Press (1997) (hardback ISBN 9780198537946) Course Materials: Supporting material, tutorial exercises and a past examination paper will appear on the web page as the module proceeds .

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6CCM334a / 7CCM334b (CM334Z) Space-Time Geometry & General Relativity

Lecturer: Professor N Lambert Web page: http://www.mth.kcl.ac.uk/courses Semester: Second Teaching arrangements: Three hours of lectures each week, and there maybe additional tutorials. Prerequisites: No formal requirements but students should be familiar with special relativity as in Special Relativity and Electromagnetism (cm331). Forbidden Combinations: It is not possible to take both this course and the Physics department course CP3630, General Relativity and Cosmology. It is not possible to take this course and the course 7CCMMS38, Advanced General Relativity, in the same year. Assessment: The courses will be assessed by a two hour written examination at the end of the academic year. Assignments: During the lectures problems will be given and then discussed the following week. Complete solutions will be made available. It is crucial that students work through these problems on their own. Aims and objectives: The aim of the course is to show how the concept of a 4-dimensional manifold provides a model for spacetime and gravity, with the geometric notions of metric and curvature leading to Einstein's general theory of relativity. The course develops differential geometry from simple cases and includes tensor calculus and covariant differentiation, as well as solutions to Einstein's field equations. Syllabus: Equivalence principle and special relativity. Basics of Geometry: Tensors, Geodesics, Connections. Einstein’s equations. Schwarzchild solution: bending of light, perihelion shift of Mercury. Cosmology: FRW, Big Bang and inflation. Books: The lecture notes taken during the lectures are the main source and there are many good books but in particular try: Hartle, “An Introduction to Einstein’s General Relativity”, Benjamin Cummings, 2003. Wald, “General Relativity”, Chicago, 1984

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6CCM338a (CM338Z) Mathematical Finance II: Continuous Time

Lecturer: Dr P Emms Web page: http://www.mth.kcl.ac.uk/courses/cm338.html Semester: Second Teaching arrangements: Two hours of lectures and a one hour tutorial weekly. Prerequisites: 6CCM388A (CM388), 4CCM141A (CM141A) essential, 5CCM241A (CM241X) advisable. Assessment: One 2 hour examination in May/June. Assignments: Exercise sheets will be given out regularly. In addition, it is essential that students work through the theory as the module progresses. Aims and objectives: This module aims to introduce students to a number of topics in continuous-time mathematical finance theory, along with the associated probabilistic background. The approach will be applied and practical in character, while at the same time mathematically rigorous. Syllabus: Students will receive an introduction to elements of the following topics: Stochastic processes in continuous time, Brownian motion; Elements of continuous-time martingale theory; Ito calculus, elementary stochastic differential equations; Absence of arbitrage, forward prices; Asset pricing in continuous time; Geometric Brownian motion asset model; Option pricing in continuous time, Black-Scholes-Merton model, PDE methods; Introduction to continuous-time term structure models Books: Lecture notes for the previous combined discrete and continuous time course are “Financial Mathematics: An Introduction to Derivatives Pricing” by Hughston & Hunter (1999). These are available from the Mathematics Department Office. This module expands on those notes using the course text book “Stochastic Calculus for Finance II: Continuous-Time Models”, 2nd Edition, Springer (2008) by S. E. Shreve. It will be assumed that you are familiar with the material in “Stochastic Calculus for Finance I: The Binomial Asset Pricing Model”, 2nd Edition, Springer (2008) by S. E. Shreve. Other good books for background reading

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1. M. W. Baxter and A. J. O. Rennie, Financial Calculus, Cambridge University Press (1996).

2. J. C. Hull, Options, Futures, and Other Derivatives, Prentice-Hall (Seventh Edition, 2008).

3. R. Jarrow and S. Turnbull, Derivative Securities, Southwestern Press (1999). 4. B. Oksendal, Stochastic Differential Equations, Springer-Verlag (Sixth Edition,

2007). 5. P. Wilmott, Derivatives, Wiley (1998).

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6CCM350a / 7CCM350b (CM350Z) Rings and Modules

Lecturer: Dr DR Solomon

Web page: http://www.mth.kcl.ac.uk/courses/cm350.html (or via links from King's Maths home page)

Semester: First Teaching arrangements: Three hours of lectures per week plus a 1 hour tutorial every other week. Prerequisites: CM121A/4CCM121A/5CCM121B Introduction to Abstract Algebra and CM222A/5CCM222A/6CCM222B, Linear Algebra. If either has not been taken, the lecturer must be consulted before registering for the module. Assessment: By a 3hr. written examination at the end of the academic year. Assignments: Exercise sheets will be distributed weekly in lectures. Full solutions will be provided and particular points discussed in tutorials. Doing the exercises and attending lectures and tutorials are essential to following the course and so must be considered compulsory. Aims and objectives: This is a second module in abstract algebra. It aims to develop the general theory of rings (especially commutative ones) and then study in some detail a new concept, that of a module over a ring. Both abelian groups and vector spaces may be viewed as modules and important structure theorems for both follow from the general theory. The theory of rings and modules is key to many more advanced algebra courses e.g. Algebraic Number Theory. It can also help with others, e.g. Galois Theory, Representation Theory and Algebraic Geometry. Syllabus: Basic concepts of ring theory: subrings, ideals, quotient, product, matrix and polynomial rings; factorisation in integral (euclidean, principal ideal) domains. Basic concepts of module theory: submodules, quotient modules, direct sums, homomorphisms, finitely generated, cyclic, free and torsion modules, annihilator ideals. Matrices and finitely generated modules over a principal ideal domain: Equivalence of matrices, structure theory of modules, applications to abelian groups and to vector spaces with a linear transformation. Books (Rough decreasing order of suitability.): 1) B. Hartley and T.O. Hawkes, `Rings, Modules and Linear Algebra', Chapman and Hall, 1970. 2) N. Jacobson, `Basic Algebra I', W.H. Freeman and co., 1974 3) M.E. Keating, A first Course in Module Theory, Imperial College Press, 1998. 4) J.A. Beachy, `Introductory lectures on rings and modules', Cambridge University Press, 1999

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5) J.J. Rotman, `A First Course in Abstract Algebra, With Applications', 3rd edition, Pearson Prentice Hall, 2006. 6) R.B.J.T. Allenby: `Rings, Fields and Groups: an Introduction to Abstract Algebra', 2nd edition, Edward Arnold, 1991. .

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6CCM351a (CM351A) Representation Theory of Finite Groups Lecturer: Dr K. Rietsch Web page: http://www.mth.kcl.ac.uk/courses Semester: Second Teaching arrangements: Three hours of lectures per week (in the second semester); some lectures can be used as tutorials and question sessions. Prerequisites: Introduction to Abstract Algebra, Linear Algebra, Groups and Symmetries (or equivalents). Assignments: There will be some assignments for practice. Assessment: The course will be assessed by an examination in the summer examination period. Aims and objectives: The aim of this module is to develop the basic theory of linear representations and characters of finite groups over the complex numbers. Syllabus: The basic definitions and standard properties of linear representations of finite groups over the complex numbers (in particular Schur’s lemma and Maschke’s theorem). The relation between representations and characters, the orthogonality relations and other fundamental properties of characters and character tables. Application of the above results to performing explicit calculations for groups of small order. One of the following more advanced topics will be covered: induction and restriction of representations and characters, algebraic integers and their applications to characters of finite groups, or representations over the real numbers Books, course material: Walter Ledermann: “Introduction to group characters''. The first half of: J-P. Serre, "Linear representations of finite groups". James & Liebeck: "Representations and Characters of Groups"

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6CCM356a (CM356Y) Linear Systems with Control Theory Lecturer: Dr DA Lavis Web page: www.mth.kcl.ac.uk/courses/cm356.html Semester: First Teaching arrangements: Three hours of lectures each week, one of the weekly lectures will be used in part to discuss assignments. This module has overlapping material with 6CCM357a and the two modules are taught concurrently. Prerequisites: Undergraduate students taking this module must have taken 4CCM131A Introduction to Dynamical Systems. (This restriction does not apply to postgraduate students who may take 6CCM356a as an allowed undergraduate module.) Assessment: The module is assessed by a 2 hour written examination at the end of the academic year. Assignments: Weekly assignments are set. Aims and objectives: To develop the theory of the use of Laplace transforms for the solution of linear differential equations and to apply this knowledge to linear control theory. Syllabus:

Laplace transforms and Z transforms. Transfer functions and feedback. Controllability and observability. Stability: the Routh-Hurwitz criterion. Optimal control: Euler-Lagrange equations. The Hamiltonian-Pontryagin method, bounded control functions and Pontryagin's

principle; bang-bang control, switching curves.

Books: S. Barnett and R. G. Cameron, Introduction to Mathematical Control Theory, O.U.P. (1985) and O. L. R. Jacobs, Introduction to Control Theory, O.U.P. (1993) are both useful references. There are multiple copies of each in the library and they can be bought on Amazon.

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6CCM357a (CM357Y) Introduction to Linear Systems with Control Theory Lecturer: Dr DA Lavis Web page: www.mth.kcl.ac.uk/courses/cm356.html Semester: First Teaching arrangements: Three hours of lectures each week, one of the weekly lectures will be used in part to discuss assignments. This module has overlapping material with 6CCM356a and the two modules are taught concurrently. Prerequisites: Undergraduate students taking this module must not have taken 4CCM131a Introduction to Dynamical Systems. (Those who have should take 6CCM356a.) The only postgraduates permitted to take this module are Graduate Diploma students. Assessment: The course is assessed by a 2 hour written examination at the end of the academic year.

Assignments: Weekly assignments are set. Aims and objectives: To develop the theory of the use of Laplace transforms for the solution of linear differential equations and to apply this knowledge to linear control theory. Syllabus:

• Linear differential equations: integrating factors and the D-operator method. • Systems of linear differential equations: autonomous systems, bifurcations and the

stability of equilibrium points. • Linearization of non-linear systems. • Laplace transforms and Z transforms. • Transfer functions and feedback. • Controllability and observability. • Stability: the Routh-Hurwitz criterion. • Optimal control: Euler-Lagrange equations.

Books: S. Barnett and R. G. Cameron, Introduction to Mathematical Control Theory, O.U.P. (1985) and O. L. R. Jacobs, Introduction to Control Theory, O.U.P. (1993) are both useful references. There are multiple copies of each in the library and they can be bought on Amazon.

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6CCM359a (CM359X) Numerical Methods Lecturer: Dr I Pérez Castillo Web page: http://www.mth.kcl.ac.uk/courses/ (or via links from King’s Maths home page) Semester: First Teaching arrangements: Three hours of lectures each week and one hour tutorials. In each of the first two weeks there will also be a one-hour computer laboratory session. Prerequisites: Basic theory of polynomials, linear equations and matrices, calculus, intermediate value theorem, mean value theorem, Taylor’s theorem with remainder. First year course in Maple. (No previous knowledge of Excel is assumed.) Assessment: One 45-minute practical (computer based) Excel test near the end of the semester, which counts for 20% of the final mark. Moreover, up to 10% of the final mark can be achieved by volunteering during tutorials. The remaining 70-80% of the marks are assessed by a two-hour written examination at the end of the academic year. Assignments: Exercise sheets will be handed out weekly. For the first two weeks, homework must be submitted electronically (as email attachment). After that, work will not be collected, but solutions to exercises will be discussed during tutorials. Exercise sheets will be placed on the web page, as the module proceeds. Aims and objectives: To learn the theory and practice of numerical problem solving; to learn to use Excel spreadsheets, and Maple. Syllabus: Solution of non-linear equations. Approximation of functions by polynomials. Numerical differentiation and integration. Numerical solution of ordinary differential equations, and systems of linear equations. Rates of convergence, and errors. The algorithms developed will be implemented in Excel spreadsheets or in Maple. Books: R Burden & J Faires, Numerical Methods (3ed), Brooks-Cole 2003 D Kincaid & W Cheney, Numerical Analysis (3ed), Brooks-Cole 2002 R Burden & J Faires, Numerical Analysis (8ed), Brooks-Cole 2005 E Joseph Billo, Excel for Scientists and Engineers: Numerical Methods, Wiley 2007

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6CCM360a (CM360X) History and Development of Mathematics Lecturer: Dr L Hodgkin Web page: http://www.mth.kcl.ac.uk/courses/ Semester: Second Teaching arrangements: 2 hours of lectures per week. Prerequisites: None. Assessment: One assessed essay, 2000-2500 words (25% of credit). Two hour written examination (75% of credit). Assignments: Beyond the assessed essay, there are no set assignments. Aims and Objectives: This course aims to make you familiar with the broad outlines of the history of mathematics; to show how to interpret past mathematical writings, and how to construct a historical argument. Syllabus: Ancient mathematics; the Greeks; the Islamic world; medieval and Renaissance mathematics; the scientific revolution; the invention of the calculus; non-euclidean geometry; the rigorous approach and problems of foundations; the twentieth century. Books: The History of Mathematics --- A Reader, eds J Fauvel and J Gray, (Open University, 1987) (basic reference text, choice of readings) plus a choice of the following surveys: A History of Mathematics --- An Introduction, V J Katz (Addison-Wesley, 1998) A Concise History of Mathematics, D Struik (Dover, 1987) The History of Mathematics --- An Introduction, D M Burton (McGraw Hill, 1997) The Fontana History of the Mathematical Sciences, I Grattan-Guinness (Fontana 1997) A History of Mathematics, C Boyer and U Merzbach (Wiley, 1989) A Contextual History of Mathematics, R Calinger (Prentice-Hall, 1999) There will also be notes for the course on sale at the beginning of the semester.

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6CCM380a (CM380a) Topics in Applied Probability Theory This module will consist of four ‘mini-modules of 10-12 hours duration, and will thus enable students to gain a satisfactory understanding of the key concepts and applications of a selection of important topics in both pure and applicable mathematics. Students need only attend any selection of THREE of these four mini-modules. Web page: http://www.mth.kcl.ac.uk/courses/cm380.html

(or via links from King's Maths home page) Semester: First and Second Teaching arrangements: Two hours of lectures per week Assessment: This is solely by means of a single two-hour examination at the end of the academic year, consisting of one selection for each of the mini-modules. Each of the four selections will have equal weight and students may answer questions from any selection of at most three of the sections. The mini-modules which will be offered this year are listed below. In each case, there are few pre-requisites beyond the material which is covered in the relevant core modules from the first and second year.

Game Theory Lecturer: Professor AN Pressley Prerequisites: Linear methods Assignments: Exercise sheet handed out each week. Solutions will be provided. Aims and objectives: The module aims to give an introduction to the theory of two-person zero-sum games. It should enable you to go on to more advanced topics involving linear programming, as well as applications in the theory of financial markets and economics. Syllabus: Two-person zero sum games, game trees, pure strategies, mixed strategies, optimal strategies, minimax theorems, Shapley-Snow algorithm. Books: Most books are either too advanced or depend on knowledge of other fields such as economics. I have prepared a set of printed notes to accompany the module which are available from the departmental office.

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Markov Chains Lecturer: Dr I Pérez Castillo Prerequisites: 4CCM113a (CM113A) Linear methods, 4CCM111a (CM111A) Calculus I and 4CCM112a (CM112A) Calculus II, 4CCM141a (CM141A) Probability and Statistics Assignments: Problems will be set each week. Aims and objectives: The module aims to introduce the basic concepts of finite-state, discrete-time Markov chains and to illustrate these with applications to a range of problems such as random walks and simple statistical mechanical models. Outline Syllabus: Definition of Markov chains, forward and backward equations, positive matrices, ergodicity, stationary states, Perron-Frobenius theorem. Random walks with absorbing and reflective boundaries. Interacting walkers, detailed balance, Boltzmann distributions. Possible extensions: Reaction-diffusion systems, kinetic constraints. Books: G R Grimmett and D R Stirzaker, Probability and Random Processes, OUP, 3rd edition, 2001. W Feller, An Introduction to Probability Theory and Its Applications, Wiley, 3rd edition, 1968. Notes: To be confirmed; skeletal lecture notes may be made available. Introduction to Information Theory Lecturer: Dr R Kühn

Prerequisites: Mainly 4CCM111a (CM111A) Calculus I, 4CCM112a (CM112A) Calculus II, 4CCM141a (CM141A) Probability and Statistics

Assignments: Problem sheets will be made available via the course web page.

Aims and objectives: The course aims to give an introduction to concepts and methods for quantifying information, and analysing the transmission of informaion and various forms of information processing, including coding and data analysis

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Syllabus: The concept of information; introduction to Shannon's information theory: definitions and properties, with proofs, of the main tools for quantifying information, e.g. Shannon entropy, relative entropy, conditional entropy, differential entropy, mutual information; coding theory. Books: TM Cover and JA Thomas, `Elements of Information Theory', Wiley 1991 Notes: A set of self-contained lecture notes prepared by ACC Coolen will be available at the departmental office. Time Series Lecturer: Dr E Katzav Prerequisites: Calculus 1 (4CCM112a), Linear Methods (4CCM113a), Probability and Statistics 1 (4CCM141a/5CCM141b), Probability and Statistics 2 (5CCM241a/6CCM214b) Assignments: Problem Sheets will be made available via the module webpage. Aim and objectives: The module aims at giving the students a basic understanding of the methods and mathematical theory of time series. Syllabus: Stationary processes, auto-correlation and autocovariance functions; Moving Average (MA) processes, Auto-Regressive (AR) processes and Auto-Regressive/Moving Average (ARMA) processes; correlogram; spectral analysis, periodogram; elements of estimation and forecasting and applications to empirical data. Books: Hamilton, J.D., (1994). Time Series Analysis. Princeton. Falk N., (2006) Time Series Analysis - Examples with SAS, University of Wurzburg.

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6CCM388a (CM388Z) Mathematical Finance I: Discrete Time Lecturer: Dr C Buescu

Web page: http://www.mth.kcl.ac.uk/courses/cm388.html

Semester: First Teaching arrangements: Two hours of lectures per week. One further hour will be used for lecture or tutorial as required. Prerequisites: Probability and Statistics I (or equivalent) 4CCM141A(CM141A) Assessment: One 2-hour written examination at the end of the academic year. Assignments: Exercise sheets will be posted on the module webpage. Aims and objective: This module aims to model the evolution of asset prices using the methodology of no-arbitrage in complete markets. The binomial asset pricing model will be the (mathematically easy!) vehicle used to introduce (profound!) financial concepts and necessary probability notions. This facilitates an intuitive understanding of terminology, preparing the student for the continuous-time equivalent, as well as providing a powerful practical tool. Syllabus: Asset price in discrete time, random walks, conditional expectation, elements of discrete-time martingale theory, the binomial asset pricing model, option pricing in discrete time, and -time permitting- discrete time term structure models and/or discrete time portfolio theory. Books: The material covered will be similar to that in the book (although extra material might replace some portions): Steven E. Shreve: Stochastic Calculus for Finance I: The Binomial Asset Pricing Model, (Springer Finance)

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6CCMCS02 / 7CCMCS02 Theory of Complex Networks Lecturer: Dr. J. van Baardewijk Web page: http://www.mth.kcl.ac.uk/courses-10-11/cmcs02.html Semester: First Teaching arrangements: Two hours of lectures each week. Prerequisites: Good knowledge of probability concepts, multivariate calculus and linear algebra. Assessment: The module will be assessed by a two-hour written examination at the end of the academic year. Assignments: Problems will be handed out regularly. The students are expected to attempt solving these problems. The problems are regarded as examinable material. Aim of the course:

Present the basic concepts of the theory of complex networks. Introduce various techniques which should enable the student to partake in active

research in the field. Syllabus: Concepts of local- and global measures of network structure. Adjacency matrix, vertex degree, clustering coefficient, degree distributions, degree correlations. Example networks. Eigenvalue spectra, Laplacian. Spectra of random matrices. Random graph ensembles. Complexity and entropy. Generating function methods. Giant components. Percolation. Path length characteristics. Evolving networks, preferential attachment, scale-free networks. Derivation of power-laws. Books: M.E.J. Newman, A.L. Barabasi, D. Watts, “The Structure and Dynamics of Networks”, Princeton University Press (2006). S.N. Dorogovtsev, J.F.F. Mendes, “Evolution of Networks”, Oxford University Press (2003). S.Bornholdt, H.G. Schuster, “Handbook of Graphs and Networks, from the Genome to the Internet”, Wiley (2003) R. Pastor Satorras, M.Rubi, A.Diaz-Guilera, “Statistical Mechanics of Complex Networks”, Cambridge University Press (2004). Course notes: Follow as lectures progress.

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6CCMCS05 / 7CCMCS05 Mathematical Biology Lecturer: Dr E Katzav Web page: http://www.mth.kcl.ac.uk/courses/cmcs05.html (or via links from King’s Maths home page) Semester: 2 Teaching arrangements: Two hours of lectures each week. Prerequisites: Some background in Ordinary Differential Equations and Probability Theory is required, e.g. 4CCM131A and 4CCM141A. Assessment: The module will be assessed by a two-hour written examination at the end of the academic year. Assignments: Exercise sheets will be given out. Aims and objectives: Mathematical biology is a very active and fast growing interdisciplinary area in which mathematical concepts, techniques, and models are applied to a variety of problems in developmental biology and biomedical sciences. Many biological processes can be quantitatively characterized by differential equations. This course introduces students to a variety of models mainly based on ordinary differential equations and techniques for analyzing these models. Mathematical concepts on nonlinear dynamics and chaos will be introduced. Population models (predator-prey, competition), epidemic models and reaction enzyme kinetics will be discussed. Some probabilistic modelling of molecular evolution will also be introduced. No previous knowledge of biology is necessary. Syllabus: Continuous population models for single species; Discrete population models for single species; Continuous population models for interacting species; Modelling infectious disease transmission/spread using ODEs; Reaction kinetics; Introduction to DNA and modelling of molecular evolution Books: The following book contains a substantial portion of the module: J.D. Murray, Mathematical Biology, Vol I, 3rd Edition, Springer, 2002.

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7CCMMS01 (CM424Z) Lie Groups and Lie Algebras

Lecturer: Dr B Doyon Web page: See http://www.mth.kcl.ac.uk/courses Semester: Second Teaching arrangements: Two hours of lectures per week. Prerequisites: Basic knowledge of vector spaces, matrices, groups, real analysis. Assessment: One two-hour written examination at the end of the academic year. Assignments: Exercises taken from the main notes and books. Solutions will be provided (see above). Aims and objectives: This course gives an introduction to the theory of Lie groups, Lie algebras and their representations. Lie groups are essentially groups with continuous parameters, in such a way that the elements form a manifold. They arise in many parts of mathematics and physics, often in the form of matrices satisfying certain conditions (e.g. that the matrices should be invertible, or unitary, or orthogonal). One of the beauties of the subject is the way that methods from many different areas of mathematics (algebra, geometry, analysis) are all brought in together. The course should enable you to go on to further topics in group theory, differential geometry, quantum field theory, string theory and other areas. Syllabus: Definitions of the basic structures: Lie algebras and Lie groups. Examples of Lie groups and Lie algebras. Matrix Lie groups, their Lie algebras, the exponential map, Baker-Campbell-Hausdorff formula. Abstract Lie algebras, examples: sl(2), sl(3) (maybe), Poincare algebra. Representations of Lie algebras, sub-representations, Schur's Lemma, tensor products. Cartan-Weyl basis, classification of simple Lie algebras (without proof). Books: There is no book that covers all the material exactly as taught, but the following will be useful: 1. BC Hall: An Elementary Introduction to Groups and Representations. arxiv:math-ph/0005032v1 (see also BC Hall: Lie Groups, Lie Algebras and Representations: An Elementary Introduction. Springer 2003) 2. JE Humphreys: Introduction to Lie Algebras and Representation Theory. Springer 1972 3. ML Curtis: Matrix Lie Groups. Springer 1984 4. R Gilmore: Lie groups, Lie algebras and some of their applications. Krieger 1994

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7CCMMS03 (CM422Z) Algebraic Number Theory

Lecturer: Professor FI Diamond

Web page: http://www.mth.kcl.ac.uk/courses/cmms03.html (or via links from King's Maths home page)

Semester: Second

Teaching arrangements: 2 hours of lectures per week. 1 further hour will be used for lecture or tutorial as required.

Prerequisites: Normally students should have taken Rings and Modules (CM350A/6CCM350A/7CCM350B) and be familiar with the elementary theory of field extensions (degree, minimal polynomials and algebraicity, embeddings eg as contained in the early part of the syllabus for Galois Theory (CM326Z/6CCM326A/7CCM326B)). If either condition is not met, the lecturer must be consulted before registering for the course.

Assessment: By a 3 hour written examination at the end of the academic year.

Assignments: Exercise sheets will be distributed weekly in lectures. Full solutions will be provided. Doing the exercises and attending lectures and tutorials are essential to following the course. For this reason they are compulsory. Aims and objectives: To give a thorough understanding of the àrithmetic' of number fields (finite extensions of Q) and their rings of integers, making use of abstract algebra. We shall note the analogies and differences between this arithmetic and that of Q and Z (e.g. unique factorisation may not hold). This motivates the study of ideals of the ring of integers, the class group and units. Concrete examples will illustrate the theory. This course provides a foundation for studies in modern (algebraic) number theory and is an esssential ingredient of some other areas of algebra and arithmetic geometry.

Syllabus: Polynomials and field extensions (brief reminders and terminology). Number fields. Norm, trace and characteristic polynomial. The ring of integers, integral bases, discriminant. Quadratic fields. Cyclotomic fields. Non-unique factorisation of elements, ideals, unique factorisation of ideals, norms of ideals, class group. Lattices, Minkowski's Theorem, computation of the class group. Extra topics (as time allows): Applications to Diophantine equations, Units, Dirichlet's Unit Theorem. Books (Rough decreasing order of suitability. All are good and recommended): 1. Ian Stewart and David Tall, Àlgebraic Number Theory and Fermat's Last Theorem', 3rd ed., AK Peters, 2001 2. Richard Mollin, Àlgebraic Number Theory', Chapman and Hall, 1999 3. Daniel Marcus, `Number Fields' (3rd, corrected reprint) Springer-Verlag, 1995. 4. Pierre Samuel, Àlgebraic Theory of Numbers', Hermann, 1970. 5. Jurgen Neukirch, Àlgebraic Number Theory', Springer-Verlag, 1999.

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7CCMMS08 (CM414Z) Operator Theory Lecturer: Professor E Shargorodsky

Web page: http://www.mth.kcl.ac.uk/courses/cmms08/414Z.htm (or via links from King’s Maths home page) Semester: First Teaching arrangements: Two hours of lectures each week, together with a half hour informal tutorial. Prerequisites: 6CCM321a (CM321A) and 5CCM222a (CM222A) or equivalents (that is, a course in analysis using normed spaces and a course in linear algebra). Assessment: The module will be assessed by a two hour written examination at the end of the academic year. Assignments: Exercise sheets will be given out. Solutions handed in will be marked and difficulties discussed in class. In addition, it is essential that students work through the theory as the module progresses. Aims and objectives: This module will introduce you to the terminology, notation and the basic results and concepts of Banach and Hilbert spaces. The goal is to establish one major theoretical result (the spectral theorem for compact self-adjoint operators) and demonstrate some applications. The relation of the subject with other branches of mathematics (Fourier analysis, complex functions, differential equations) will be indicated. This course should prepare you for reading the literature of a wide variety of subjects in which Hilbert space ideas are used. Syllabus: Elementary properties of Hilbert and Banach spaces. Orthonormal bases. Fourier expansions. Riesz representation theorem. The adjoint. Orthogonal projections. Spectral theory of bounded linear operators. The spectral theorem for compact self-adjoint operators. Applications to differential and integral equations. Further topics as time permits chosen from: the spectral theorem for bounded selfadjoint operators; comments on unbounded operators and applications; Fredholm operators. Books: The module will be self-contained so there are no required texts but the following books are suitable: 1. E. Kreyszig, Introductory Functional Analysis with Applications. Wiley. 2. B. Bollobas, Linear Analysis. Cambridge University Press. 3. H.G. Heuser, Functional Analysis. Wiley. 4. A.N. Kolmogorov and S.V. Fomin, Elements of the Theory of Functions and Functional Analysis. Vol. 1 Graylock, Vol. 2 Academic Press. Supplementary book list: 5. W. Rudin, Functional Analysis. Mc Graw-Hill Book Company. 6. M. Schechter, Principles of Functional Analysis. Academic Press. 7. G.K. Pedersen, Analysis Now. Springer-Verlag.

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7CCMMS11 (CM418Z) Fourier Analysis

Lecturer: Dr B Noohi Web page: via links from King’s Maths home page Semester: Second Teaching arrangements: Two hours of lectures each week.

Prerequisites: Both CM221A and CM321A, or similar analysis courses using normed spaces. Assessment: The course will be assessed by a two hour written examination at the end of the academic year. The course will involve supplementary reading on Sobolev spaces and distributions in one and higher dimensions. This will make up 15% of the final exam mark. Assignments: Exercise sheets will be given out. Aims and objectives: The purpose of the module is to introduce the notions of Fourier series and Fourier transform and to study their basic properties. The main part of the module will be devoted to the one dimensional case in order to simplify the definitions and proofs. Many multidimensional results are obtained in the same manner, and those results may also be stated. The Fourier technique is important in various fields, in particular, in the theory of (partial) differential equations. It will be explained how one can solve some integral and differential equations and study the properties of their solutions using this technique.

Syllabus: Series expansions. Definition of Fourier series. Related expansions. Bessel's inequality. Pointwise and uniform convergence of Fourier series. Periodic solutions of differential equations. The vibrating string. Convolution equations. Mean square convergence. Schwartz space S. Fourier transform in S. Inverse Fourier transform. Parseval's formula. Solutions of differential equations with constant coefficients. Books: A book covering most of the module is: H. Dym and P. McKean, Fourier series and integrals, Academic Press, 1972.

Notes: http://www.mth.kcl.ac.uk/~ysafarov/Lectures/Past

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7CCMMS18 (CM437Z) Manifolds __________________________________________________________________________________ Lecturer: Dr PP Cook Web page: http://www.mth.kcl.ac.uk/courses/ Semester: First Teaching arrangements: Two hours of lectures per week Prerequisites: Ideally 5CCM211a (CM211A), 6CCM321a (CM321A), 5CCM222a (CM222A) and 6CCM327a (CM327Z), but knowledge of multivariable calculus and basic linear algebra, together with a willingness to read up some topology and any other missing background, should be sufficient. Assessment: There will be a 2 hour written examination at the end of the academic year Assignments: Exercises will be set as the module proceeds. Aims and objectives: The module aims to provide an introduction to differential geometry and topology, both for students whose interests are in pure mathematics and for those who are studying theoretical physics and other areas of applied mathematics. The basic objects of study are manifolds, which allow one to translate familiar ideas from vector calculus to curved space. Applications to topology and theoretical physics will be discussed as time allows. Syllabus: Definition and examples of topological spaces and manifolds; functions between manifolds; the tangent space; the tangent bundle; vector fields; Lie derivatives; tensor fields; affine connections; torsion; curvature; covariant derivatives; parallel transport; manifolds with metrics; the Levi-Civita connection; differential forms; exterior calculus and integration on manifolds. If time permits additional topics such as de Rham cohomology and fibre bundles will be discussed. Books: No one book will be followed. Here is a selection, in no particular order, which might be useful. S.S. Chern, W.H.Chen & K.S.Lam: Lectures on Differential Geometry, World Scientific, 1999. C. Isham: Modern Differential Geometry for Physicists. World Scientific, 1989. I. Madsen, J. Tornehave: From Calculus to Cohomology, CUP, 1997. S.Kobayashi, K.Nomizu: Foundations of Differential Geometry, Vol. I, Wiley, 1963. M.Nakhara: Geometry, Topology and Physic, IOP, 1990. M. Crampin & F.A.E. Pirani: Applicable Differential Geometry, Cambridge, 1986. M.Spivak: A Comprehensive Introduction to Differential Geometry, Berkeley, 1979.

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7CCMMS19 (CMMS29) Modular Forms

This module has been suspended for 2010/11

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7CCMMS20 Algebraic Geometry Lecturer: Dr D Panov Web page: http://www.mth.kcl.ac.uk/courses/ (or via links from the King’s web page) Semester: Second Teaching arrangements: Three hours of lectures each week, together with a one-hour tutorial. Aims and objectives: The aim of this module is to introduce the basic notions of algebraic geometry including algebraic varieties and algebraic maps between them. Along the way, students will encounter many examples and will see how theorems in algebra can be used to prove geometric results about algebraic varieties. Brief outline of syllabus: Affine and projective algebraic varieties, the Hilbert Nullstellensatz, the Hilbert basis theorem, the Zariski topology, rational/algebraic maps between algebraic varieties, the dimension of an algebraic variety, tangent spaces, singularities, the blowing up of the plane at a point. Assessment: The full 100% of the mark is based on a two-hour written examination at the end of the academic year. Assignments: Five exercise sheets will be handed out during the term and solutions will be posted on the module webpage. Books: Algebraic Geometry: A First Course (by J. Harris) Undergraduate Algebraic Geometry (by M. Reid) Algebraic Geometry (only chapter I) (by R. Hartshorne)

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7CCMMS31 (CM436Z) Quantum Mechanics II Lecturer: Dr N Gromov Web page: http://www.mth.kcl.ac.uk/courses/ Semester: First Teaching arrangements: Two or three hours of lectures per week; some lectures can be used as tutorials and question sessions. Prerequisites: Introductory quantum theory (as offered by the Maths or the Physics Department), some understanding of special relativity, groups and symmetries, and of Newtonian mechanics. Assignments: There will be weekly assignments which all students should complete as far as possible. Solutions will be distributed the week after. Assessment: The module will be assessed by an examination in the summer examination period. Aims and objectives: The module deals with selected chapters from quantum mechanics, building upon the notions introduced in introductory courses on quantum theory. Apart from discussing fundamental examples like the hydrogen atom and new phenomena like spin, the module also provides concepts and mathematical tools useful in more advanced areas like quantum field theory. Syllabus: Main topics will include bound states of the Hydrogen atom; angular momentum, spin, representations of SU(2); symmetries in quantum mechanics; relativistic quantum mechanics (Dirac equation); perturbative methods. Additional topics may include scattering states in central force problems; Feynman path integrals. Books, course material: Copies of lecture notes will be distributed to the students, along with problem sheets and solutions. Useful books are: B.H. Bransden, C.J. Joachain, Quantum Mechanics L.I. Schiff, Quantum Mechanics E. Merzbacher, Quantum Mechanics K. Hannabuss, An Introduction to Quantum Theory R. Feynman, Lectures on Physics, vol. III

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7CCMMS32 (CM438Z) Quantum Field Theory Lecturer: Dr D Martelli Web page: http://www.mth.kcl.ac.uk/courses/ Semester: First Teaching arrangements: Two hours a week. There are no tutorials for this course. Prerequisites: Classical mechanics, basic quantum mechanics, basic special relativity. Some familiarity with linear algebra and calculus. Assessment: The course will be assessed by a two-hour written examination at the end of the academic year. Assignment: Homework will be assigned during the course. Difficulties with the material will be explained. Aims and objectives: To provide basic foundational material in quantum field theory. Syllabus: Relativistic quantum mechanics: Klein-Gordon equation; Dirac equation. Classical field theory: Lagrangian; Hamiltonian; Noether theorems; Energy momentum tensor. Free field theory: Quantisation of scalar field; Fock spaces; Normal ordering; Time ordering; Feynman propagator. Interactions: perturbation; Wick’s Theorem; Feynman diagrams; regularization; renormalization.

Books: It will be helpful to read parts of the following texts: M. Maggiore, A Modern Introduction to Quantum Field Theory, Oxford University Press M. E. Peskin and D.V. Schroeder, An Introduction to Quantum Field Theory, Westview Press C. Itzykson and J.-B. Zuber, Quantum Field Theory, McGraw-Hill S. Weinberg, The Quantum Theory of Fields, Vol 1, Cambridge University Press

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7CCMMS34 (CM435Z) String Theory and Branes

Lecturer: Professor PC West Web page: http://www.mth.kcl.ac.uk/courses Semester: Second Teaching Arrangements: Two hours of lectures each week Prerequisites: The module assumes that the students have an understanding of special relativity and quantum field theory. In addition the student should be familiar with General Relativity. Assessment: The module will be assessed by a two-hour written examination at the end of the academic year. Assignments: During the lectures problems will be given and complete solutions will be made available. It is crucial that students work through these problems on their own. Aims and Objectives: The main aim of the module is to give a first introduction to string theory which can be used as a basis for undertaking research in this and related subjects. Syllabus: Classical and quantum dynamics of the point particle, classical and quantum dynamics of strings, brane dynamics including D-branes and more advanced topics. . Reading List: The lecture notes taken during the lectures are the main source. However, some of the material is covered in: Green, Schwarz and Witten: String Theory 1, Cambridge University Press. B. Zwiebach: A First Course in String Theory, Cambridge University Press. Becker, Becker and Schwarz, String Theory and M-Theory, Cambridge University Press. E. Kiritsis, String theory in a Nutshell, Princeton University Press.

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7CCMMS38 (CM433Z) Advanced General Relativity Lecturer: Professor PC West Web page: http://www.mth.kcl.ac.uk/courses Semester: Second Teaching arrangements: Two hours of lectures each week Prerequisites: Students should be familiar with Special Relativity, Classical Lagrangian mechanics and had some previous introduction to General Relativity. Students with no previous exposure to General Relativity should take Spacetime Geometry and General Relativity (7CCMMS334b/CM334Z). Note that both modules cannot be taken in the same year. Assessment: The module will be assessed by a two hour written examination in May/June. Assignments: During the lectures problems will be given and complete solutions will be made available. It is crucial that students work through these problems on their own.

Aims and objectives: This module provides an account of General Relativity aimed so that a student can follow current research in this as well as related areas of theoretical physics.

Syllabus: Review of manifolds and their tensor fields; metrics, the Riemann and Ricci tensors, covariant derivatives and geodesics. Einstein's field equations and Lagrangian formulation. Black holes including their causal structure and more advanced topics. Reading List: The lecture notes taken during the lectures are the main source. There are many good books on General Relativity and in particular try D'Inverno, Introducing Einstein's Theory of Relativity, Clarendon Press. Hawking and Ellis, The Large Scale Structure of Space-time, C.U.P. S. Weinberg, Graviation and Cosmology, Wiley. Adler, Bazin, and Schiffer, Introduction to General Relativity,McGraw-Hill, R. Wald, General Relativity, University of Chicago Press.

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7CCMMS41 Supersymmetry and Gauge Theory Lecturer: Professor N Lambert Web page: http://www.mth.kcl.ac.uk/courses Semester: Second Teaching arrangements: Two hours of lectures each week Prerequisites: No formal requirements but students should be familiar with quantum field theory, special relativity as well as an elementary knowledge of Lie algebras. Assessment: The courses will be assessed by a two hour written examination at the end of the academic year. Assignments: During the lectures problems will be given and complete solutions will be made available. It is crucial that students work through these problems on their own. Aims and objectives: This course aims to provide an introduction to two of the most important concepts in modern theoretical particle physics; gauge theory, which forms the basis of the Standard Model, and supersymmetry. While gauge theory is known to play a central role in Nature, supersymmetry has not yet been observed but nevertheless forms a central pillar in modern theoretical physics. Syllabus: Maxwell’s equations as a gauge theory. Yang-Mills theories. Supersymmetry. Vacuum moduli spaces, extended supersymmertry and BPS monopoles. Books: The lecture notes taken during the lectures are the main source but see also D. Bailin and A. Love: Supersymmetric Gauge Field Theory and String Theory, Taylor and Francis. L. Ryder: Quantum Field Theory, Cambridge University Press P. West: Introduction to Supersymmetry, World Scientific P. Freund, Introduction to Supersymmetry, Cambridge University Press

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Projects The BSc Project Option 6CCM345a (CM345C) Third year BSc students may elect to do a project. The topic must be of a generally mathematical nature and the project must be supervised by a member of staff. Students are advised to discuss this option and obtain the agreement of a member of staff to act as supervisor before the beginning of their third year. A project title, outline and supervision plan must be agreed with the supervisor and a form submitted, signed by the supervisor, to Dr N Gromov by Monday 11 October 2010. Registration is not complete until this has been done. The results of the project must be submitted, as a dissertation of 5,000-10,000 words, to the project supervisor by 16.00 on Wednesday 23 March 2011. Two copies are required. The dissertation will be examined by the project supervisor and a second examiner, the latter to be appointed by the Chair of the Board. The two examiners will also conduct an oral examination of the candidate. A rough guide to the general areas in which members of staff may be willing and available to supervise projects in 2010/2011 is as follows: Algebra / Number Theory DJ Burns, FI Diamond, PL Kassaei Analysis / Differential Equations AB Pushnitski, Y Safarov, E Shargorodsky. Geometric Analysis SG Scott Geometry D Panov, AN Pressley, K Rietsch, G Tinaglia Disordered Systems and Neural Networks A Annibale, E Katzav, I Pérez Castillo, PK Sollich. A list of the possible projects will be published on the module page. Students should feel free to approach members of staff with topics from other areas. A document Information for Students on the Project Option is available from the module web page giving further details. The MSci Project 7CCM461a (CM461C) All fourth year MSci students are required to complete a project on a mathematical topic. This involves writing a report of between 5,000 and 10,000 words, and giving a 20 minute seminar to staff and fellow students. The project counts as a full unit, which makes it a very important part of the final year. Each student will have a supervisor; the supervisor’s task is to advise, not to direct the project, but students should feel free to consult as necessary, and in particular are advised to show the supervisor a draft of the report at an early stage. The choice of supervisor is by agreement between the student and the member of staff. A list of the possible projects will be published on the module page.

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At registration in the Department, each fourth year student will be given a form on which to state the topic and provisional title of his or her project. This must be signed by the supervisor and returned to Dr N Gromov by Monday 11 October 2010. Registration is not complete until this has been done. There will be informal seminars during the revision period at the beginning of the second semester. While it is not expected that the projects will be near completion at that point, students should be able to give at least an account of the background and an indication of what they hope to accomplish. The deadline for submission of projects is 16.00 Wednesday 23 March 2011.

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‘With Management’ programmes The information provided below is for students on the following programmes:

• BSc Computer Science with Management (with a year abroad/in industry) • BEng/MEng Engineering with Business Management (with a year in industry) • BSc Maths with Management & Finance • BA French with Management

Modules Semester 1 4CCYM129 - Organisational Behaviour 5CCYM212 - Marketing 6CCYM325 - Business strategy & Operations Management Semester 2 4CCYM110 - Economics 5CCYM210 - Accounting 6CCYM339 - Human Resource Management Please note that these modules are not run by your department nor by the Management Department, therefore if you have any queries regarding the above modules please use the contact details listed below. Timetables Information regarding the timetables for all with management modules can be found on line at www.kcl.ac.uk/schools/nms/current/ug/management. Any changes that are made to the timetable and any revision lectures will be listed on this web page. E-learning For most modules you will find lecture notes and aids via the College’s e-learning system (www.kcl.ac.uk/elk). You will be asked to submit your coursework via this system and any class changes and important information related to your management modules will be posted here. It is your responsibility to make sure you have access to the correct modules and that you check it regularly for any announcements. Attendance Attendance at lectures and tutorials is compulsory and is monitored. You will be sent warnings if your attendance is unsatisfactory and you may not be permitted to sit the examination. Regular attendance is essential if you are to keep abreast of the material being taught.

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Submission of Coursework You will be informed by your lecturer of the time and place to submit your coursework. Unless specifically told otherwise, you should submit coursework online via the King’s e-learning service by 17:00 on the day of the deadline. Please ensure you have access to the correct modules and assignments in e-learning well before the deadline (www.kcl.ac.uk/elk) If you need to request an extension to a coursework deadline you must follow the procedure outlined under ‘Mitigation, Extension requests & EDR2 Requests’ in your School handbook. Please read the information given carefully before submitting an Extension Request Form, which should be handed in to your department. If you miss the deadline then you will no longer have access to submit the coursework online and must follow the procedure outlined under ‘Mitigation, Extension requests & EDR2 Requests’ in your School handbook. Any work submitted after the deadline MUST be accompanied by a Mitigating Circumstances Form, and handed in to Lucy Ward (see contact details below). Coursework should not be submitted directly to the lecturer in a lecture, tutorial or at any other time, unless they have requested this in addition to the online submission Staff Dr Norman Borrett - Director of Studies 6CCYM325 - Business strategy & Operations Management Email: [email protected] Ms Mia Pranoto 4CCYM129 - Organisational Behaviour 6CCYM339 - Human Resource Management Email: [email protected] TBC Visiting Lecturer 5CCYM210 - Accounting Email: [email protected] Mr Jon Kitto Visiting Lecturer 5CCYM212 - Marketing Email: [email protected] Dr John Simister Visiting Lecturer 4CCYM110 – Economics Email: [email protected] Mrs Lucy Ward General Administrative Queries Room S1.31 Email: [email protected] Tel: 020 7848 2267

Further information, timetables and any updates related to these modules will be available on line at: www.kcl.ac.uk/schools/nms/current/ug/management

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4CCMY129 - Organisational Behaviour Lecturer: Mia Pranoto Module Code: 4CCMY129 Exam - C/W ratio: 80 – 20 Module credit value: 15 Semester: First Examined: May/June Aims and Objectives The course aims to introduce students to problems and issues involved in the effective management of organisations. It highlights behaviours, structure and processes that are part of organisational life. On completion of this course, students should be able to: • Understand and explore the how, what, why and when of OB as viewed and practised by

managers • Consider the relationship between individuals and organisational systems • Explore interpersonal influence and group behaviours for effective management • Analyse organisational structure and design that influence organisational effectiveness • Evaluate alternative social science theories used in practice Outline Syllabus The Field of Organisational Behaviour; Work Motivation Theory; Design of Reward and Motivation Systems; Design of Work; Group Processes and Teamworking; Organisational Processes - Decision Making and Communication; Leadership and Management Style; Management Control; Power and Authority; Conflict - Management and Resolution; Organisational Structure and Design; Organisational Culture and Performance; Organisational Development and Change; Human Resource Management - Policies and Practices. Coursework: One 1500 word essay Course Structure: 20 hours lectures 9 hours tutorials Assessment: 80% written examination 20% coursework Recommended Reading Robbins, S. and Judge, T. (2007) Organizational Behaviour, 12th edition FT Prentice-Hall

(compulsory) Fincham, R. and Rhodes, P. (2005) Principles of Organizational Behaviour, 4th edition Oxford Press Huczynski, A. and Buchanan, D. (2004) Organizational Behaviour: An Introductory Text 5th edition FT Prentice Hall Kreitner, R., Kinicki, A. and Buelens, M. (2002) Organisational Behaviour, 2nd European Edition McGraw Hill. Osland, J. S., Kolb, D. A. and Rubin, I. M. (2001) Organisational Behaviour: An Experiential Approach, 7th Edition Prentice-Hall.

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4CCMY110 – Economics Lecturer: Dr. John Simister Module Code No: 4CCMY110 Exam - C/W ratio: 80 – 20 Module credit value: 15 Semester: Second Normally examined: May/June

Aims and Objectives The aims of the course are to: • Explain consumer behaviour, and behaviour by firms, and government economic policies; • Provide students with the fundamental analytical tools to tackle economic problems. On completion of the course, students should be able to: • Identify issues (such as unemployment) which are central to economics; • Apply techniques and concepts in the course, to the analysis of economic problems; • Discuss effects of economic policy on economic variables, and its role in improving welfare. Outline Syllabus • Consumer behaviour • Supply and demand • Perfectly competitive markets • Monopoly • Pollution and other externalities • Production and consumption as parts of a single system • The ‘multiplier effect’ • The labour market (unemployment; trade unions; the minimum wage). • Welfare economics: the market and the state (market failure, poverty and inequality). • Development in the “Third World” Coursework: One assessed essay. Course Structure: 20 hours lectures 10 hours tutorials. Assessment: 80% written examination 20% coursework. Recommended Reading Compulsory Joseph E. Stiglitz and Carl E. Walsh Economics Supplementary David Begg, Stanley Fischer and Rudiger Dornbusch Economics Richard Lipsey and Alec Chrystal Economics Michael Parkin, Melanie Powell and Kent Matthews Economics John Sloman Economics

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5CCMY210 - Accounting Lecturer: TBC Module Code: 5CCMY210 Exam - C/W ratio: 80 – 20 Module credit value: 15 Semester: Second Normally examined: May/June

Aims and Objectives The aims of this course are to: • Provide an introduction to management and financial accounting and the types of information

each provides. • Examine basic financial issues faced by managers in business organisations and use

accounting data in order to assist managerial decisions. • Enable interpretation of the financial performance and position of organisations through an

understanding of the accounting concepts and procedures used in preparing financial statements.

On completion of this course, students should be able to: • Describe the functions of accounting in business organisations and distinguish between

management and financial accounting. • Locate sources of financial data relevant to business organisations and utilise the information

in written reports and analyses. • Explain the issues relating to cost classification and apply the procedures of absorption and

marginal costing in allocating and apportioning overhead costs and in performing basic break-even analysis.

• Identify and describe different types of business organisations and their principal sources of financing.

• Identify and explain the purpose of financial statements for limited companies. • Prepare from a trial balance the Profit and Loss Account and Balance Sheet for a limited

company, including calculations for depreciation of fixed assets and provisions for losses on stock and debtors.

• Explain the accounting concepts and conventions, which are used in the preparation of financial statements.

• Calculate and use basic accounting ratios to evaluate the financial performance and position of business organisations.

Outline Syllabus Limited companies and their financing; reporting financial position: the Balance Sheet; reporting operating performance: the profit and loss account; accounting treatment of fixed assets; interpretation of financial statements; introduction to management accounting and cost classification; marginal costing and break-even analysis; overheads and absorption costing; budgetary planning and control; standard costing and variance analysis. Coursework: Written Report (1,500 words) Course Structure: 10 three hour lecture/workshops

Assessment: 80% written examination 20% coursework

Recommended Reading Dyson, John R. Accounting for Non-Accounting Students (Seventh Edition), Prentice Hall (ISBN 978-0-273-70992-0)

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5CCMY212 - Marketing

Lecturer: Jon Kitto Module Code No: 5CCMY212 Exam - C/W ratio: 80 – 20 Module credit value: 15 Semester: First Normally examined: May/June Aims and Objectives The aims of this course are to: • Introduce students to fundamental and established theories of marketing and its role in a

business & social context. • Demonstrate how the elements of the marketing mix are combined to create a marketing plan. • Describe the key aspects of marketing management. On completion of this course, students should be able to: • Relate knowledge gained to other elements of the business management course & to real

business situations. • Utilise the inputs necessary to develop and implement a marketing plan. • Reflect critically on marketing practices and consumer behaviour in the current business

environment.

Outline Syllabus Introduction to marketing., the marketing environments, consumer behaviour, marketing information & research, managing products & services, channels of distribution, marketing communications, marketing planning, international marketing & ethics in marketing.

Coursework: One 2,000 word report assignment with accompanying presentation

Course Structure: 20 hours lectures 10 hours seminars


Recommended Reading Compulsory Kotler P., Wong V., Armstrong G., and Saunders J. (2007) Principles of Marketing, 4th European Edition, Pearson Mason, C. and Perreault, W. (2001) The Marketing Game! (with Student CD ROM), Irwin Supplementary Blythe J. (2001) Essentials of Marketing, 2nd edition, FT/Prentice Hall Enis B., Cox K., Mokwa M., (1990) Marketing Classics: A Selection of Influential Articles, 8th edition, Prentice Hall International (library text) Brassington, F. and Pettitt, S. (2004) Essentials of Marketing, Pearson

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6CCMY325 – Business Strategy and Operations Management Lecturer: Norman Borrett Module Code No: 6CCMY325 Exam –C/W ratio: 80-20 Module Credit Value: 15 Semester: First Normally examined: May/June Aims and Objectives The main aims of the course are to: Provide a through grounding in a range of corporate level business management topics to complement the material covered in the specific management modules as part of the joint honours ‘with Management’ undergraduate degree programmes.

On completion of the course, students will have acquitted an in-depth knowledge of a variety of corporate level general management techniques and applications to allow them to contribute to and make operational management decisions immediately the enter industry and to understand that operations of an organisation at strategic level.

Outline Syllabus

1) Business Strategy 2) Capital investment decision and corporate planning 3) Forecasting 4) Decision making theories and risk analysis 5) Product management, design and development 6) Quality, reliability and maintenance management 7) Legal and ethical considerations of management 8) Health and Safety and risk management 9) Intellectual property 10) Globalisation

Coursework: 3 pieces of written work, at 750 words each.

Course Structure: 36 hours lectures/tutorials

Assessment: 80% written examination 20% coursework Recommended Reading Mintzberg, H., Quinn, J. B., and Ghoshal, S. (1998a) The Strategy Process, Europe, Prentice Hall Mintzberg, H., Ahlstrand, B., and Lampel, J. (1998b) Strategy Safari, London, Prentice Hall Porter, M.E. (1980) Competitive Strategy: Techniques for Analysing Industries and Competitors, New York: Free Press Wheelen, Thomas L. and Hunger, J David (2003) Strategic Management and Business Policy, Ninth Edition, Prentice Hall Lock, Handbook of Engineering Management, Heineman Payne, Chelsom and Reavill, Management for Engineers, Wiley Schermoerhorn, Management, Wiley

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6CCMY339 – Human Resource Management Lecturer: Mia Pranoto Module Code No: 6CCMY339 Exam - C/W ratio: 80 – 20 Module credit value: 0.5/15 Semester: Second Normally examined: May/June Aims and Objectives The aims of the course are to:

• Extend the students understanding of the theory and practice of Human Resource Management

• Locate HRM within both the context of organisations and the field of contemporary management theory and practice.

On completion of this course, students should be able to:

• Evaluate the hard and soft approaches to HRM.

• Evaluate the significance of people as a strategic resource and be able to outline the main types of strategic models that have emerged.

• Analyse organisational structures and processes and be able to locate these within broad categories e.g. flexible firm model.

• Analyse and evaluate different types of involvement and participation at the workplace.

• Identify the key issues in the effective management of pay.

• Evaluate the case for training and development (T&D), recognise external factors which influence T&D e.g. role of government.

• Identify the importance of recruitment and selection as a function of the HRM process and be able to evaluate the appropriateness of different methods commonly applied.

• To understand and explain some of the reasons behind the changing nature of employee relations from the perspective of the employee, management and trade unions.

Outline Syllabus Work and employment; Industrial Relations; Personnel Management and HRM; The Various Forms of HRM; Strategic HRM; HRM in Context: Management and Employee Objectives; Organisational Culture; Employee Engagement and Commitment; Organisational Objectives and Outcomes; Forms of Participation; HRM; Trade Unions; Statutory Regulation and the Employment Relationship; HRM Policy, Procedures and Processes.

Coursework: One 1,500 word essays

Course Structure: 20 hours lectures 9 hours tutorial


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9. SAFETY CHECK LIST Please ensure that you have details of all the items listed below – ask your supervisor. You can either tick the box to show that you have been informed about the details, or make a note for your information.

Please hand a copy of this form, when completed, to your Departmental Office.

NAME (please print): Student ID: SUPERVISOR: Date:

Emergency Phone Number 2222

Health Centre Phone Number 020-7848 2613

Your Nearest Fire Extinguisher

Types of Fire Extinguishers

Your Fire Exit Route

Your Fire Assembly Area

Your Nearest First Aid Box

Your Nearest Spill-Kit

Names & Tel Numbers of First Aiders

Emergency Procedures

Lone Working

Smoking, Eating and Drinking

Lab Coats and Safety Spectacles Tidiness

DSE use (working at a computer)

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10. ETHICS IN MATHEMATICS Ethics plays a role in virtually all aspects of human activity. Although use of the term often brings to mind great issues involving human suffering, ethics are also at play in day to day life. We would like to bring to your attention some ethical rules that we expect to be followed by all of our students, graduates and staff throughout their mathematical careers. Perhaps the most important role that ethics plays specifically for mathematics is simply that of honesty and integrity when solving mathematical problems and proving theorems. Ultimately the truth in mathematics always comes out (although it may take hundreds of years). Being caught in a position where you are found to have mislead or fabricated evidence is considered a deeply serious breach of standards and will have a very negative, if not devastating, effect on your reputation and career. 1. A mathematician shall never knowingly put forward incorrect statements or calculations and claim that they are correct. 2. A mathematician shall always endeavour to determine which statements are true and which are false by logically sound processes of deduction and proof. 3. A mathematician shall never attempt to mislead others as to the truth or falsity of a proposition. 4. When making statements a mathematician shall always be clear as to whether they are false, believed to be true, or known to be true. In the later case a mathematician must be able to provide direction as to where the proof of the statement can be found. 5. A mathematician shall always give appropriate credit to the work of others in accordance with standard referencing and plagiarism protocols. 6. A mathematician shall not knowingly engage in research, or assist the research of others, which is intended to cause public harm. IMA Code of Conduct In addition to the academic-related rules listed above there are many ethical standards that any employee of a company or institute will be expected to uphold. In general these will depend upon the nature of the job and the contract that the mathematician has with the employer. Below are a set of rules that were obtained from the code of conduct for members of the Institute of Mathematics and its Applications. It is offered as a guide to students as to what is likely to be expected of them by their employers and is in line with codes of conduct for many professional institutions. A code of working conduct designed to cover all eventualities must necessarily be posed in general terms expressing broad ethical principles. The rules proposed indicate the manner in which mathematicians are expected to conduct themselves in a number of frequently-occurring situations. In other situations, mathematicians are required to conduct themselves in accordance with the principle that, in any conflict between a mathematician 's personal interest or the interests of an employer or sponsor and fair and honest dealing with members of the public, duty to the public must prevail. 1. A mathematician shall have regard to protection of the public interest as determined by criminal and civil legislation. 2. A mathematician in the position of an employer, in addition to meeting the relevant regulations and standards, shall set fair and reasonable terms and conditions of employment.

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3. A mathematician shall not improperly disclose any information concerning an employer’s business nor that of any previous employer. 4. A mathematician shall inform an employer in writing of any potential conflict between personal interest and faithful service to the employer. 5. A mathematician shall not accept remuneration in connection with services rendered to an employer other than from the employer or with the employer's consent; nor shall a mathematician of the department receive directly or indirectly any undeclared royalty, gratuity or commission, for any article or process used in connection with employment if such royalty, gratuity, or commission conflicts with the employer's terms and conditions of employment. 6. A mathematician shall not offer to provide or receive in return, any payment or commission or otherwise as the inducement for the introduction of business from a client. 7. A mathematician shall not, except where specifically so instructed, handle clients' monies or place contracts or orders in connection with work on which engaged when acting as an independent consultant. 10. A mathematician called upon to give an opinion shall give an opinion that is objective and reliable, shall have sought authorisation where this is appropriate, and have due regard to the likely consequences of any such statement. 11. A mathematician shall only undertake service where as a mathematician, the required level of competence is possessed. 12. A mathematician shall accept responsibility for personal work and for the work of subordinates done under direction, seeking always to conform to recognised good practice including quality standards.

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11. INDEX

Absence............................................................................................................................14 Administrative Matters ....................................................................................................13 Assessment and Records Centre.....................................................................................5 August Resits...................................................................................................................35 BSc Project.....................................................................................................................140 BSc/MSci Mathematics........................................................................................41, 46, 48 BSc/MSci transfers ..........................................................................................................38 Calculators .......................................................................................................................29 Change of Degree Course...............................................................................................72 Class Tests.......................................................................................................................24 Code of Conduct..............................................................................................................21 Contact Details...................................................................................................................3 Coursework ......................................................................................................................23 Departmental Information ...............................................................................................16 Departmental Office.........................................................................................................13 Disclaimer...........................................................................................................................6 Ethics in Mathematics ...................................................................................................151 Examination Regulations ................................................................................................27 Examination Results........................................................................................................34 French and Mathematics BA..........................................................................................66 Further information ...........................................................................................................5 IMA Code of Conduct ....................................................................................................151 Introduction......................................................................................................................10 Joint Honours Courses ...................................................................................................50 Mathematics and Computer Science BSc .....................................................................51 Mathematics and Computer Science MSci ....................................................................54 Mathematics and Philosophy BA ...................................................................................68 Mathematics and Physics BSc .......................................................................................56 Mathematics and Physics MSci......................................................................................59 Mathematics and Physics with Astrophysics BSc........................................................63 MathSoc............................................................................................................................15 Mission Statement ...........................................................................................................12 Mitigating Circumstances ...............................................................................................30 Module/Course Unit Listing ............................................................................................72 MSci in Mathematics .......................................................................................................41 MSci Project ...................................................................................................................140 Plagiarism.........................................................................................................................39 Pop-In Tutorials ...............................................................................................................23 Preface................................................................................................................................5 Prizes ................................................................................................................................19 Programmes Of Study.....................................................................................................40 Progression......................................................................................................................35 Projects...........................................................................................................................140 Projects and Essays........................................................................................................26 Safety Check List ...........................................................................................................150 Safety Procedures ...........................................................................................................19 Special Examinations Arrangements.............................................................................28 Staff/Student Committee .................................................................................................19

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Structure of the Department ...........................................................................................11 Student Presentations.....................................................................................................25 Term dates........................................................................................................................12 The Link-up System.........................................................................................................14 Tutor System....................................................................................................................13 Walk-in Tutorials..............................................................................................................22 With Management’ programmes ..................................................................................142 Workload ..........................................................................................................................26

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How the System Works 10

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