Department of Mathematics
King’s College
Strand
London
WC2R 2LS
Fax: 020 7848 2017
Telephone: 020 7848 (followed by the appropriate extension number)
Name E-mail Address Room No. Ext No.
Dr. A.D. BARNARD tony.barnard@kcl.ac.uk 524 2245
Dr. D. BURNS david.burns@kcl.ac.uk 413 2863
Prof. A.C.C. COOLEN tcoolen@mth.kcl.ac.uk 406 2235
(IPNN Msc Co-ordinator)
Prof. E.B. DAVIES E.Brian.Davies@kcl.ac.uk 420 2698
Dr. J.A. ERDOS john.erdos@kcl.ac.uk 430 2225
(Head of Department)
Mr. S. FAIRTHORNE fairthorne@iclway.co.uk 531 2877
Dr. W.J. HARVEY bill.harvey@kcl.ac.uk 407a 2828
(Postgraduate Admissions Tutor)
Dr. L.H. HODGKIN luke.hodgkin@kcl.ac.uk 418 2223
Prof. P. HOWE phowe@mth.kcl.ac.uk 419 2853
Prof. L. HUGHSTON lane.hughston@kcl.ac.uk 408a 2855
(Financial Mathematics MSc Co-ordinator)
Dr. G. IORI
Dr. L.J. LANDAU larry.landau@kcl.ac.uk 422 2219
Dr. D.A. LAVIS david.lavis@kcl.ac.uk 532 2240
Dr. G. Papadopoulos gpapas@mth.kcl.ac.uk 412 2227
Prof. A.N. PRESSLEY anp@mth.kcl.ac.uk 525 2861
(Chairman of the Postgraduate Affairs Committee)
Dr. H.C. RAE hamish.rae@kcl.ac.uk 407 2860
Dr. A. RECKNAGEL
Prof. D.C. ROBINSON David.C.Robinson@kcl.ac.uk 414 2221
Dr. F.A. ROGERS alice.rogers@kcl.ac.uk 416 2242
(Postgraduate
Tutor)
Prof. Y. SAFAROV ysafarov@mth.kcl.ac.uk 417 2215
(Mathematics MSc Co-ordinator)
Prof. P.T. SAUNDERS peter.saunders@kcl.ac.uk 421 2218
Dr. S. SCOTT sscott@mth.kcl.ac.uk 409 2778
Dr. J.R. SILVESTER jrs@kcl.ac.uk 413a 2864
Dr. P. SOLLICH psollich@mth.kcl.ac.uk 408 2875
Dr. D.R. SOLOMON solomon@mth.kcl.ac.uk 411 1165
Prof. R.F. STREATER ray.streater@kcl.ac.uk 435 2220
Dr. G.M.T. WATTS gmtw@mth.kcl.ac.uk 405 1013
Prof. P.C. WEST pwest@mth.kcl.ac.uk 434 2224
Dr. I.F. WILDE ivan.wilde@kcl.ac.uk 522 2854
Dr. M. ZERVOS mihail.zervos@kcl.ac.uk 530 2633
Administrative Staff
Miss S. GLASS samantha.glass@kcl.ac.uk 432 2107
(Postgraduate Secretary)
Miss A. LYLES annabelle.lyles@kcl.ac.uk 432 2217
Miss H. MORTON hilary.morton@kcl.ac.uk 432 2216
The information in this handbook is provided to help you in planning your work and in choosing courses. It is in your interest to consult fully with your Course Adviser, who must approve your choice of courses. You must also ask your Course Adviser for approval of any subsequent changes.
The information has been compiled by the Department and the School Office, and is valid for the 2000/2001 academic session only. Some of the items refer to rules and regulations that apply to students in the Mathematics Department only, others to all students in the School of Physical Sciences and Engineering. Please note that any rules and regulations outlined here exist in addition to College Regulations.
If at any point the information given here conflicts with College or University Regulations, then this document is wrong. The information is believed to be correct at the time of going to press, but it does not cover everything and some items may be subject to change. For definitive information you should consult the College and University Regulations.
Students are individually responsible for keeping themselves up to date with information posted on the Departmental Notice Boards (opposite the Mathematics Office). This is particularly important with regard to registration and examination information.
Contact Details 1
1. THE DEPARTMENT 5
1.1 Diary and Registration Information 2000/2001 5
Dates to Remember 5
1.2 Departmental Information 6
1.3 School of Physical Sciences & Engineering 8
1.4 Safety 9
2. STRUCTURE OF COURSES 10
3. APPROVED COURSES IN 2000/2001 14
3.1 Course Outlines 14
3.2 Plagiarism 18
4. EXAMINATIONS 20
5. COLLEGE INFORMATION 22
6. DEPARTMENTAL STAFF 24
All postgraduate courses at King's College are run on a semester basis.
First semester: 25 September 2000 - 15 December 2000
Second semester: 8 January 2001 - 23 March 2001
Examination period: 23 April 2001 - 8 June 2001
All enquiries on Thursday 21 September and Friday 22 September should be made only to the Postgraduate Admissions Tutor, Dr Bill Harvey.
Induction Day Meeting in Room 521
11.00 – 11.30 Talks by the Head of Department, Dr John Erdos, Dr Bill Harvey and Prof ACC Coolen and Prof Lane Hughston
12.00 – 13.00 Assignment of supervisors
14.00 – 17.00 Discussion of course options with supervisors.
Afternoon Tea in room 521
School of Physical Sciences & Engineering Enrolment session at 11.00am in the Great Hall Strand Building.
4.00pm - Mathsoc Link-Up Party (Location to be confirmed- please check notice board outside room 432)
Lectures begin.
Training Course for experienced tutorial assistants in room 521 from 2.00pm to 5.00pm
Training Course for new tutorial assistants in room 521 from 9.30pm to 5.00pm
School Research Day – Council Room and Great Hall
Deadline for Exam Entry Form to be submitted (a provisional list of courses)
End of first semester
Second semester begins
PhD students meet their supervisors to discuss methods of assessing progress
Find out when and where examinations take place
Deadline for submission of MSc Project Titles to Course Advisor
End of second semester
Revision week, examinations begin
Examinations end
Deadline for submission of MSc projects (3 copies)
WARNING : Problems have arisen in the past over variation of dates between colleges. Students attending courses at other colleges must satisfy themselves about when courses begin and end and the time and place of examinations, and be prepared to stay in London to complete the courses if necessary.
Dates and
arrangements concerning exam registration, and the communication of
examination results, will be posted on the notice boards.
A Course Advisor will be assigned to each MSc or Diploma student to help him/her to plan their course of study. The student’s advisor may help in deciding on the choice of project and a supervisor for the project. For help questions arising in a course, ask the lecturer. For personal problems, students may consult either their course advisor or the Postgraduate Tutor, Dr Alice Rogers. For general advice about administration of the MScs see The Postgraduate Secretary, Sam Glass.
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 course. 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 be penalised. 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.
Always keep yourself up to date by regularly consulting the notice boards. The Mathematics Department Notice Boards are situated opposite the Departmental Office on the fourth floor of the Strand Building. There is also an undergraduate student notice board in room 437.
To enable the Department to communicate with you, it is most important that you supply term-time and home addresses. Please inform the Departmental Office promptly of any changes.
Two other important avenues of communication used by students and staff are the Mathematics Department pigeon-holes and the College electronic mail network. Staff pigeon-holes are in the Departmental Office (Room 432) and postgraduate pigeon-holes are just outside thee Office. PLEASE CHECK YOUR MAIL REGULARLY
Most students studying mathematics as part of their degree will attend one or more course units with a computing component. In addition to this electronic mail (e-mail) is used for the dissemination of information to students and for communication between students and their tutors, and students are required to check their e-mail regularly. All new students will be registered automatically to use the College e-mail system. Terminal facilities are widely available throughout all the campuses of the College and at some halls of residence. The Terminals within the department for postgraduate students are located in room 426.
If you normally use an email service (like hotmail), rather than your college account, then you should ensure that the department has this email address. You should also set ‘mail forwarding’ to that account from your college account so that mail does not stay unread. Computing Centre Advisory will help you do this.
PLEASE CHECK YOUR EMAIL REGULARLY
Much information about the department (including this document) is available on the departmental web page (www.mth.kcl.ac.uk). Course notes and example sheets for many of the courses are also available through the web page. You should ensure that you are familiar with the use of these facilities.
At present the Department has two committees, which require postgraduate representatives.
The Staff/Student Committee is intended to provide a channel of communication between all students and staff and a forum for discussion of matters of common concern. It meets several times throughout the year and at least once every semester. Postgraduate students should elect one representative during the first month to sit on each of these committee meetings. Any student who wishes to raise an issue with the committee is entitled to do so, by consulting their student representative (or any other member). The current staff members are Dr A D Barnard, Dr J A Erdos, Dr M J Laird, Dr B L Luffman and Dr S Scott. A full membership list, plus the dates of meetings will be displayed on the notice board and in room 437
The Postgraduate Affairs Committee usually meets at least once every semester to discuss various topics such as postgraduate admissions, facilities, emerging research culture and any other relevant issues. The current staff members of the committee are Prof A Pressley (Chair), Dr WJ Harvey (Admissions Tutor), Prof Safarov (MSc Course Organiser), Dr FA Rogers (Postgraduate Tutor), Prof ACC Coolen (IPNN Course Organiser), Dr P Sollich, Dr S Scott, Dr G Watts, Prof L Hughston (Financial Mathematics Course Organiser) plus two postgraduate student representatives.
MathSoc is a student-run society with membership open to all students in the Mathematics Department. MathSoc events provide opportunities for students to meet socially and to develop their interests in mathematics outside lectures.
MathSoc organises talks by guest speakers throughout the year, the Mathsoc Annual Boat Party, the Department's annual weekend away at Cumberland Lodge in Windsor Great Park, and other occasional social events. The weekend at Cumberland Lodge is viewed by all who go as the highlight of the year. There are talks and discussions on topics of mathematical interest as well as plenty of leisure-time to enjoy the beauty of Windsor Great Park.
Further information about MathSoc can be obtained from their web pages, accessible via the Departmental home page, www.mth.kcl.ac.uk/mathsoc
MathSoc officers can be contacted via the pigeonholes in Room 437, the Union or e-mail. There will be a MathSoc Link-Up party at the start of the year.
The School Office is the central administrative office for the School of Physical Sciences and Engineering, comprising the Departments of Chemistry, Computer Science, Management, Mathematics, Physics, and the Division of Engineering (Electronic and Mechanical). The School Office is located on the main corridor of the Main Building (ground floor) in room 31B. Office hours are from 9.30-12.30 and from 14.00-16.30. The student administrative database is maintained here and the office provides a central point of contact for Undergraduate and Postgraduate Admissions, School Accounts, School Committees and general advice on College regulations. You will need to visit the School Office if you wish to change your degree course, alter your examination entries or interrupt your studies - more details are given below and in Sections 2.4 and 4.
Your permanent (home) and local (term time) addresses are kept on the student administrative database. Important information such as examination candidate numbers and re-enrolment literature is sent out to you at the address we have for you on our records. Usually, we send information to your permanent address during the summer vacation, and to your local address at all other times. It is therefore vital that you keep the School Office informed of all changes of address. Change of address forms are kept at the counter and will be actioned immediately. You should also notify the Departmental Office of all changes.
An Interruption of Studies means officially suspending your studies for an agreed period, and then returning to resume your studies on an agreed date.
Withdrawal from College means withdrawing from your course and from the College on a permanent basis. If you are transferring to another institution, this is also withdrawing from College.
If you wish to take either of these steps you should first discuss your intentions with your tutor, and then collect and complete the appropriate form from the School Office. If you are in receipt of a Local Authority Award, the School Office will inform your local authority once the form has been processed, although you should also keep them informed of your movements.
The Departmental Administrator acts as the Safety Officer. The Department has a Safety Notice Board for the display of relevant notices. A list will be displayed of First Aiders who have been trained to give immediate medical help in the event of an accident. Whilst the Medical Centre 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.
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.
MSc Mathematics (Pure and Applied)
Course Advisor: Prof Y Safarov
Full-time: one calendar year
Part-time: two calendar years
Curriculum
Candidates will take eight courses on either Pure and Applied Mathematics and Mathematical Physics from the list approved for this degree under the guidance, and with the approval of their programme advisors.
Candidates can take at most two half-unit undergraduate courses.
A candidate may be allowed to take up two half-unit MSc courses at another University of London College provided that these have been approved by the student’s programme advisor and by the Head of the Department.
Candidates must submit a project in the form of a thesis of approximately 10,000 words. Full-time students will research and write their theses after the summer examinations. Part-time students may wish to spread the work on their thesis over the two year period but are expected to devote to it an amount of time equivalent to that of the full-time students.
A full-time student normally attends four courses during the first semester and four courses during the second semester, but a student may, with the approval of the programme advisor, attend three courses during one semester and five during the other.
A part-time student normally takes four courses during the first year and four courses during the second year, but a student may, with the approval of the programme advisor, attend five courses in one year and three in the other.
MSc Information Processing and Neural Networks
Course Advisor: Prof ACC Coolen
Full-time: one calendar year
Part-time: two calendar years
Curriculum
Each student must attend the two one-semester core courses of the programme (see below) and six further one-semester courses, chosen from the list of approved optional courses (see below) in consultation with the course adviser.
Semester 1:
Core course: CM451Z Neural Networks (an undergraduate course)
Options: EEM210 Communication Theory
MA314 Theory of Algorithms (LSE)
EEM345 Digital Signal Processing
CMFM02 Introduction to Derivatives Pricing
CSMNAN Numerical Analysis
Semester 2:
Core course: G30 Advanced Neural Networks
Options: MA409 Computational Learning Theory (LSE)
CPM104 Digital Image Processing
CMNN4 Information Theory in Neural Networks
CM335Z Non-Linear Dynamics / Chaotic Dynamics (UG course)
CMNN13 Statistical Mechanics of Neural Networks
CMFM04 Stochastic Analysis
A student will also undertake an individual project, following the written examinations leading to a thesis of approximately 10,000 words in length.
MSc Financial Mathematics
Course Advisor: Prof L Hughston
Full-time: one calendar year
Part-time: two calendar years
Curriculum
Each student must attend eight one-semester courses. The programme as a whole to be subject to the approval of the programme advisor.
Full-time
First semester
- three compulsory courses: CMFM01, CMFM02, CMFM03
- one optional course chosen from: CMFM06, CMFM05, CM354X, CM451Z.
Second semester
- two compulsory courses chosen from: CMFM04, CMFM07, CMFM08, CMFM09.
- three elective courses chosen from: CMFM04, CMFM05, CMFM06, CMFM07, CMFM08, CMFM09, CM354X, CM451Z, CM452Y, CM355X, CM335Z, CM352Y plus any course numbered CMMS.. or CMNN.. from the list of courses approved for the MSc in Mathematics.
Candidates can take at most two undergraduate courses.
A student who has already passed CM338Z Financial Mathematics, or a substantially equivalent course, can replace CMFM02 with CMFM05, CMFM06, or another elective courses taken from the list above.
A student will also undertake an individual project and submit a report thereon, which shall not exceed 10,000 words in length (CMFM50).
A full-time student normally attends four courses during the first semester and four courses during the second semester, but a student may, with the approval of the programme advisor, attend three courses during one semester and five during the other.
The individual project is normally taken during the final year of study.
Assessment information
(i) 8 half-unit courses for examination.
(ii) One individual project of approximately 10,000 words.
Written examinations: May/June of that session
Individual project: to be completed by September of the final year.
Each student will write a thesis on an individual research project of approximately 10,000 words. The thesis is due early in September. The precise deadline for handing in the theses is announced in June. The examiners may conduct an oral examination on the subject of the research project to decide on the final mark of the thesis.
A part-time student may complete the examination either
a) by entering in his final year for the whole examination; or
b) by entering half the written papers in the first year and the remaining papers in the final year of study.
Progression Requirements
In order to progress to the research project, students will be required to have achieved a pass (i.e. 50% or more) in at least five of the written examinations. In those cases where the relevant examination results are available only after June 1 (when the research project will have started), and are found to be insufficient for the student to progress, a student will be asked to terminate the project. In borderline cases, the examiners may conduct an oral examination to decide on progression
Progression Requirements for Part-Time Students
In order to progress from year one to year two, a part-time student should normally have passed all the courses for which s/he is registered for that year. However, a student who fails one or more examinations in her/his first year of study may, at the discretion of the Examiners, be permitted to proceed to her/his second year of study.
Requirements for the award
To obtain the MSc in Mathematics degree the student must pass at least six courses and the project and obtain an average mark over eight courses plus the project of at least 50%.
A candidate who passes all eight courses at the first attempt obtains an average course mark of at least 60% and obtains at least 60% for the individual project will be considered for the award of Merit.
A candidate who passes all eight courses at the first attempt, obtains an average course mark of at last 70% and obtains at least 70% for the individual project, will be considered for the award of Distinction.
Marking scheme, including classification boundaries
The pass mark for each element of the programme is 50%. The following marks will be graded as follows:
Mark Range Grade
70-100 Distinction
60-69 Merit
50-59 Pass
Fail
Provision and conditions for reassessment and compensation.
See the Academic Regulations for postgraduate students for reassessment provision and conditions.
A candidate who fails one or more written examinations at the first attempt and fails to satisfy the written examination component of the requirements for the award of the MSc degree may, at the discretion of the Board of Examiners, be reassessed on one occasion.
The reassessment shall consist of resitting, at the next following examination, some or all of those written examinations for the courses which the candidate failed at the first attempt. A candidate may only resit a written examination for a course at the next following examination for that course.
A candidate who fails the project at the first attempt must re-register for the project in the next academic year. The second attempt must be completed in the time-frame allocated for the project in that academic year.
Credit transfer provisions
Not applicable.
Postgraduate Diploma
Course co-ordinator: Prof Y Safarov
Full-time: One year
Curriculum
Students are normally expected to attend between six and eight half-unit courses, excluding first year undergraduate courses, as approved by the Head of Department. See the undergraduate version of How The System Works.
Assessment information
Normally a single written examination on between six and eight of the courses taken (some of which may include a coursework component).
Written papers: May/June
Requirements for the award
A candidate must pass five out of eight subjects.
Marking scheme, including classification boundaries
The pass mark is 40%.
Recommendations for an award are made by the Board of Examiners based on the results in the examinations taken. For a Pass the course-unit value of the courses passed should normally be to the value of at least two and a half course units. A ‘Merit’ is awarded for a pass with F > 50, a ‘Distinction’ for a pass with F > 70. The ‘1 year’ F indicator is calculated as follows: F = (1/6)(sum of the best six marks) + (1/30)(sum of the remaining marks).
Mphil/PhD Mathematics
Please see Department of Mathematics Handbook for Research students.
This part of the handbook gives a provisional list of half-unit courses, which may be modified before the session begins. Be reminded that you should always consult your Course Adviser about prerequisites for the courses and your intended programme. Course Advisers are identified in Section 2 of this booklet.
Please remember that members of staff are always glad to be consulted; this includes consultation by students who are not attending the particular staff member's course. The names of staff members willing to help with each course will be publicised on departmental notice boards and given on the information sheet for the course.
At the start of each course, the lecturer will hand out a Course Information Sheet, which includes more detailed information about the course.
Courses marked with a u indicate undergraduate level course options
Applied Probability and Stochastics (CMFM01)
Dr M Zervos
Sample
spaces, probabilities, random variables, conditional expectation.
Moments, generating functions, characteristic functions. Gaussian
random variables, central limit theorem, strong law of large numbers.
Markov chains, Chapman Kolmogorov equation, classification of states,
stationary distributions, ergodicity. Random processes, martingales,
Brownian motion, Poisson process. Entropy and information.
Introduction to Derivatives Pricing (CMFM02)
Forward prices, discounting, arbitrage-free pricing; binomial trees, derivatives pricing in discrete time by use of binomial lattices, geometric Brownian motion, volatility and drift, martingales and conditional expectation, Ito calculus, hedging portfolios, replication, Black-Scholes model, put-call parity. Risk premium, risk-neutral measure.
Financial Markets (CMFM03) for MSc Financial Mathematics students only
This course presents an overview of the world's financial markets, and a concise mathematical formulation of the main characteristics of financial instruments and trading practice, with an emphasis on quantitative aspects of options, futures, and other derivatives. Topics covered include: Spot markets for stocks, bonds, currencies, commodities. Forward markets. Commodity futures, financial futures. Stock options, index options, currency options, commodity options, interest rate options, options on futures. Interest rate swaps, currency swaps. Corporate bonds, treasury bonds, inflation-linked products. Energy and credit markets. Structured products, OTC derivatives.
Exotic Derivatives (CMFM08) for MSc Financial Mathematics students only
Dr G Iori
This
course surveys pricing and risk management techniques for a number of
important financial derivatives. Topics covered include: American,
barrier, quanto, forward-starting, Asian, lookback, compound, range,
Bermudan, and passport options; options to exchange one asset for
another, dual-asset knock-out options, and basket options; options on
swap rates, barrier swaptions, flexicaps, and convertible bonds.
Gamma and vega hedging. Interest rate risk management.
Derman-Kani-Dupire treatment of implied volatility smiles. Credit
derivatives, defaultable bonds. Energy and weather derivatives.
Portfolio Risk Management (CMFM09) for MSc Financial Mathematics students only
DrTheory of risk aversion and utility, with applications. Arbitrage-free multi-asset financial markets. Trading strategies, consumption and portfolio value processes, expected utility from consumption and terminal wealth. Portfolio optimisation, solution of Merton problem. Transaction costs, market incompleteness, portfolio constraints, convex duality techniques.
Lie Groups and Algebras (CMMS01)
Matrix (Lie) groups. Examples (GLn, Un, On, Spn, Heisenberg groups, Galilean, Lorentz, Poincaré groups). Exponential and logarithm of a matrix, 1-parameter subgroups, Lie algebras. Basic representation theory, examples (su(2), su(3), su(n)). Relation with spherical harmonics. Semisimple and solvable groups, Engel's and Lie's theorems.
Basic Analysis (CMMS05)
A self-contained excursion through some fundamentals of functional analysis. Topics to be discussed: Banach spaces, open mapping and closed graph theorems, Hahn-Banach theorem, dual spaces, Banach-Alaoglu theorem.
Operator Theory (CMMS08)
Hilbert and Banach spaces. Riesz representation theorem. The adjoint. Orthogonal projections. Spectral theory of bounded linear operators. Spectral theorem for bounded linear operators. Spectral theorem for compact operators. Applications to differential and integral equations.
Spectral theory of Markov chains (CMMS09)
The course will study the spectral properties of operators associated with Markov Chains and random walks on graphs. Topics to be discussed: Markov transition matrices, invariant states, ergodicity, continuous time Markov chains, the infinitesimal generator, etc.
Fourier Analysis (CMMS11)
Fourier Analysis on the circle; Fourier series and Fourier transform on the line and on Rn. L2-Fourier transform. Parseval's formula, Schwartz classes S and S'. Applications in analysis and theory of PDE.
Manifolds (CMMS18)
Manifolds and functions; vectors and vector fields; tensors and tensor fields; Lie derivative; differential forms and exterior derivative; covariant derivatives, connections, torsion and curvature; metrics and Riemannian geometry; integration; symplectic geometry; further topics in differential geometry.
Quantum Field Theory (CMMS32)
Dr G. Papadopoulos
A
basic course in quantum field theory which develops the subject using
path integrals. Perturbation theory, Feynman diagrams and an
introduction to renormalisation are covered. Quantum Mechanics
formalism, density matrix, hydrogen atom, symmetries, groups,
especially $SU(2)$ and $SO(3)$, Wigner's theorem. Particle of spin
1/2 in an electromagnetic field; Pauli equation. Introduction to
relativistic quantum mechanics and the Dirac equation.
Point Particles and Strings Theory (CMMS34)
Prof P.C. West
An introduction to modern string theory starting from a relativistic point particle. Elementary supersymmetry is discussed and applied to the particle case. The bosonic string is defined and quantised. The superstring is introduced.
Advanced General Relativity (CMMS38)
Einstein's field equations, physically significant solutions, black holes and gravitational waves. Lagrangian and Hamiltonian formulations of general relativity. The global structure of spacetime
Dr I F Wilde (Second semester)
This is an essentially self-contained rigorous course on complex analysis. Whilst the notion of differentiation of a function of a complex variable would seem to be a trivial extension of its real variable counterpart, it turns out that complex differentiability has far reaching consequences. For example, it implies that the function possesses derivatives of all orders. This is in stark contrast to the situation familiar from real analysis. Furthermore, such functions always have power series representations (Taylor series). Curiously enough, much of the theory of differentiable functions is tackled with the help of complex integration. A study of singularities of complex functions allows some rather difficult integrals from real variable theory to be computed quite easily (via the Residue Theorem). The subject has a high visual appeal, thanks to the realization of the complex numbers as the plane.
Dr W J Harvey (First semester)
An introduction to the study of the main geometries on Euclidean space which exhibits the distinctive character of each. Euclidean geometry: real vector spaces; conics; orthogonal groups. Projective geometry: projective line and plane; algebraic curves. Hyperbolic geometry: upper half plane and Möbius transformations; Poincaré’s metric.
Dr D Burns (First semester)
This course combines linear algebra with the basic theory of abstract rings and groups to develop an elegant theory of fields and their extensions. This is then shown to provide a common formal framework for solving several historically significant problems in geometry and algebra. Galois Theory is also particularly important in Algebraic Number Theory and has some applications to Riemann Surfaces etc.
The course starts with a review of rings, fields, polynomials and factorisation. The basic concept of an `extension' of fields is then introduced. First applications are made to simple questions of algebraicity/transcendence and constructibility (e.g. of regular polygons) with compass and ruler. The theory is then refined by studying normal and separable extensions and their automorphisms. This results in the definition of the Galois group and the Galois Correspondence. Examples are given. Finally, the theory of `soluble groups' is invoked to establish a criterion for the solubility of a polynomial by radicals. This is applied to prove the insolubility of the general quintic.
Other applications of Galois Theory that may be treated in more or less detail during the course include: finite fields, cyclotomic fields and the solution of cubic and quartic polynomials.
Dr L J Landau (Second semester)
The aim of this course is to introduce and develop the basic ideas and results of mathematical logic and the theory of computation. These results are important for an understanding of the foundations and limitations of mathematics. There are no prerequisites.
Constructing proofs forms an important part of a mathematician's activities, and a careful analysis of what constitutes a proof will be given within the framework of the predicate calculus. Topics covered include the propositional calculus, the axioms and rules of deduction of the predicate calculus, and truth in an interpretation. Mathematical systems within the predicate calculus with equality, such as group theory, number theory, and set theory, will be considered.
A formal mathematical system is an algorithm for producing theorems, an algorithm which may be carried out by a computer. There is thus a close link between a formal system and computation. The basic ideas of computation will be considered using the URM, the unlimited register machine. A universal program which can emulate every program will be obtained. The results of Gödel and Turing on limitations of formal mathematical systems and computers will be discussed: incompleteness and undecidability.
The course aims to introduce students to Einstein’s theory of gravitation. The aim of this course is to show how quite sophisticated mathematics - differential geometry - can be used to model space-time, leading to a theory of gravitation. While being of great intrinsic interest and beauty, this course is also essential for anybody wishing to have a good understanding of modern theoretical physics.
Dr D A Lavis (Second semester)
Topics covered in this course include first order linear systems of ordinary differential equations; autonomous systems, phase portraits, stability; non-linear systems, linearisation; Laplace transforms, the transfer function, Routh-Hurwitz criterion for stability, and more advanced transfer function methods. In control theory, the course covers: the rank criterion for controllability, linear feedback and optimal control, including Euler-Lagrange methods and introduction to Hamiltonians; the Hamiltonian-Pontryagin method, bounded control functions, Pontryagin's principle; big-bang control; switching curves.
Quantum Mechanics II (CM436Z) u
Quantum Mechanics formalism, density matrix, hydrogen atom, symmetries, groups, especially SU(2) and SO(3), Wigner's theorem. Particle of spin 1/2 in an electromagnetic field; Pauli equation. Introduction to relativistic quantum mechanics and the Dirac equation
Neural Networks (CM451Z) u
Dr H Rae
This
introductory course covers the basics of neural information
processing. Subjects include neuron models (graded response,
McCulloch-Pitts, stochastic binary neurons, coupled oscillators),
learning in layered neural networks (linear separability,
perceptrons, error backpropagation, dynamics of learning) and the
operation of recurrent neural networks (creation of attractors,
analysis via Lyapunov functions, Hopfield model, analysis of
dynamics).
Advanced Neural Networks (G30)
Radial basis functions and function approximation. Self-organising maps and learning vector quantisation. Bayesian analysis of learning in layered networks; regularisation and generalisation. Gaussian processes. Support Vector Machines.
Information Theory in Neural Nets (CMNN4/G31)
Prof ACC
Coolen
Information theory: entropy (joint and relative),
Shannon's theorems relating entropy to optimal coding. Application to
neural networks: Boltzmann machine learning, unsupervised learning in
feed-forward networks by maximum information preservation,
quantifying efficiency of associative memories.
Statistical Mechanics of Neural Networks (CMNN13/G32)
Application of statistical mechanics methods to analyse and quantify operation and learning in neural networks. Exact solutions, obtained by replica theory, theory of stochastic processes, path integrals, including: statics and dynamics of attractor neural networks, Gardner theory, dynamics of learning.
The Academic Registrar has requested that the following University of London statement of plagiarism should be publicised in all departments. This has particular relevance for project work.
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, that is, the presentation of another person's thoughts or words as though they were your own, must be avoided, with particular care in coursework and essays and reports written in your own time. Direct quotations from the published or unpublished work 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. Failure to observe these rules may result in an allegation of cheating.
Certain lectures provide comprehensive hand-outs of lecture notes. The direct repeating of these ‘parrot fashion’, either whole or in part, in examinations is severely frowned upon. It is obviously acceptable, however, to express such ideas and concepts in your own words.
It is a requirement that, before submitting any document, all students should consult the appropriate member of staff.
Please read carefully (and also the College Regulations if you have concern on matters not covered here). This is important and affects YOU personally. Remember – ignorance is no excuse for failure to comply!
Two examiners from the Department are assigned to each course. One is normally the member of staff who gave the course and this examiner is responsible for setting the paper. The other examiner ensures that the paper is accurate and reasonable. The questions are then vetted by a visiting examiner who is from another University or a different London College. The scripts are marked by both examiners and moderated by the same visiting examiner. The aim is to achieve a standard which is broadly comparable with other highly ranked university Mathematics Departments. There is no fixed proportion of first class marks or of failures.
The title of your degree will normally be that of your field of study (see Section 2). MSc Mathematics students may have their specialist area included in their degree title e.g. MSc Mathematical Physics.
Course-unit registration forms (your entry for the course-units in which you wish to be examined) will be supplied by the department at enrolment and MUST be completed by the end of the second week of the session for all subjects (whether taught in the first or second semesters, or both). NB Sometimes two different course units have lectures in common. In these instances, you MUST ensure that you are registered for the unit you intend to take, and which is appropriate to your programme of study. Before completing your entry, you must discuss the programme with your Course Adviser whose signature indicating approval of your course of study is needed. You will receive more detailed information regarding examination procedures when you are sent confirmation of your course-unit registration to your term-time address early in the second semester. It is your responsibility to check your entry. It may be possible to amend the list at a later date if you wish to change your choice of subjects, but this will not be possible after the deadline announced by the College. Any amendments must be approved by your Course Adviser and must be submitted in writing by completing a form in the School Office.
Your course-unit registration is one of the most important things you will do during the year. Failure to follow registration procedures correctly may well result in you being unable to sit your examinations. It is the individual student’s responsibility to meet the deadlines.
If you had any illness at the time of, or prior to, the examination which you feel may have affected your examination performance, or if you are prevented from attending any examination through illness, a legible medical certificate from a recognised medical practitioner and a written explanation (if necessary) must be submitted to the School Office as soon as possible and within seven days of the date of the examination concerned. A replacement request, or request for consideration form must be completed. Replacement examinations are offered in August at the discretion of the Chairman of the School Board of Examiners, but the situation concerning replacement examinations is currently under review.
For more details you should read the leaflet concerning examinations, which the Registry sends to all candidates.
Students with long term problems, such as visual impairment or dyslexia, should bring this to the attention of the School Office as early as possible before the examinations, so that appropriate arrangements can be discussed.
If you absent yourself from an examination without good cause you may adversely affect your degree prospects. All examination entries in your approved degree programme are taken into account, and so an absence will count as a failure, and count as one of the at most two attempts you are allowed for each examination.
You may withdraw from an examination without this penalty, but then any re-entry will be counted towards the maximum of 8 half units (excluding re-sits) that may be taken in the following year. Also, if the course is not given in the next year, you may not be allowed to re-enter. Under current regulations, if it has to be a choice between withdrawing or absenting yourself from a course unit, being absent is usually the more advantageous option. The main exception is when you withdraw in order to repeat the year.
If you are in any doubt, you should discuss matters of this kind with your tutor. In any case, the Regulations stipulate that at least seven days notice before the first examination must be given of any proposed withdrawal and you must consult your Course Adviser and obtain the appropriate consent.
The dates and arrangements for the communication of results and consultations concerning progress will be posted on the notice boards.
Room 2B, Main Building 020 7848 2331
King's College London has a number of its own Halls of Residence, as well as access to the Intercollegiate Halls of the University of London. All full time undergraduates entering the College for the first time on courses of two or more years' duration are guaranteed the offer of one year's residence in one of these Halls. Full details are available from the Accommodation Office, which is situated in Room 2B, Main Building. Office hours are 9.45-13.00 and 14.00-16.00. They deal also with flats and other forms of accommodation.
Room 5B, Main Building 020 7848 4416
The College runs a Careers Advisory Service from Room 5B, Main Building, Strand, where much useful information may be obtained about opportunities for graduates. Talks by representatives of large employers are arranged, as are visits to companies. Students in their final year at College are urged to watch the notice boards for details. In the Mathematics Department, Dr L J Landau is responsible for careers advice and keeps details of job opportunities.
The association of former students of the college is called King's College London Association (KCLA), membership of which is free. Apart from an annual reception and dinner, KCLA keeps its members informed about developments in the college and news of our graduates by a Newsletter. Overseas branches have recently been formed in several countries. For more information, you should write to KCLA Secretary, care of the College.
020 7848 2613
King's has a comprehensive medical service covering three campuses with both male and female general practitioners and two full-time nursing sisters. In the Strand campus, the Medical Centre is situated on the third floor of the Macadam Building.
Dr. Pathmanathan, Dr. Kumar and Dr. Rady have formed a new 3 doctor Partnership to provide medical services at the Strand and Waterloo Campuses.
The new Partnership will operate the following surgery hours:
Strand
Monday 8.30 - 6pm
Tuesday 8.30 - 6pm
Wednesday 8.30 - 6pm
Thursday 8.30 - 2pm then 5pm - 6pm
Friday 8.30 - 6pm
The Doctors clinic at Waterloo is operated on a walk-in basis but if you have any queries please contact the Practise Nurse who is on site from 10am - 4.30pm, Monday to Friday on 020 7848 4241.
Waterloo
Monday 3pm - 4pm
Tuesday 3pm - 4pm
Wednesday 3pm - 4pm
Thursday Closed
Friday 3pm - 4pm
Emergency Clinic
An Emergency Clinic is in operation on a daily basis from 1pm - this is a walk in clinic operated on a first come first served basis. This is for emergency matters i.e. if you cannot wait until the next available Doctors appointment.
Outside of surgery hours or in the case of an emergency please contact the Covent Garden Medical Centre on 020 7379 7209.
If you have any questions or would like any further information, please contact Michelle Krahn - Secretary (Strand Medical Centre) 020 7848 1211, who wil be happy to help you.
Third Floor, Macadam Building 020 7848 2613
The Student Services Welfare and Information office provide an information and welfare service for all students. They operate from the third floor of the Macadam Building, from where all kinds of sympathetic help and advice are available to deal with problems of settling down, late grant cheques, registering with a local physician, and so on. They also provide handouts covering subjects such as study skills techniques, managing your money, social facilities and information for overseas students, including Home Office and employment regulations, social security and medical matters.
The student counselling service is available to any student who is encountering problems of a personal, social, domestic or other nature. Appointmens can be made on the above number.
Macadam Building 020 7848 7132
All students are automatically members of the King's College Students' Union and therefore have access to its facilities. The Union promotes the social, cultural, athletic and welfare interests of all its members by financing, organising and co-ordinating the various societies and sporting activities. It also represents its members to the College authorities and external bodies. Students are involved in decision-making at all levels, with policy being passed by the Student Representative Council, which comprises elected representatives from all departments. The day-to-day running of the Union is carried out by student officers elected each year by the student body. Communication is important and the Union provides various publications, including a regular magazine called ROAR. Students are also members of the ULU, the University of London Union. This gives access to additional sport and social facilities in their Bloomsbury premises and the chance to mix with students from other London Colleges. The Union is situated in Malet Street, telephone 020 7664 2000.
Room 36A, Main Building 020 7848 2042
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Head of Department and Reader in Mathematics: J A Erdos, MSc, PhD
Professors: C J Bushnell, BSc, PhD A C C Coolen, MSc, PhD E B Davies, MA, DPhil, FRS, FKC P S Howe, BSc, PhD L P Hughston, MA, Dphil A N Pressley, MA, DPhil D C Robinson, MSc, PhD Y Safarov, BSc, PhD, DSc P T Saunders, BA, PhD R F Streater, PhD, DIC, LFS P C West, BSc, PhD
Emeritus Professor of Mathematics: J G Taylor, BSc, MA, PhD
Readers: D J Burns, MA, PhD W J Harvey, BSc, PhD L H Hodgkin, BA, DPhil L J Landau, MA, PhD F A Rogers, BA, PhD I F Wilde, BSc, PhD, DIC
Honorary Visiting Appointments: Senior Research Fellow : FAE Pirani, DSc Senior Lecturer: A R Pears, MA, PhD Research Fellow : C Hunter, BSc,PhD
Departmental Administrator: Miss Hilary Morton
Postgraduate Secretary: Miss Samantha Glass
Undergraduate Secretary: Miss Annabelle Lyles
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Senior Lecturer: D A Lavis, BSc, PhD, FInstP, FIMA
Lecturers: A D Barnard, MA, PhD G Iori, BA,PhD H C Rae, BSc, PhD A Recknagel, PhD S Scott, BSc, DPhil J R Silvester, MA, PhD P Sollich, MPhil, PhD G M T Watts, BA, PhD M Zervos, MSc, PhD
Advanced Fellows: M Gabadiel, MA, PhD N Lambert, PhD G Papadopolous, PhD D Solomon, BA, PhD
Visiting Lecturers: S Fairthorne, BSc P A Goodinson, BSc, PhD M Linch, BS, PhD B L Luffman, BSc, PhD A Watts, BSc
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