EMS-SMF-SMAI MEETING ON APPLIED MATHEMATICS

AND APPLICATIONS OF MATHEMATICS

10-13 February 2003, Nice

The European Mathematical Society, the Societé Mathématique de France, and the Societé de Mathématiques Appliques et Industrielles organised this Meeting, with support from the Université de Nice Sophia-Antopolis (Laboratoire J A Dieudonné).  The programme was chosen by an international scientific committee, which was chaired by Pierre-Louis Lions (France) and Sergei Novikov (USA/Russia), with Alain Damlamian acting as coordinator.

At an impressive opening ceremony at the Palais des Congrés Acropolis, we were welcomed by Rolf Jeltsch (recent President of EMS), Michel Théra (President of SMAI), Michel Waldschmidt (President of SMF), by Civic and University representatives and by John Kingman, who had been elected as President of the EMS for four years from 1 January 2003.

The pattern of the Meeting involved Plenary lectures and about 45 mini-symposia, one of which was sponsored by the London Mathematical Society.  Moreover there was a Special EMS Event on “Electronic Databases” and two round-table discussions, one on “Mathematics in developing countries (led by Michel Jambu) and one on “Education” (led by Gérard Tronel).

As the title of the meeting emphasizes, the scope of the Meeting was very broad, including both Applied Mathematics as such and applications of mathematics in the biological, physical and medical sciences, in engineering, and in finance.  Both the plenary lectures and the mini-symposia illustrated this breadth.

The first Plenary lecture was given by David Levermore (Maryland) on “Fluid Dynamical Limits for the Boltzmann equations”, and during the four-day meeting other Plenary lectures were given by Alfred Bruckstein (Technion, Haifa) on “Why the ant-trails look so straight and nice: or mathematics of multi-agent interaction”, by Robert Eisenberg (Chicago) on “Ion Channels as natural nano devices ripe for mathematical analysis”, by Roland Glowinski (Houston) on “Numerical simulation of incompressible viscous flow in regions with moving or free boundaries”, by Roland Keunings (Louvain) on “Memory fluids: mathematical and numerical challenges”, by Pascal Massart (Orsay) on “Model selection: a non-asymptotic view based on concentration inequalities”, by Marek Musiela (BNP-Paribas, London) on “Linear and non-linear valuation methods used in finance and insurance”, by Bernard Prum (d’Evry) on “Statistical analysis of genomic data”, René Schoof (Rome) on “Algorithms for factoring integers and computing discrete logarithms” and by Enrique Zuazua (Madrid) on “Dynamics, control and numerics”.

The 45 mini-symposia were grouped as follows”-

1.         Control theory, optimization, operations research and system theory;

2.         Applications of mathematics in biology, including genomics, medical imaging, models in immunology, modelling and simulation in biological systems;

3.         Scientific computation, including ab-initio computations and molecular dynamics;

4.         Meteorology and climate, including global change;

5.         Financial engineering;

6.         Signal and image processing;

7.         Nonlinear dynamics;

8.         Probability and statistics;

9.         Inverse problems;

10.     Fluid dynamics;

11.     Materials science;

12.     Applied geometry.

The London Mathematical Society sponsored and financed a Mini-symposium on “New Mathematical Developments in Signal Processing”; this was organised by David Broomhead (UMIST) and Jaroslav Stark (Imperial College), and had contributions from Patrick Flandrin (Lyon), John McWhirter (LMS Member and IMA President) and Tim Sauer (Virginia), following an introduction by Jaroslav Stark.

The writer found the quality of the Plenary lectures and the Mini-Symposia to be very high.  And, moreover, discussions with colleagues from other European countries and from North America and elsewhere were valuable and stimulating.

Members of the Meeting were privileged to attend receptions at the Palais des Congrès Acropolis and at the Université de Nice.  The hospitality of the EMS and of our French hosts was much appreciated, as was expressed on our behalf by John Kingman, President of the EMS, and by other Society Presidents at the Reception at the Université de Nice.

For my own part, as a member of the Scientific Committee, I would like to express by appreciation of the fine work of coordination done by Alain Damlamian.  Also I wish to acknowledge with pleasure the support of The Royal Society through a Conference grant.

Trevor Stuart

WELCOME TO MATHBANK

(www.mathbank.soton.ac.uk)

The aim of this article is to introduce readers to the MathBank website, the result of a project undertaken through the award of a National Teaching Fellowship in 2000.

The purposes of the website have changed little since the original conception as outlined in the MSOR Newsletter in August 2000 [1]. The development phase of the project is now substantially complete. The aim is to provide a database of teaching resources for lecturers who may not have invested in the use of technology in their teaching in a radical way, but who rely on high quality exposition based on well-structured explanation, with appropriate problems. Many lecturers find themselves having to teach courses on standard material, with a syllabus which perhaps does not fit the emphasis given in particular textbooks on the subject. Under those circumstances it is tempting to prepare the material “from scratch”, with an eclectic use of printed resources for proofs, problems and examination questions. A considerable investment of time is necessary to accomplish this, and it would be really convenient to be able to take the textbook and simply customize it to the needs of the particular course. For example, you may be teaching a mathematics course for second year engineering students covering some parts of Fourier Series, some types of partial differential equations approached only by separation of variables, and some special functions chosen by the Mechanical Engineering department. The nearest textbook is designed for electronic engineers and so the coverage is not quite right and a number of the problems are inappropriate. This is where Mathbank may be able to help you. The intention is to save the lecturing community as a whole the unnecessary time and labour in such an enterprise, by providing a resource bank of notes, problems, examination questions and perhaps other items which can be downloaded and then customized. It is important that the database be easily accessible, and searchable, and that the material be available in formats which colleagues can easily manipulate. It is important too, that the database should not be static, so that new material can be added and that this should be a reasonably straightforward process. It is hoped that these criteria have been met. The Fellowship funds enabled us to employ programming expertise from the University of Southampton Geodata Unit to provide the structure we wanted.

Let’s see what happens if we log in and put in the word “Fourier” to search. We are presented with a list of resources that are available. An item in this list may be a single document, like an examination question and solution. It may be a directory containing several documents, the directory as a whole having a name or classification containing the search word, or it may be a Resource, which in the structure of the database is an object containing several directories. This may be something like a book, with each chapter being a separate directory, and then each “bite-sized” section of notes being a single document identified by an appropriate keyword. The search list will give some information about the item in question, which will have been supplied by the person who knows best, namely the original author who uploaded it onto the site.

What is there at the moment? Well, I have been fortunate in having the support of many of my Southampton colleagues in kindly supplying material: mainly lecture notes, problem sheets and exam questions. We used some of the project funds to pay undergraduates during a summer vacation to turn a lot of this handwritten or typed material into LaTeX. The students learned extremely rapidly and became very efficient and remarkably accurate in their use of LaTeX. Subsequently one of our recent MMath graduates about to start a PhD was paid to upload this material and catalogue it, supplying keywords and assigning each item to a category in a subject list which was constructed using a mixture of sources including the SEFI European Engineering Mathematics syllabus lists [2]. Because all this comprised the initial construction phase of the site, it looks as if I am the author of all the documents. This is not so!

When we have done a search, or when we are browsing, how do we know what each item contains in detail? For such a database whose documents can potentially be of many different formats (in fact there is no practical restriction in our case) the inclusion of effective previewing facilities is a considerable problem. We decided not to attempt this on a systematic basis, but instead to do two things: (1) to encourage anyone who uploads a set of documents to write an index file as a .txt file; a more detailed specification (maybe a sentence) for each item can then be given, and the file can be viewed without downloading, and (2) to provide PDF versions as well as LaTeX or other versions where possible (in the case of documents which we uploaded a script was written to do this).

Is the site going to be useful? This depends on two things – first, on the quality of the documents and the willingness of colleagues to use them to save time and unnecessary labour, and second, the willingness of colleagues to share their own materials and upload them onto the site.

Do you have an examination paper to set for your first year engineering mathematics class? You can find lots of questions on Mathbank, either by searching for the keyword “engineering” or by searching by topics (one variable calculus, matrices etc.). If you see a whole directory of questions look at the index file to see which ones will be of particular interest. Now download the ones you want. You might find a couple which fit your requirements exactly, or there might be some which you simply want to adapt, by changing the coefficients or the functions involved. You are free to do that, and since you have been able to download the LaTeX file itself it is easy to edit.

So, if you have some material you are willing to share, what should you do? First, become a registered user. Now if you have 50 problems and solutions they may all be on a similar topic, so your resource may consist of a single directory. We don’t expect you to upload 50 files separately. Turn the 50 files into a .zip file. There is the facility to upload this and for it to be automatically unpacked into its 50 constituents. Then for each document you can catalogue it and supply keywords. This is not difficult to do, and the Introduction, accessed from the front page, provides helpful instructions. The cataloguing is in some sense the most important part of the process, since it directs documents to users doing a search.

Will the site be useful? That depends on you, both as a user and as a provider. As a user it doesn’t matter if the site doesn’t contain exactly what you want: you can adapt and minimise labour. Material uploaded should not be copyright. As a provider do not be modest about your offerings. If a resource like this takes off and gets well used it will be of benefit to the mathematical community as a whole.

My final word is a big thank you to my colleague Jim Renshaw whose advice and expertise has been invaluable throughout the development of MathBank.

Keith Hirst

University of Southampton

[1] Keith Hirst MathBank, A Resource Bank for Teachers and Learners. MSOR Newsletter, August 2000, p.8.

[2] Société Européenne pour la Formation des Ingénieurs (European Society for Engineering Education) A Core Curriculum in Mathematics for the European Engineer N.C. Steele, Plymouth/Coventry, 1991, p.37, ISBN 2-87352-001-9

This article originally appeared in MSOR Connections in November 2002. It is reproduced here with permission.