During the academic year 1986-1987, representatives of Universität Kaiserslautern (D), Johannes Kepler Universität Linz (A), Technische Universiteit Eindhoven (NL), University of Oxford (UK), Università di Milano (I), Norges Teknisk Naturvitenskapelige Universitet (Trondheim, N) and Rolf Nevanlinna Instituutti (Helsinki, SF, acting as coordinating centre for several cooperating Finnish universities) formed the European Consortium for Mathematics in Industry (ECMI) and initiated two year postgraduate programmes, where industrial problem solving is a prominent aim using mathematics.
The purpose of these industrial mathematics programmes is expressed by the mission statement of ECMI:
- To promote the use of mathematical models in industry.
- To educate industrial mathematicians to meet the growing demand for such experts.
- To operate on a European scale.
Various implementations of industrial mathematics programmes are available at the ECMI partner universities. Typically the programmes consists of a two year master programme (120 ECTS) which can be entered after a bachelor degree in mathematics or applied mathematics. Other educational backgrounds can qualify for entry but should be based on a minimum of three year undergraduate study at university level. The students can chose between two lines of study, the first one is techno-mathematics and the second one is econo-mathematics.
| Technomathematics covers subjects related to modelling of technical subjects as encountered in mechanics, pharmacy, electronics, chemistry, physics, bioengineering, civil engineering, etc. |
| Econo-mathematics on the other hand deals with problems like e.g. planning and scheduling, operation analysis, quality control, statistics, distribution management, financial decision processes and data communication. |
The ECMI partner universities offer industrial mathematics programmes which typically includes the following elements
| A mandatory common course work for one or both of the two lines of study, techno-mathematics and econo-mathematics. Each line may typically comprise mandatory lectures and exercises corresponding to a minimum of 30 ECTS. |
| An individual selection of special topics. We suggest the workload to be about 40 ECTS, but this can vary. |
| Practical training in mathematical modelling, organized in regular modelling seminars, and participation in one ECMI international Modelling Week. Suggested workload 10-20 ECTS. |
| A master thesis project of at least 30 ECTS involving a real industrial problem, preferably carried out in an interdisciplinary environment involving participants from industry. |
| A student exchange programme requiring each ECMI student to spend a period at another participating university or do a final master thesis project abroad. |
The core courses of techno-mathematics and econo-mathematics should cover the following topics
| Techno-mathematics | Econo-mathematics |
|
Modelling seminar and introduction to techno-mathematics Ordinary and partial differential equations Scientific computing Optimization and statistics |
Modelling seminar and introduction to econo-mathematics Computational methods Optimization and statistics Discrete mathematics Difference and differential equations |
The core subjects are to provide a broad background within subjects relating to techno-mathematical disciplines and/or econo-mathematical disciplines. In the introductory year the students should become familiar with simulation and statistical software such as Matlab, Maple, Mathematica, SAS and others. Later the students will specialize within one or two subjects. All classes are given in English to facilitate exchanges as necessary.
| Exchange abroad - normally with an ECMI Centre - other countries' institutions by approval by the ECMI Educational Committee. The exchange can be either studying one semester at another ECMI Centre or an industrial placement. |
| International Modelling Week, organized annually by an ECMI center, and European aspect. |
| An industrial placement. This could alternatively be an industrially orientated project carried out at an ECMI Centre. Recommended duration 6 months, but keeping quality more important than duration. |
| The study is completed by a thesis/report on the industrial placement work. It must be presented in English and contain both mathematics and industrial relevance. The latter normally evidenced by a supporting letter from the industry stating the importance of the thesis work, however, taking the judgement of the Centre into account. |
| Certification available at different levels based upon time period. A full transcript of studies undertaken to accompany Certificate. The Certificate is issued by the ECMI Educational Committee based on two review reports of the thesis by two of four ECMI reviewers. |
In assessing the extent of the programme the ECTS framework shall be used, that is 30 ECTS points per semester or 60 ECTS points per year. (For a student of normal ability 1 credit point = 20 hours study.) For trimesters of 12 months duration without vacations, 90 ECTS points per year is granted. Most importantly, any ECMI Programme of study must be flexible enough to conform to the Centres own rules and regulations allowing the student to gain the institution's own award. Furthermore, we can extend the programme to training industrial PhDs.
We welcome co-operation with institutes and universities which intent or already contribute to industrial mathematics. This includes both scientific and educational contributions within the spirit of ECMI, that is applying and developing mathematical tools for industry and providing interdisciplinary educational programmes within industrial mathematics.
ECMI centres are universities that have joined the network (ECMI membership is free for all universities) and fulfilled certain criteria in their educational programme. Orientation towards real life applications and industrial problems must be visible in educational style and contents. More precisely a university can obtain a status of Educational centre in ECMI Network after
| 1: Setting up a master of science level programme in industrial mathematics, technomathematics or equivalent title. |
| 2: Submitting the programme description for evaluation by ECMI Educational Committee. |
| 3: Inviting a inspection visit by a panel of reviewers chosen by ECMI Educational Committee. |
Today the following ECMI universities offer industrial mathematics programmes.
| University of Kaiserslautern | Technical University of Dresden | Johannes Kepler University || University of Milan | Technical University of Eindhoven | Technical University of Denmark |
| University of Oxford | University of Strathclyde | University of Bristol |
| Lappeenranta University of Technology | Chalmers University of Technology | Lund University |
| The Norwegian University of Science and Technology |
| Wroclaw University of Technology | The Autonomous University of Barcelona | Carlos III University, Madrid |
| University of Novi Sad | University of South Hampton | Technical University of Graz |
| University of Grenoble | University of Rouen |
European School for Mathematics in Industry (ESIM)
ESIM is funded by the EU ERASMUS MONDUS programme and it is managed by the University of Eindhoven, The Netherlands, University of Kaiserslautern, Germany, and Johannes Kepler University, Linz, Austria. The programme is for students outside Europe.
Mathematics Curricula for Technological Development, Novi Sad, Serbia.
The project is funded by the EU TEMPUS III programme (PROJECT CD_JEP-17017-2002) and organized by University of Novi Sad, Serbia, Technical University of Dresden, Germany, Lappeenranta University of Technology, Finland, and University of Milan, Italy.