Joint MSc "MathMods" Mathematical Modelling in Engineering: Theory, Numerics, Applications

MathMods is a 2-year Joint European MSc in Mathematical Modelling in Engineering and it takes place in 3 universities:

• University of L'Aquila (Italy).
• University of Hamburg (Germany).
• University of Côte d'Azur in Nice (France).

The Consortium can also count on the collaboration with associated academic institutions, and can rely on the effective support of several companies, research institutes, and non-profit organizations in different aspects of the project.

Our MSc programme is aimed at satisfying the need of experts that may be able to apply rigorous mathematical modelling and computational techniques to solve problems in all areas of engineering.

The MathMods programme is entirely taught and conducted in English, and what makes it so special is the dynamic mobility scheme, which enables our students to spend their postgraduate years in two or even three different European countries. You'll be indeed studying in central Italy for your first semester, then move to Germany for the second term, and finally move again to 1 of our 3 partners for your second year, based on the mobility path you'll be assigned.

Aims

Mathematical modelling lies at the heart of most current technological innovations and has become a fundamental tool in many fields of engineering. Essentially multidisciplinary in its applications, mathematical modelling and simulation is in its own right a key technology that is bound to increase its presence within efficient industries and business innovation departments. The proposed program reflects this multidisciplinarity, drawing on the unifying mathematical aspects from the various and often separate engineering disciplines. This allows the development of an essentially unified methodological approach to modelling and simulation of real engineering challenges.

Mathematical modelling refers to the use of mathematics and related computational tools to bring real-world, challenging, and important socio-economic and industrial problems into a form simple enough so that a good solution can be found in a reasonable time while keeping the relevant features of the problem. Constructing models requires knowledge of enough mathematical theory, methods of solution which are really effective and efficient, computational tools at hand to do it, some knowledge of the field of application, and communicative skills to understand the important elements from experts in that field. Our master's program tries to put together all these elements to produce professionals able to work in different relevant fields with the highest intellectual level and state-of-the-art tools.

Effective modelling and simulation is an art that requires a lot of practice, so that problem solving, project development, and teamwork are aspects that should be highlighted in any training program, as our Consortium knows perfectly. On the other hand, the abstraction behind the specific application is necessary to realize that the same base tools can be applied, with the needed changes, to very different situations in various engineering fields.

The MathMods Master's degree course consists of a cycle of four semesters starting each September and awarding 30 ECTS credits each (thus 120 ECTS credits in total). The mobility scheme involves two different locations, at least, over the whole program. The first year is common for all students: this is meant to provide for a homogeneous knowledge platform across the whole group. The second year is divided into four study paths (aka specializations, branches, or tracks), which reflect our partners' field of research and excellence. Students will eventually spend their fourth semester preparing their Master's Thesis.

• Semester 1: Theory at UAQ, Italy
• Semester 2: Numerics at UHH, Germany
• Semester 3: Applications at one of our partners
  • Mathematical models in social sciences (UAQ, Italy)
  • Mathematical modeling and optimization (UAQ, Italy)
  • Modeling and simulation of complex systems (UHH, Germany)
  • Mathematical modeling applications to finance (UCA, France)
• Semester 4: Thesis at UHH / UAQ / UCA

Here are the main features of the MathMods Joint MSc:

• MathMods MSc is structured into 4 semesters (a cycle of 2 academic years starting each September)
  • The first year is common to all students. This is meant to provide for a homogeneous knowledge platform across the whole group of students. Students will spend their first semester (focused on Theory) at the University of L'Aquila (Italy) and their second semester (centered on Numerics) at the University of Hamburg (Germany).
  • The second year is dedicated to Applications as well as thesis preparation and is divided into four study pathways (aka specializations, branches, tracks), which reflect each partner's field of excellence. Students will spend their third and fourth semesters at one of our partner universities, depending on the mobility scheme they will be assigned.
• Each semester awards 30 ECTS credits so in all 120 ECTS credits
• All courses are taught in English
• Attendance to courses is compulsory
• Students will also attend (and acquire the related credits of) a course of basic Italian language (first semester) and German language (second semester). Students will also have the opportunity to attend local language courses during their second year (spent at one of our partners).
• Each student will be assigned a mobility scheme, which will involve two different destinations at least over the whole program. This means that each student will have the great opportunity to do their graduate studies in two or even three different European destinations, including Italy (semester 1), Germany (semester 2), then again Italy, Germany, or France for their Year 2. Please note that students cannot decide their own mobility scheme, which will be settled by the MathMods Scientific Committee, instead, during the first semester. The committee will do its best to reach a compromise between the choices made by each student on their application and the need for allocating a balanced number of students to each partner university. Refer to the FAQs for more details.
• Upon successful completion of their studies and dissertation of their thesis, students will be awarded a Joint Master's Degree, depending on the country where they spend their second year.

The Study Course in “Mathematical Modeling” (Class: LM44) is an international and multi-university course. It comes from decades of experience of the Erasmus Mundus Programme “MathMods - Mathematical Modelling in Engineering: Theory, Numerics, Applications”. From the Academic Year 2019-2020 this Master Programme is jointly managed by a Consortium composed by:

• University of L’Aquila (Italy)
• University of Hamburg (Germany)
• University of Côte d'Azur in Nice (France).

The Study course proposed awards a joint degree. The duration of the program is standard: 120 credits in 2 years. The study course is entirely taught in English.

The specific objective of the Master Degree in “Mathematical Modelling” is to train an engineer particularly prepared for designing, developing, and managing complex models and systems, intended both in the Engineering sense (automatic control complex systems) and in that of mathematical modeling (modeling, numeric simulation, and complex systems optimization). To this purpose, the student is first of all provided with in-depth knowledge of mathematics in fields such as mathematical analysis, numerical analysis, scientific calculus, optimization, and control theory. Such competencies are mainly methodological and concern both the fields characterizing the mathematical, physical, and informatics disciplines and the engineering disciplines, the last ones particularly in the academic disciplines ING-INF/04 – Systems and Control Engineering and ING-INF/05 – Information Processing Systems. Then, the student will specialize in the use of different methodological approaches aimed at modeling, simulation, and control of complex systems touching also other subjects characterizing both fields. These methodological approaches include:

• Modeling and simulation of continuous media (fluid dynamics, also computational);
• “agent-based” modeling (aimed for example at studying emerging behaviors in complex systems or at robotics);
• Networks modeling and control;
• Advanced optimization (intended both as optimization of control systems and in the sense typical of operational research), with the aim of formulating, analyzing, and simulating complex models and systems in different application contexts typical of engineering.

During his/her educational path, the student shall develop the pleasure for studying and the ability to use in general the principles and methods of Mathematics as well as the sensitivity to adjust its use to the specific peculiarities of the problem to be solved, the accuracy of the desired solution, also from a technological point of view, and the sustainable investment of time and money.

Description of the educational path

The educational plan is organized as follows:

1. The first semester is common to all students and will be spent at The University of L’Aquila. Common knowledge to all the different specializations that the student will select is provided, basically focusing on advanced aspects of theoretical mathematics and, secondly, on competencies in engineering disciplines typical of systems and control engineering.
2. The second semester will be spent in Hamburg (Germany). Its aim is to harmonize the knowledge of informatics, computational, and numerical aspects. It will focus mainly on numerical analysis and information processing systems.
3. The second year will orient towards extremely advanced fields of the international, scientific-technological research world. Each partner university offers pathways that reflect their own competencies and potentials. The specializations offered are in line with the background acquired during the first year and allow to deepen some of the different methodological approaches described above. Several specializations, mainly with applications to engineering, shall be offered. They include control and advanced optimization methods with industrial applications, modeling, and simulation of complex systems, simulation of deterministic and stochastic models – both discrete and continuous.

By the end of the educational path, the student must work on a thesis project under the guidance of an advisor, which shall then be approved by the graduation committee. During the thesis work, the host institution's local coordinator is responsible for assigning an advisor to the student; students’ proposals shall anyhow be accepted. The thesis subject may also concern an issue proposed by a company. In such a case the company shall choose a person within the company itself responsible for following the student’s work, especially if the thesis activity shall be carried out on their premises. Anyhow, the local coordinator shall also assign the student an academic advisor, who will be responsible for the thesis work development, accuracy, and scientific quality.

Considering that this is an international, multi-university study course of excellence, requests of individual study plans shall be jointly examined by the three members of the Consortium to assure that these study plans comply with the legislation in force in the countries of the institutions which will award the degree title.

Employability

The area of applied mathematics on which this project is focused is a fundamental scientific field for a number of key technologies and sciences. The areas of the proposed tracks connect very well with various branches of the European high-tech industry, and one of the goals of the project is to enhance these connections by means of the release of well-prepared professionals and researchers.

What can be said as a general learning outcome is that an engineer and modeling specialist will be able not only to properly select a model of the mathematical accuracy required for the given complexity of a physical system but also – as an expert in the mathematical aspects of the problem – to design new models of his/her own, combining suitably the theoretical, numerical and applied points of view. There is a strong need for the offered training, as it combines the two pillars of applied mathematics: (1) Modelling and (2) Numerics/ Simulations. And this, across several fields of applications where the same methodological approach (based on hierarchies of models) is applied.

All our nodes have long-lasting contacts and collaborations with industry, and the students of MathMods can base on these contacts when seeking employment opportunities outside academia. But in fact, we want their competitiveness to be based on the MSc degree awarded, which we would like to become a reference worldwide. Up to now, all MathMods graduates, as far as we know, are occupying the type of positions they sought.

Career opportunities for graduates will typically arise in research and development laboratories, especially those defining and testing numerical models and procedures, either working for a specific sector or with a broader scope. Also, in big or medium-size enterprises possessing their own research department or a division with an orientation towards research, in public or privately held Sector Technology Centres, and at computing centers involved in data processing or the creation of numerical codes for the industry.

Academic opportunities

The graduates will be able to apply successfully for PhD programs if they wish so, as has happened for the three already completed cycles. In all the countries of the Consortium members, the program has been validated as enabling the holder of the MSc degree to enter a local PhD program. A good percentage of our students seem true to prefer pursuing a PhD before going to the industry or returning to their countries of origin. The intended level of the program, together with the initial selection of the students, allows affirming that most of them could follow a successful academic career, after a suitable PhD.