MATHS DISC
study programme
The proposed MATHS-DISC educational programme has the classical structure of 2 years articulated in 4 semesters/study periods.
SPECIALISATION
5 UNIVERSITIES
-
2 YEARS
120 ECTS
INTERNSHIPS
SCHOLARSHIPS
WIDE NETWORK
WORLDWIDE
5 universities for 8 educational pathways
CICO
Computational Intelligence & Complex Systems Optimization
Specialisation Path
UNIVR, ULIS or UGAHPCQF
High Performance Computing Quantum And Computational Fluid Dynamics
Specialisation Path
BUW, UGA or UNIVRSML
Scientific Machine Learning
Specialisation Path
ISKPI, BUW or UGAFIN
Computational Finance & Circular Economy
Specialisation Path
BUW, ULIS or UNIVRMED
Health and Biomedicine
Specialisation Path
ISKPI, ULIS or UNIVRLOGT
Logistics & Transports
Specialisation Path
ULIS, UGA or UNIVRAGR
Agrifood, fisheries, environment
Specialisation Path
ULIS, UNIVR or UGANRG
Energy Markets
Specialisation Path
BUW, UGA or ULISSpecialize through the 8 main fundamental domains for the digital and ecological transition
The MATHS-DISC Committee helps each student in the choice of a personalized educational path, according to her/his mathematical background and her/his cultural and mobility preferences.
Each university offers you the possibility of specializing in specific areas. At the end of the first semester you must define your specialisation path and the university where you will study during the third and fourth semester.
Study programme in detail
Semester 1
FOUNDATIONS/BACKGROUND
First semester may take place at any University of the MATHS-DISC Consortium
The first semester is dedicated to the fulfilment of some basic foundational mathematical requirements (FO) (differential equations, functional analysis, probability and statistics, numerical analysis) and to the acquisition of basic / background concepts in mathematical modelling (MO), computer programming and simulation (CS).
Choice of the Semester 1 University
Made by the Study Plan Committee (SPC) taking into account each student's mobility path wishes and previous mathematical background, in order to ensure a complete basic preparation and an even student distribution among the host Universities.
First semester activities will include virtual meetings and a joint MSODE seminar delivered weekly by invited scholars, accessible through the MATHS-DISC e-learning platform.
First semester courses are mainly foundational and compulsory, see the first semester modules table below.
First semester modules table
- UNIVR (Università degli Studi di Verona)
- BUW (Bergische Universität Wuppertal)
- ISKPI (Igor Sikorsky Kyiv Polytechnic)
- ULIS (Universidade de Lisboa)
- UGA (Université Grenoble Alpes)
| Course | Type | Area | ECTS |
|---|---|---|---|
| Math. Modelling in the applied sciences | Mandatory | MO | 6 |
| Functional Analysis | Mandatory | FO | 12 |
| Partial Differential Equations | Mandatory | FO | 6 |
| Elective course in CS | Elective | CS | 6 |
| TOTAL | 30 |
| Course | Type | Area | ECTS |
|---|---|---|---|
| Computer simulation 1 | Mandatory | CS | 11 |
| Computer science 1 | Mandatory | FO | 9 |
| Numerical methods 1 | Elective | FO | 8 |
| Mathematical Machine Learning | Elective | CS | 8 |
| Modeling Seminar Mathematics | Mandatory | 2 | |
| TOTAL | 30 |
| Course | Type | Area | ECTS |
|---|---|---|---|
| Modelling of Complex Systems | Mandatory | MO | 6 |
| Numerical Methods of Mathematical Physics | Mandatory | FO | 5 |
| Geometric Modelling | Mandatory | MO | 4 |
| Architecture and Technologies of Big Data Systems | Mandatory | CS | 4 |
| Data Mining | Mandatory | CS | 5 |
| English language | Mandatory | 1,5 | |
| Basics of Research | Mandatory | 3 | |
| TOTAL | 28.5 |
| Course | Type | Area | ECTS |
|---|---|---|---|
| Numerical Functional Analysis and Optimization | Elective | FO | 6 |
| Numerical Methods for Ordinary Differential Equations | Elective | FO | 6 |
| Linear model analysis | Elective | MO | 6 |
| Multivariate analysis | Elective | FO | 6 |
| Computational Statistics | Elective | CS | 6 |
| Probability Theory | Elective | FO | 9 |
| TOTAL | 39 |
| Course | Type | Area | ECTS |
|---|---|---|---|
| Object oriented & Software design | Mandatory | CS | 3 |
| Applied probability and statistics | Mandatory | FO | 6 |
| Signal and image processing | Mandatory | MO | 6 |
| Partial differential equations and numerical methods | Mandatory | FO | 6 |
| Geometric Modeling | Mandatory | MO | 6 |
| Language courses | Mandatory | FO | 3 |
| TOTAL | 30 |
Semester 2
METHODS
Acquisition of a solid knowledge
The second semester is dedicated to the acquisition of a solid knowledge along the main axes of the programme: Computing & Simulation (CS), Modelling & Optimisation (MO), Data Science & AI (DA).
More precisely, two slightly different profiles are proposed, which share a basic training in DA:
- The first emphasises Computing & Simulation (CS) methods and takes place at BUW.
- The second emphasises Modelling & Optimisation (MO) methods and takes place at UNIVR.
The courses at BUW are mainly compulsory, while at UNIVR students can choose between deterministic or stochastic Modelling & Optimisation (MO) methods.
Second semester modules table
| Course | Type | Area | ECTS |
|---|---|---|---|
| Optimization | Mandatory | MO | 6 |
| Numerical methods for PDEs | Elective | CS | 6 |
| Stochastic calculus | Elective | MO | 6 |
| Numerical Modelling and Optimization | Elective | MO | 6 |
| Statistical Learning | Elective | DA | 6 |
| Numerical methods for PDEs | Elective | CS | 6 |
| Stochastic calculus | Elective | MO | 6 |
| Numerical Modelling and Optimization | Elective | MO | 6 |
| Statistical Learning | Elective | DA | 6 |
| Analytical Mechanics | Elective | MO | 6 |
| Statistical Learning | Elective | DA | 6 |
| One elective course | Elective | MO-CS-DA | 6 |
| One elective course | Elective | MO-CS-DA | 6 |
| Sustainable Entrepreneurship | Elective | 6 | |
| TOTAL | 30 |
| Course | Type | Area | ECTS |
|---|---|---|---|
| Computer simulation 2 | Mandatory | CS-DA | 13 | Bayesian Learning | Mandatory | DA | 7 |
| Numerical methods 2a - 2b | Mandatory | CS | 8 |
| Atmospheric physics 1 | Elective | MO | 8 |
| Computational electromagnetics 1 | Elective | MO | 8 |
| Computational finance 1 | Elective | CS | 8 |
| Particle Detector Project | Elective | MO | 8 |
| Molecular and Materials Modelling 1 | Elective | DA | 8 |
| The Standard Model of Elementary Particle Physics | Elective | MO | 8 |
| Many Particle Theory | Elective | MO | 8 |
| Statistical Field Theory | Elective | MO | 8 |
| Introduction to Quantum Field Theory | Elective | MO | 8 |
| TOTAL | 36 |
Semester 2
MASTER WORKSHOP
Designed to foster interdisciplinary teamwork
At the end of the second semester, during the summer period (usually by end July), the whole students cohort meets for an intensive two-week Master Workshop organised at one of the Universities or at an ECMI teaching centre. Student participation is mandatory and is fully refunded. The MW activities consist of:
- Team activities on industrial problem modelling (cf. ECMI Modelling Week).
- Presentation of second year internship/Master thesis opportunities at the academic and industrial Consortium partners.
- Crash courses or lectures on urgent topics.
- Seminars on societal and industrial challenges.
- Tutoring, mentoring, networking activities within the Master Alumni Association.
The Master Workshop is designed to foster interdisciplinary teamwork, cooperation and communication skills, and also to pave the way for each student’s second year's major cultural choices. It is also a strong unifying moment for students to exchange opinions and experiences and to build the future MATHS-DISC Alumni Association.
Semester 3
SPECIALISATION
Advanced courses in the 8 different specialised educational pathways
The third semester is dedicated to advanced courses in the 8 different specialised educational pathways (SP) related to the CS-MO-DA enabling technologies, which also provide a specific background preparation for the final Master's thesis (MT) project.
Each SP and most MT topics are offered by several Universities, so as to respect student’s wishes on study and mobility plans.
Third semester courses are mainly elective and have to be chosen in accordance with the SP followed by the student.
An overview of the third semester courses offered by each University for the different SPs can be found in the tables of third semester modules below.
Other elective courses can be found in the general course catalogue of each University and are therefore not listed in these module tables.
Third/fourth semester modules table
- UNIVR (Università degli Studi di Verona)
- BUW (Bergische Universität Wuppertal)
- ISKPI (Igor Sikorsky Kyiv Polytechnic)
- ULIS (Universidade de Lisboa)
- UGA (Université Grenoble Alpes)
| Course | Type | Area, EP | ECTS |
|---|---|---|---|
| Discrete optimization and decision making | Elective | CICO, LOGT, AGR | 6 |
| Foundations of Data Analysis | Elective | DA | 6 |
| Mathematical modelling in the applied sciences | Elective | NRG, AGR, MED | 6 |
| Computational Game Theory | Elective | CICO, LOGT | 12 |
| Logistics, operations and supply chain | Elective | LOGT | 12 |
| Mathematical finance | Elective | FIN, NRG | 12 |
| Numerical methods for mathematical finance | Elective | FIN, NRG | 12 |
| Statistical Models for Data Science | Elective | DA | 12 |
| Data Fitting and reconstruction | Elective | CS | 12 |
| Statistical methods for business intelligence | Elective | FIN, NRG | 12 |
| Machine learning for data science | Elective | DA | 12 |
| Reinforcement learning | Elective | CICO | 12 |
| Data Visualization | Elective | DA | 12 |
| Parallel programming | Elective | CICO | 12 |
| Mining Massive Datasets | Elective | DA | 12 |
| Natural Language Processing | Elective | CICO | 12 |
| Advanced Programming for AI | Elective | CICO | 12 |
| One elective course | Elective | ANY PATH | 6 |
| Complementary activity/transverse skills | Elective | ANY PATH | 4 |
| Master thesis | Master thesis | 30 | |
| TOTAL | 60 |
| Course | Type | Area, EP | ECTS |
|---|---|---|---|
| Numerical methods 3 | Mandatory | HPCQF, NRG | 6 |
| Introduction to the Atmospheric Physics | Elective | CS | 8 |
| Atmospheric Physics 2b | Elective | CS | 8 |
| Computational electromagnetics 2 | Elective | HPCQF | 8 |
| Computational Finance 2 | Elective | FIN, NRG | 8 |
| Computational Fluid Mechanics 2 | Elective | HPCQF | 4 |
| Computational Fluid Mechanics 3 | Elective | HPCQF | 4 |
| Computational Fluid Mechanics 4 | Elective | HPCQF | 4 |
| Computational Fluid Mechanics 5 | Elective | HPCQF | 4 |
| Computational Fluid Mechanics 6 | Elective | HPCQF | 4 |
| Detector Physics | Elective | CS | 8 |
| Imaging in medicine IMG2 | Elective | MED | 8 |
| Molecular and Material Modelling 2 | Elective | NRG | 8 |
| Cosmology and General Relativity | Elective | MO | 8 |
| Advanced Quantum Mechanics | Elective | MO | 8 |
| Master thesis | 30 | ||
| TOTAL | 60 |
| Course | Type | Area, EP | ECTS |
|---|---|---|---|
| Modelling of Biomedical Systems and Processes | Mandatory | MED | 5 |
| Applied Modelling | Mandatory | MED | 4 |
| Project Management | Elective | FIN | 5 |
| Econometrics | Elective | FIN | 4 |
| Text Mining | Elective | SML | 4 |
| Deep Reinforcement Learning | Elective | SML | 4 |
| Generative AI | Elective | SML | 5 |
| Thesis Preparation | Mandatory | SML, MED | 4 |
| English Language | Mandatory | 2 | |
| Pedagogy | Mandatory | 2 | |
| Internship + Master Thesis | 30 | ||
| TOTAL | 58 |
| Course | Type | Area, EP | ECTS |
|---|---|---|---|
| Numerical Analysis of Partial Differential Eqs | Elective | CICO, MED | 6 |
| Numerical Optimal Control | Elective | LOGT | 6 |
| Computational Methods in Finance | Elective | FIN | 6 |
| Biostatistics | Elective | MED | 6 |
| Applied Bayesian Statistics | Elective | MED, AGR, LOGT | 6 |
| Reliability and Quality Control | Elective | AGR, LOGT | 6 |
| Introduction to Stochastic Processes | Elective | FIN, NRG | 6 |
| Time Series Analysis | Elective | AGR, LOGT, FIN, NRG | 6 |
| Mathematical Modelling and Applications | Elective | Any path | 6 |
| Mathematical Models in Biomedicine | Elective | MED | 6 |
| Mathematical Statistics | Elective | CICO, MED | 6 |
| Introduction to Mathematical Finance | Elective | FIN, NRG | 6 |
| Statistical Methods in Data Mining | Elective | Any path | 6 |
| Master Thesis | 30 | ||
| TOTAL | 60 |
| Course | Type | Area, EP | ECTS |
|---|---|---|---|
| An introduction to shape and topology optimization | Elective | SML | 30 |
| Computational biology | Elective | MED | 30 |
| Efficient methods in optimization | Elective | CICO | 30 |
| Differential Calculus, Wavelets and Applications | Elective | CICO | 30 |
| Fluid mechanics and granular matter | Elective | HPCQF | 30 |
| Geophysical imaging | Elective | HPCQF | 30 |
| GPU Computing | Elective | HPCQF | 30 |
| Handling uncertainties in (large-scale) numerical models | Elective | CICO | 30 |
| Modelling Seminar | Elective | ANY PATH | 30 |
| Optimal transport: theory, applications and numerical methods. | Elective | CICO | 30 |
| Quantum Information & Dynamics | Elective | HPCQF | 30 |
| Software Development Tools and Methods. | Elective | CS | 30 |
| Statistical learning: from parametric to nonparametric models | Elective | DA | 30 |
| Temporal, spatial and extreme event analysis | Elective | MO | 30 |
| Advanced Machine Learning: Applications to Vision, Audio and Text | Elective | SML | 30 |
| Data Science Seminars and Challenge | Elective | ANY PATH | 30 |
| From Basic Machine Learning models to Advanced Kernel Learning | Elective | SML | 30 |
| Learning, Probabilities and Causality | Elective | SML | 30 |
| Mathematical Foundations of Machine Learning | Elective | SML | 30 |
| Natural Language Processing & Information Retrieval | Elective | SML | 30 |
| Research project/ Master Thesis | Mandatory | 30 | |
| TOTAL | 60 |
Semester 4
INTERNSHIP/MASTER THESIS
Finally, the fourth semester is dedicated to the Master's thesis project, which addresses a problem related to the industrial and societal challenges for the digital and green transition towards a sustainable, resilient and human-centred industry and society.
The Master's thesis can be carried out in an academic research laboratory or institute, or during an internship with an associated partner, or even during another short mobility period.
Any semester
COMPLEMENTARY ACTIVITIES
TRANSVERSAL/SOFT SKILLS
Complementary elective courses not related to the subject of study or transversal skills courses, such as foreign language courses or courses on specific topics related to industrial innovation and societal challenges, such as start-up entrepreneurship, sustainable development, patent law, principles of circular economy, are organised each semester by the consortium Universities, taking advantage of their specific expertise in the field. They are delivered in hybrid mode and made available in the common centralised e-learning platform.
Complementary seminars and study groups involving european networks like ECMI and EU-MATHS-IN, industrial and academic partners are offered on a regular basis to identify problems, needs, requirements and opportunities arising from industry and local areas, as well as to exchange and share experiences, skills and best practices between the Universities.