PC1. Fundamentals of deterministic optimization
Concepts and optimality conditions. Modelling techniques. Classification of problems
PC2. Convex problems
Convexity. Particular case of linear programming. Duality theory. Post-optimal sensitivity analysis. Goal-orientated programming
PC3. Unrestricted non-linear optimization
Linear search and confidence region statistics. Gradient and 2nd order numerical methods in Python code. Wolfe conditions. Convergence and rate
PC4. Constrained non-linear optimization
Karush-Kuhn-Tucker optimality conditions. Quadratic programming. Penalty and barrier methods. Algorithms based on decomposition
PC5. Discrete modelling
Combinatorial and integer optimization. Branch-and-bound and branch-and-cut techniques. Hamilton and Euler cycles. Network flows. Large-scale or NP-hard problems. Heuristics and meta-heuristics. Iterated local search. Genetic algorithms and evolutionary strategies. Classical examples

Assessment throughout the semester:
Analysis of 2 case studies throughout the semester and a test on the date of the 1st Exam Period. One of the case studies is individual and the other is carried out in a group. Each case study (which will be analysed using a structure pre-defined by the professor) and the respective discussion will have a weight of 25% in the final grade, with a minimum grade of 75,. The average obtained in the case studies must be equal to or greater than 9.5 points. The test has a weight of 50% in the final grade and a minimum grade of 7,5. Possibility of oral proof if appropriate.

Exam assessment (1st Exam Period if chosen by the student, 2nd Exam Period, and Special Exam Period):
Individual face-to-face exam (100% of the final grade).

Mandatory

"- Luenberger, D. G. and Ye, Y, (2016) Linear and Nonlinear Programming, 4th Edition, Springer. - Beck, A. (2023) Introduction to nonlinear optimization: theory, algorithms and applications with Python and MATLAB, 2nd Edition, SIAM Series on Optimization. - Wright, S. and Recht, B. (2022) Optimization for Data Analysis, Cambridge University Press. - Taha, H.A. (2017). Operations Research: an introduction, 10th Ed., Pearson. - Bertsekas D. (1998) Network Optimization: Continuous and Discrete Models, MIT, Athena Scientific Publisher. - Bäck, T. (1996) Evolution Strategies, Evolutionary Programming, Genetic Algorithms, Oxford University Press, New York. - Conn, A.R., Scheinberg, K. and Vicente, L.V. (2009) Introduction to Derivative-Free Optimization, SIAM Series on Optimization. - Miettinen, K. (1999) Nonlinear Multiobjective Optimization, Kluwer. - Boyd, S. and Vandenberghe, L. (2009) Convex Optimization, 7th edition, Cambridge University Press "

Optional

"- Bonnans, J.F, Gilbert, J.C., Lemarechal, C. and Sagastizábal, C.A. (2006) Numerical Optimization: Theoretical and Practical Aspects, Springer Verlag. - Nocedal, J. and Wright, St. (1999) Numerical optimization, Springer Verlag. - Barabási A. (2016) Network Science, Cambridge University Press. - Ragsdale, C.T. (2017). Spreadsheet Modeling and Decision Analysis: A Practical Introduction to Business Analytics. 8th Ed. Cemgage Learning. - Sundaram, R. K. (2011) A First Course in Optimization Theory, Cambridge University Press. - Hillier, F.S. Lieberman, G.J. (2014). Introduction to Operations Research, 10th Ed.. McGraw-Hill. - Rao, S.S. (1996) Engineering Optimization: Theory and Practice, John Wiley & Sons, Canada. - Solomon, J. (2015) Numerical Algoritms/ Methods for Computer Vision, Machine Learning, and Graphics, CRC Press."

CP1. Teoria da medida e integração
- Conjuntos mensuráveis e medida de Lebesgue
- Funções mensuráveis
- Integral de Lebesgue
- Teoremas de convergência
- Espaços Lp e desigualdades fundamentais
- Teorema de Radon- Nikodym
CP2. Espaços de Banach e Espaços de Hilbert
- Espaços normados
- Completude e espaços de Banach
- Dualidade
- Teorema de Hahn-Banach
- Espaços de Hilbert
- Teorema da representação de Riesz
- Operadores lineares limitados
- Teorema espectral de operadores compactos e auto-adjuntos
CP3. Séries e Transformadas de Fourier
- Séries de Fourier
- Transformada de Fourier
- Aplicações: processamento de sinal e equações diferenciais

Assessment Throughout the Semester:
- Six individual exercise sheets distributed over the semester, accounting for 20% of the final grade.
- Individual project developed throughout the semester, including a written report, an implementation component in Python, and a final presentation, contributing 30% to the final grade.
- Final in-person test, weighted 50% of the final grade, with a minimum passing score of 8.5 out of 20.
- All assessment components are subject to discussion.

Assessment by Examination:
(1st Examination Period if chosen by the student, 2nd Examination Period, and Special Examination Period)
- In-person exam accounting for 100% of the final grade.

Mandatory

"E. M. Stein & R. Shakarchi, Real Analysis: Measure Theory, Integration, and Hilbert Spaces (1st ed.), Princeton University Press, 2005. ISBN 978-0-691-11386-9 E. M. Stein & R. Shakarchi, Functional Analysis: Introduction to Further Topics in Analysis (1st ed.) Princeton University Press, 2011. ISBN 978-0-691-11387-6 E. M. Stein & R. Shakarchi, Fourier Analysis: An Introduction (1st ed.) Princeton University Press, 2003. ISBN 978-0-691-11384-5

Optional

" H . Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations (1st ed.), Springer, 2011. ISBN: 978-0-387-70914-7 G. B. Folland, Real Analysis - Modern Techniques and Their Applications (2nd ed.) John Wiley Amp. Sons Inc., 2007. ISBN: 978-0-471-31716-6

I - Mathematical Modeling.
1. The use of differential equations in model building.
2. Classic examples of dynamical and equilibrium models.
3. Classification of differential equations.

II - Ordinary Differential Equations (ODEs).
1. Notable examples of ODEs.
2. Existence and uniqueness of solutions (Picard-Lindelöf).
3. First-order ODEs.
4. Qualitative methods for autonomous ODEs.
5. Equilibrium and stability.
6. Systems of linear first-order ODEs.
7. Linear ODEs of higher order.
8. Homogeneous equation, characteristic equation, and the method of variation of parameters.
9. Numerical methods for solving ODEs (Euler and Runge-Kutta).

III - Partial Differential Equations (PDEs).
1. Notable examples of PDEs.
2. Classification of PDEs (heat equation, wave equation, Laplace equation).
3. Separation of variables.
4. Fourier series and convergence.
5. The Laplace transform.
6. Numerically solving the heat equation using finite differences.

Assessment throughout the semester
- 3 sets of exercises carried out throughout the semester, with a weight of 60% in the final grade (20% each set), done individually.
- 2 individual research projects carried out throughout the semester (with delivery of a written report and an implementation in Python), with a weight of 40% (20% each) in the final grade. The presented projects are subject to discussion.

Assessment by exam (1st Exam Period in case of student's choice,2nd Exam Period and Special Season Period):
Exam (100% of the final grade).

Mandatory

"1. William E. Boyce and Richard C. di Prima, “Elementary Differential Equations”, 10th edition, John Wiley & Sons (2012). 2. Martin Braun, “Differential Equations and Their Applications: An Introduction to Applied Mathematics”, 4th edition, Springer (1993). 3. Pedro M. Girão, “Introdução à Análise Complexa, Séries de Fourier e Equações Diferenciais”, 2ª edição, IST press (2022). 4. Richard L. Burden and J. Douglas Faires, “Numerical Analysis”, Brooks/Cole, Cengage Learning (2010)."

Optional

PC1: Error Theory
A-stability, zero-stability, consistency and global convergence.
PC2: Numerical Methods for Nonlinear Equations and Systems of Equations
Simple iteration methods and convergence acceleration.
PC3: Function Approximation and Numerical Integration
Hermite interpolation, spline interpolation, complexa and trigonometric interpolation, least squares method and numerical quadrature for function approximation and integration.
PC4: Numerical Methods for Linear Algebra and Numerical Optimization
Numerical methods for solving large-scale systems of linear equations.
Implementation of algorithms for LU, QR, and SVD decomposition.
Application of numerical linear algebra in real-world problems, such as data analysis and machine learning.
PC5: Implementation in Python
Development of efficient algorithms in Python to solve complex numerical problems.
Practical case studies, promoting a deep understanding of theoretical concepts through practical application.

1. Assessment Methods
- Assessment throughout the semester:
* Completion of two projects throughout the semester, one individual and one group project, and taking an in-person exam on the date of the 1st Examination Period.
* Each project will be analyzed according to a structure defined by the professor and will be accompanied by a discussion.
* Each project contributes 30% to the final grade.
* The in-person exam contributes 40% to the final grade.
* Minimum required grade for each project and the in-person exam: 7 points (in 20).
* Necessary average for continuous assessment: equal to or higher than 9.5 points (in 20).
- Examination Assessment (1st, 2nd Exam Periods and Special Examination Period)
* In-person exam that accounts for 100% of the final grade.

Possibility of holding oral discussions.

Mandatory

"Gupta R.K., (2019). Numerical Methods: Fundamentals and Applications. Cambridge University Press. Kong Q, Siauw T., Bayen A.M. (2021). Python Programming and Numerical Methods: A Guide for Engineers and Scientists. Elsevier Inc. Cohen H. (2011). Numerical Approximation Methods. Springer New York. Ford W. (2015). Numerical Linear Algebra with Applications - using MATLAB. Elsevier. Burden R., Douglas Faires J. (2005). Numerical Analysis. Brooks/Cole Cengage Learning. Kress R. (1998). Numerical Analysis. Springer-Verlag"

Optional

"Allen, M.B., Isaacson, E.L. (2019). Numerical analysis for applied science. John Wiley & Sons, Inc. Rossun G. (2018). Python Tutorial Release 3.7.0. Python Software Foundation. Christian C. (2017). Differential Equations: A Primer for Scientists and Engineers, Second Edition. Springer International Publishing."

PC1. Introduction to Complex Systems
Definition and characteristics
Concepts of emergence and self-organisation
Examples from natural and artificial systems
PC2. Modelling of Dynamical Systems
Applied differential equations
Stability analysis and bifurcations
Introduction to chaos and non-linear systems
PC3. Graphs and Complex Networks
Fundamentals and structural and functional metrics
Network models: random, small-world, and scale-free networks
Introduction to neural networks and GNNs
PC4. Agent-Based Modelling
Concepts and applications of agent-based models
Implementation of models using platforms such as NetLogo
Case studies in social and biological systems
PC5. Computational Tools
Programming in Python for modelling and simulation
Use of specialised libraries for analysis and prediction
Data analysis and visualisation
PC6. Interdisciplinary Applications
Ecological, economic, and financial systems
Population dynamics and epidemic modelling

Approval in the course results from obtaining 10 values (0-20 scale) in one of the assessment modalities.

Assessment throughout the semester:
Resolution of four tasks throughout the semester: two individual and two group tasks. Each task (whose analysis will be developed with a pre-defined structure by the professor) and their respective results and discussion carry a weight of 20% in the final grade. Additionally, there is a written in-person exam with a weight of 20%. All components (tasks and exam) require mandatory completion, and the average grade must be above 9.5 values (0-20 scale) for approval.

Exam evaluation (1st Exam Period, if chosen by the student, 2nd Exam Period, and Special Period):
In-person exam (100% of the final grade)

Mandatory

"Nino Boccara, Modeling Complex Systems, second edition, Springer, 2010 Hiroki Sayama, Introduction to the Modeling and Analysis of Complex Systems, Open SUNY, 2015 Steven Strogatz, Nonlinear Dynamics and Chaos : with Applications to Physics, Biology, Chemistry, and Engineering, Westview Press, a member of the Perseus Books Group, 2015 Henrik Jensen, Complexity Science: The Study of Emergence, Cambridge University Press, 2023 Zhiyuan Liu and Jie Zhou, Introduction to Graph Neural Networks, Morgan & Claypool Publishers. 2020"

Optional

"Paul Fieguth, An Introduction to Complex Systems: Society, Ecology, and Nonlinear Dynamics, Springer, 2017 Stefan Thurner, Rudolf Hanel, and Peter Klimek, Introduction to the Theory of Complex Systems, Oxford University Press, 2018 Mark Newman, Networks, second edition, Oxford University Press, 2018 Arkady Pikovsky, Michael Rosenblum and Jürgen Kurths, Synchronization: A universal concept in nonlinear sciences, Cambridge University Press, 2001 Susanna Manrubia, Alexander Mikhailov, Damián Zanette, Emergence of Dynamical Order: Synchronization Phenomena in Complex Systems, World Scientific Publishing, 2004"

S1: Introduction to unsupervised learning methods: fundamental concepts, types of algorithms and practical applications;
S2: Principal component analysis (PCA): fundamental concepts, steps and practical applications;
S3: Clustering techniques: hierarchical clustering and probabilistic clustering, exploration of algorithms and practical applications;
S4: Association rules: frequency of items and association rules, Apriori algorithm and practical applications.

Passing the course requires a mark of 10 (scale 0-20) in any of the assessment methods.
Assessment throughout the semester:
- group work with a minimum mark of 8 (30%)
- individual assignment(s) with a minimum mark of 8 (30%)
- individual face-to-face test with a minimum mark of 8 (30%)
- autonomous work throughout the semester (10%)
All components (assignments and tests) are compulsory. Passing requires a minimum mark of 10 (scale 0-20).
EXAMS (1st Exam Period, if the student chooses, 2nd Exam Period and Special Period):
The Final Exam corresponds to a face-to-face written exam (100% of the final grade). Students must obtain a minimum mark of 10 to pass.

Mandatory

"Berry, M. W., Mohamed, A., & Yap, B. W. (Eds.). (2019). Supervised and unsupervised learning for data science. Springer Nature. Hair, J. F., Black, W. C., Babin, B. J., Anderson, R. E. (2014), Multivariate Data Analysis, 7th Edition, Essex, UK: Pearson Education. Hastie, T., Tibshirani, R., Friedman, J. (2009), The Elements of Statistical Learning: Data Mining, Inference, and Prediction. 2nd ed. New York: Springer. James, G., Witten, D., Hastie, T., Tibshirani, R. (2013), An introduction to statistical learning: with applications in R, New York: Springer. Reddy, C. K. (2018). Data Clustering: Algorithms and Applications. Chapman and Hall/CRC. Vidal, R., Ma, Y., & Sastry, S. S. (2016). Generalized principal component analysis (Vol. 5). New York: Springer."

Optional

"Aggarwal, C. C., Reddy, C. K. (eds.) (2014), Data Clustering: Algorithms and Applications. Boca Raton: CRC Press. Contreras, P., & Murtagh, F. (2015). Hierarchical clustering. In Handbook of cluster analysis (pp. 124-145). Chapman and Hall/CRC. Hennig, C., Meila, M., Murtagh, F., Rocci, R. (eds.) (2016), Handbook of Cluster Analysis, Handbooks of Modern Statistical Methods. Boca Raton: Chapman & Hall/CRC. Jolliffe, I. (1986), Principal Component Analysis. New York: Springer-Verlag. Kassambara, A. (2017). Practical guide to cluster analysis in R: Unsupervised machine learning (Vol. 1). Sthda. McLachlan, G. J., Peel, D.(2000), Finite Mixture Models. New York: John Wiley & Sons. Lattin, J., D. Carroll e P. Green (2003), Analyzing Multivariate Data, Pacific Grove, CA: Thomson Learning. Sutton, R. S., & Barto, A. G. (2018). Reinforcement Learning, second edition: An Introduction (2.a ed.). MIT Press. Verdhan, V. (2020). Models and Algorithms for Unlabelled Data. Springer. Wedel, M., Kamakura, W. A. (2000), Market Segmentation. Conceptual and Methodological Foundations (2nd edition), International Series in Quantitative Marketing. Boston: Kluwer Academic Publishers."

1. Mathematical models of neurons and activation functions.
2. Hardware: AI accelerators for machine learning.
3. Efficient algorithms for matrix manipulation and tensor algebra.
4. Backpropagation and automatic differentiation.
5. Classification and regression problems with feedforward neural nets.
6. Universal aproximation theorems and asymptotic analysis.
7. Convolution networks and image recognition.
8. Regularization techniques.
9. Deep reinforcement learning.
10. Models for sustainable AI.

Assessment throughout the semester:
- Four online quizzes completed individually throughout the semester, accounting for 20% of the final grade.
- Individual research project conducted throughout the semester (including submission of a written report and a Python implementation component), accounting for 30% of the final grade. The research project should correspond to the development of a free extension of the course program, with a mandatory implementation component.
- Final in-person test accounting for 50% of the final grade, with a minimum grade of 7.5.

Exam assessment (1st Exam Period if chosen by the student, 2nd Exam Period, and Special Period): In-person exam (100% of the final grade).

Mandatory

"François Chollet, “Deep Learning with Python”, Manning, Second Edition 2021. Ovidiu Calin, “Deep Learning Architectures: A Mathematical Approach”, Springer, 2020. Maxim Lapan, “Deep Reinforcement Learning Hands On”, Packt, Second Edition 2020. "

Optional

PC1: The importance of computational mathematics in industrial and business contexts
PC2: Case study of computational mathematics applications
* Real examples of how computational mathematics is used in process optimization.
* Discussion of case studies of computational mathematical application in business/industrial contexts.
PC3: Research poject proposals
* Presentation of dissertation project proposals by faculty members.
* Criteria for evaluating the relevance, feasibility, and scientific contribution of research projects.
PC4: Scientific research methodology
* Identification of the phases of a research project and methodological approaches for defining objectives an tasks.
PC5: Literature review
* Methodologies for an effective and systematic literature review.
* Synthesis of the state of the art and critical analysis of existing literature.
PC6: Seminars and dissertation proposal presentations
* Presentation of research proposals by students.
* Discussion of the proposals.

Assessment throughout the semester:
1. Participation and Discussion in Seminar (20%):
* Assessment throughout the semester of the student's contribution in seminar sessions, including engagement, constructive feedback, and skills in applying theoretical knowledge in discussions, corresponding to LO1 and LO3.
2. Project Work (30%):
* Students will develop a research project idea, where they will apply the methods and principles discussed in seminar sessions. This work will be evaluated for its originality, structure, and indication of the practical application of mathematical concepts to real-world problems, reflecting LO1, LO2, and LO5.
3. Literature Review (30%):
* Critical and systematic review of the literature relevant to their research project, demonstrating the skills acquired in LO4 and the ability to establish a theoretical base for their work, aligned with LO3.
4. Oral Presentation (20%):
* Presentation of the research work proposal and discussion of its structure and literature review, allowing students to demonstrate communication and argumentation skills, aligning with LO2 and LO5. Each assessment component is strategically designed to evaluate different aspects of the course unit's learning objectives and ensure that students not only absorb theoretical knowledge but are also able to apply it in a context of practical research and scientific communication.
There isn't exam assessment.

Mandatory

"C. Ceia, Normas para apresentação de trabalhos científicos. 7ª ed. Lisboa: Editorial Presença, 2008. M. Saunders, P. Lewis, A. Thornhill, Research methods for business students. 4th ed. Harlow: Financial Times/Prentice Hall, 2007. Revisão de artigos científicos, teses e dissertações."

Optional

PC1. Measure theory and probability
1.1 Introduction to measure theory
1.2 Probabilistic Concepts
PC2. Brownian Motion and ""White Noise""
2.1 Motivation and Definitions
2.2 Construction of Brownian Motion
PC3. Stochastic Integrals, Itô's Formula
3.1 Motivation
3.2 Definition and Properties of the Itô Integral
3.3 Itô's Formula
PC4. Stochastic Differential Equations
4.1 Definitions and Examples
4.2 Existence and Uniqueness of Solutions
4.3 Linear Stochastic Differential Equations
PC5. Applications
5.1. Application of stochastic differential equations to dynamic phenomena.

Assessment throughout the semester:
- Four online quizzes completed individually throughout the semester, accounting for 20% of the final grade.
- Individual research project (with the submission of a written report and an implementation component in Python), weighted at 30% of the final grade. The research project should apply the knowledge of stochastic differential equations covered in the course and other relevant tools for modeling specific dynamic phenomena.
- Final in-person test accounting for 50% of the final grade, with a minimum grade of 7.5.
- The evaluation elements are subject to discussion.

Exam assessment (1st Exam Period if chosen by the student, 2nd Exam Period, and Special Period): In-person exam (100% of the final grade).

Mandatory

"Lawrence C. Evans, “An Introduction to Stochastic Differential Equations”, American Mathematical Society, First edition, 2017. Robert G. Bartle, ""The Elements of Integration and Lebesgue Measure"", Wiley, 2014."

Optional

"Carlos A. Braumann, “Introdução às equações diferenciais estocásticas e aplicações”, Sociedade Portuguesa de Estatística 2005. Bernt Oksendal, “Stochastic Differential Equations: An introduction with applications”, Springer, sixth edition, 2003."

S1: Introduction to research
S2: Formulating the problem and research objectives and planning
S3: Good practices for developing the state of the art
S4: Good practice in scientific writing and presentation of research work
S5: Writing the dissertation

The dissertation is presented in accordance with the rules and within the deadlines established by ISCTE-IUL. The dissertation will be assessed by a jury in public examinations, after the supervisor has confirmed that it has been completed and is in a position to be presented in public examinations. The assessment will be based on the scientific merit of the study, its theoretical and methodological adequacy and its discussion.
- Mid-term assessment includes: project proposal, introductory chapter, literature review, planning of the next stages of the work and a presentation on the work in progress.
- The final assessment will take into account the technical/scientific quality of the work, based on the dissertation document (A), the quality of the presentation and public discussion (B), weighted as follows: Final grade = 0.6*A + 0.4*B.

Mandatory

A bibliografia será indicada pelo docente(s) orientador(es).

Optional

"Evans, D., Gruba, P., & Zobel, J. (2014). How to write a better thesis. Melbourne Univ. Publishing. Smith, I., & Felix, M. S. (2019). A practical guide to dissertation and thesis writing. Cambridge Scholars Publishing."

Mandatory

A bibliografia será indicada pelo docente(s) orientador(es).

Optional

PC1.Controllability
I. Introduction and framework
Classic examples
II. Controllability
Controllability of linear systems
Controllability of autonomous linear systems: case without control restrictions - Kalman condition; case with restrictions on control
Controllability of non-autonomous linear systems
Controllability of nonlinear systems
PC2.Optimal control
I. Existence
Existence theorems
II. Necessary conditions for optimality
Pontryagin maximum principle
Particular cases and examples: minimum time problem; linear quadratic problem; examples of linear optimal control (Zermelo problem, the Brachistochrone problem).
PC3.Dynamic programming
General concepts in discrete and continuous time contexts
Dynamic Programming Algorithms
Examples
PC4. Numerical methods for solving optimal control problems
I. Direct methods
Algorithms
Examples
II. Indirect methods
Algorithms
Examples

Assessment throughout the semester:
- four online quizzes carried out throughout the semester with a weight of 20% in the final grade;
- individual research project (with delivery of a written report and an implementation component in Matlab/Octave or Python), with a weight of 30% in the final grade. The research project should apply the knowledge of optimal control theory covered in the course and other relevant tools for solving concrete optimal control problems.
- final test with a weight of 50% in the final grade, with a minimum score of 7.5;
- the evaluation elements are subject to discussion.

Assessment by exam (1st Exam Period in case of student's choice,2nd Exam Period and Special Season Period): Exam (100% of the final grade).

Mandatory

"D. P. Bertsekas, Dynamic Programming and Optimal Control (3rd ed), Athena Scientific, 2005, ISBN: 978-1886529267 E. Trélat, Control in finite and infinite dimension. SpringerBriefs PDEs Data Sci., Springer, Singapore, 2024. ISBN 978-981-97-5947-7 https://www.ljll.fr/trelat/fichiers/bookSB.pdf E. Trélat, Contrôle optimal : théorie & applications. Vuibert, Collection ""Mathématiques Concrètes"", 2005, 246 pages. ISBN : 271177175X Pdf file (electronic version, updated in 2023): https://www.ljll.math.upmc.fr/trelat/fichiers/livreopt2.pdf"

Optional

"E. B. Lee, L. Markus, Foundations of optimal control theory, John Wiley and Sons, Inc., New York, London, Sydney, 1967, ISBN: ‎978-0471522638 J. Miranda Lemos, Controlo no Espaço de Estados, Edição IST - Instituto Superior Técnico, 2019. ISBN: 9789898481702"

PC1. The stages of the research process
I. Types of thesis
II. Identification of research problems
III. Planning of work phases
PC2. Preparation of literature review and bibliography sources
PC3. Identify and use computational mathematics tools appropriate to the research problem
PC4. Research topics in applied computational mathematics
PC5. Preparation and presentation of the research project

Assessment throughout the semester:
- analysis of four case studies throughout the semester: two individual and two group case studies. Each case study (whose analysis will be developed with a predefined structure by the professor) and its discussion carry a weight of 25% in the final grade, with a minimum grade of 7.5 values (0-20 scale). The average grade of the case study analysis must be equal to or higher than 9.5 values (0-20 scale).

There isn't exam assessment.

Mandatory

Optional