Mathematical Modelling and Programming

The course is part of the first trimester of the PhD and Master's Programs in Science and Management of Climate Change. It is one of the core courses, providing students with some mathematical and computational tools needed to understand socioeconomic and environmental systems and apply quantitative models to describe and predict their functioning and evolution. The course is a cornerstone for understanding environmental and socioeconomic modeling, which will be explored in greater depth through applications in subsequent courses.

1. Knowledge and understanding:
* Basic calculus.
* Acquire the foundations for understanding and solving decision/optimization problems.
* Be able to define and describe some complex phenomena related to environmental and socioeconomic systems;
* Acquire the theoretical and methodological tools necessary to develop a systemic view of some resolution methods for environmental and socioeconomic decisions.
2. Ability to apply knowledge and understanding:
* Be able to choose and use appropriate mathematical tools to describe and analyze complex phenomena;
* Solve applied problems using mathematical models;
* Be able to address specific applied problems related to climate change with transversal mathematical tools.

Students are expected to have a thorough understanding of the following topics: set theory, elementary algebra, equations and inequalities (both first- and second-degree, including absolute-value inequalities), analytic geometry, functions and their properties (domain, codomain, exponential and logarithmic functions). Knowledge of the main concepts of vectors, matrices, and systems of linear equations is assumed.

Students are also expected to have at least a basic understanding of the fundamentals of calculus (derivatives of functions, and applications to monotonicity, optimization, convexity, ...).
It is ESSENTIAL that students arrive at the course already possessing these skills

1. Introduction: Course presentation, prior knowledge assessment.
2. Elements of calculus: functions and their properties, including optimization elements
3. Linear algebra: vectors, matrices and their operations, matrix inverse, eigenvalues ​​and eigenvectors
4. Elements of linear programming
5. Elements of linear dynamical systems, with particular emphasis on equilibrium stability, and a brief introduction to nonlinear dynamics (optional)
6. Elements of networks and simple graph optimization problems
7. Elements of multi-criteria decision theory, including AHP, non-additive measures, and others

Attendance at the lectures is mandatory.
Relevant teaching materials will be provided during the lectures and made available on Moodle.
Some reference books will be recommended throughout the course.

The assessment will include a final written exam, possibly followed by an oral examination. During the course, some intermediate assessment tests may be administered.

written

The instructor is responsible for ensuring the authenticity and originality of all examinations and coursework. In cases of suspected academic misconduct, an additional on-site assessment may be required during the exams, which may differ from the standard format.

For this course the votes will be expressed in thirtieths

The lectures will take place in the classroom, with explanations given on the board and supported by multimedia materials to enhance intuition and understanding of the concepts.

The suggested program is a rough estimate; the course content will depend in part on the average level of preparation of the class.

This subject deals with topics related to the macro-area "Poverty and inequalities" and contributes to the achievement of one or more goals of U. N. Agenda for Sustainable Development