Argomenti dell'insegnamento
MATHEMATICS A: 1. Basic mathematical concepts: sets, relations, functions, numbers, limits, absolute values. 2. Functions of one variable: basic properties, derivatives and their calculus, Taylor approximations, Newton’s method. 3. Convexity and single-variable optimization (Fermat’s rule and sufficient optimality conditions). 4. Elements of integration (indefinite, definite and improper). MATHEMATICS B: 1. Matrix calculus, rank and linear independence, systems of linear equations, Gaussian elimination, applications. 2. Functions of several variables: gradients, Hesse matrices, Taylor approximation, convexity and concavity. 3. Multivariable optimization, Lagrange method and economic applications. 4. If enough time remains: Basics of probability theory.

Insegnamenti propedeutici
None

Modalità di insegnamento
Lectures and exercise sessions

Obiettivi formativi
ILO (Intended Learning Outcomes) - M-1 Mathematics A for EPE ILO 1 Knowledge and understanding ILO 1.1 knowledge of mathematical techniques for solving optimisation problems; ILO 1.2 knowledge of the technical vocabulary of the subjects of this learning area; ILO 2 Applying knowledge and understanding: ILO 2.1 ability to calculate derivatives and partial derivatives; ILO 2.2 ability to calculate limits and sums of series; ILO 2.3 ability to use quantitative methods to solve problems in economics; ILO 2.4 ability to read, write and communicate in the technical language of quantitative methods in the three official languages of instruction; ILO 3 Autonomy of judgement ILO 3.1 Acquisition of the ability to judge and of the methodological tools useful for the critical analysis of data, sources, assumptions and implications of scientific practice, of the political, ethical and legal context within which economic phenomena are set and with which they interact ILO 4 Communication skills ILO 4.1 Proficiency (oral and written) in Italian, German and English, including translation between these languages. Intercultural competence. Conceptual awareness, synthesis and written expression, in particular in the drafting of scientific or science-based documents ILO 5 Learning skills ILO 5.1 Promotion of critical thinking and analytical skills to focus on complex problems in their long-term dynamics and the variety of their implications, including ethical ones ILO (Intended Learning Outcomes) - M-2 Mathematics B for EPE ILO 1 Knowledge and understanding ILO 1.1 knowledge of mathematical techniques for solving optimisation problems; ILO 1.2 knowledge of probabilistic and inferential tools for using statistical models; ILO 1.3 knowledge of the technical vocabulary of the subjects of this learning area. ILO 2 Applying knowledge and understanding: ILO 2.1 ability to calculate derivatives and partial derivatives; ILO 2.2 ability to calculate limits and sums of series; ILO 2.3 ability to use quantitative methods to solve problems in economics; ILO 2.4 ability to read, write and communicate in the technical language of quantitative methods in the three official languages of instruction; ILO 3 Autonomy of judgement ILO 3.1 Acquisition of the ability to judge and of the methodological tools useful for the critical analysis of data, sources, assumptions and implications of scientific practice, of the political, ethical and legal context within which economic phenomena are set and with which they interact ILO 4 Communication skills ILO 4.1 Proficiency (oral and written) in Italian, German and English, including translation between these languages. Intercultural competence. Conceptual awareness, synthesis and written expression, in particular in the drafting of scientific or science-based documents ILO 5 Learning skills ILO 5.1 Promotion of critical thinking and analytical skills to focus on complex problems in their long-term dynamics and the variety of their implications, including ethical ones

Modalità d'esame
A written final exam (questions and problems to solve) covering both M1 and M2 parts (M1 partial exam and M2 partial exam, respectively). Written exam of maximal 120min at the end of each module. There is no different assessment for attending and non-attending students.

Criteri di valutazione
Final grade: 50% grade for M1 partial exam, 50% for M2 partial exam. The grades of partial exams are only valid for the academic year in question. They cannot be carried over beyond that time frame.