Course 2022-2023 a.y.

• Linear algebra
• Metric Spaces
• Normed Vector Spaces
• Contractions and Fixed Points
• Convex Analysis
• Dynamic Programming

• Carry out a formal mathematical proof
• Recognize the abstract mathematical structures that underlie modern economic theories
• Master vector spaces techniques
• Solve complex dynamic optimization problems

• Apply to economics and to the social sciences the techniques of contemporary mathematics
• Work out both the quantitative and the qualitative perspectives
• Solve dynamic optimization problems which are key in Macroeconomics
• Master topological arguments which are important in Game Theory and Microeconomics

• Face-to-face lectures
• Online lectures
• Exercises (exercises, database, software etc.)

Every one/two weeks there is a problem session where mathematical problems concerning the topics taught in class are discussed and solved.

The students' assessment is based on a written exam that consists of mostly open questions which aim to measure the learning outcomes of the students:

• In particular, some questions are more theoretical, requiring statements, and/or proofs of theorems, while other questions are more "practical", like open exercises or problems. All these questions test the students' understanding of the mathematical ideas and techniques presented in the course as the language of economic modelling.
• The written exam could be taken as a general exam at the end of the course or splitted in two partial exams. Each of them has the structure described above. In the two partial exams the final grade is the average of the two marks; it is necessary to get a grade greater than or equal to 12 in both the partial exam and the average has to be greater than or equal to 18. Also, the general exam is passed with a grade greater than or equal to 18

Lecture notes