20136 - ADVANCED MATHEMATICS FOR ECONOMICS AND SOCIAL SCIENCES

Mathematics is the language in which most of modern economics is written. The course aims to provide the basic mathematical tools that students need to complete their Economics studies. Moreover, the course develops the analytical thinking skills that students need later on in their academic career.

• 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
• Exercises (exercises, database, software etc.)

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

The exam could be taken in one of these two following ways:

• 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 and the final exam.
• General exam. The exam is passed with a grade at least of 18.

Lecture notes.