20603 - OPTIMIZATION

Prerequisites: To feel comfortable in this course you should have attended at least one calculus class covering the basic concepts of function, derivative, integral as well as having a working knowledge of linear algebra (i.e. vectors/matrices).

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.

• Metric Spaces.
• Normed Vector Spaces.
• Abstract Equations.
• Contractions and Fixed Points.
• Calculus in Vector Spaces.
• 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 Economic Theory.
• 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 are a problem session where mathematical problems concerning the topics taught in class are discussed and solved.

Written exam.

Lecture notes.