5018 - MATHEMATICS AND MODELLING

The study of economic theory and the use of models for the analysis of concrete economic or business problems are activities obviously central in the DIEM curriculum. Both activities require sufficient familiarity with a toolbox containing mathematics, modelling and computer science.

This course aims to offer first a relevant part of the contents of this tool box and precisely: a basic knowledge of some mathematical tools and the very first ideas about the construction of a model.

The approach chosen for mathematical teaching is somehow different from the standard one in high schools: it stresses the intuitive side of the various topics, rather then their formal aspects and includes the use of scientific computation tools in order to build and to analyse economic and business models.

1. Linear algebra (vectors, matrices and corresponding operations), linear algebraic systems: existence of solutions and solving algorithms.
2. Sets of real vectors, neighborhoods, standard topology.
3. Numerical sequences and their limits: convergence, divergence and related properties.
4. Basic notions on functions, examples of elementary functions and their use to describe economic or financial phenomena.
5. Limits and continuity of functions: relevant properties of continous functions.
6. Elements of differential calculus for functions of one or several variables: differential, derivatives, graphical representation of functions, local and global extrema.
7. Elements of integral calculus for functions of one variable: the notion of primitive, elementary integration methods.
8. Basic information about MATHCAD.

During the course indications will be given of which parts of these textbooks will be covered.

• MIZRAHI-SULLIVAN, Mathematics for business and social sciences: an applied approach, J. Wiley&Company.
• TAN, Applied Mathematics for the Managerial, Life, and Social Sciences, 2nd Ed. Brooks/Cole, Pacific Grove, 2001.
• WANER-COSTENOBLE, Finite Mathematics and Applied Calculus, 2nd Ed., Brooks/Cole, Pacific Grove, 2001.
• SIMON-BLUME, Mathematics for Economists, W.W. Norton &Company, New York, 1994.

A midterm and an endterm written exam will be offered during each semester. The results of these exams can be used once to take the oral part. At each exam date, the students who will not use partial exams must take a written and an oral exam.