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 central in the DIEM curriculum. Both activities require sufficient familiarity with a toolbox containing mathematics, modelling and computer science.
This course aims at offering first a relevant part of the contents of this toolbox 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 than their formal aspects and includes the use of scientific computation tools in order to build and analyse economic and business models.

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

A 1^st partial written exam and a 2^nd partial written exam will be offered during the semester. The results of these exams can be used once to take the oral exam. Students who do not use the partial exams must take the general written exam.  If passed, the mark can be used to have access to the oral exam.

• BORGONOVO, Introductory Mathematics for Business and Economics, Milano, EGEA,  2004, 2^nd ed.

During the course indications will be provided on the covered parts of the following textbooks:

• C.P. SIMON, L. BLUME, Mathematics for Economists, New York, W.W. Norton & Company, 1994, 2^nd ed.
• T. BRADLEY, P. PATTON, Essential Mathematics for Business and Economics,  J. Wiley & Sons, 2000.
• D. HUGHES-HALLET, A.M GLEASON, W.G. McCALLUM, et al., Calculus, J. Wiley & Sons, 2002, 3^rd ed.
• A. MIZRAHI, M. SULLIVAN, Mathematics for business and social sciences: an applied approach, J. Wiley & Company.
• S. WANER, S.R. COSTENOBLE, Finite Mathematics and Applied Calculus, Brooks/Cole, Pacific Grove, 2001, 2^nd ed.