Economics and Finance

The main objective of the course is to provide the mathematical basis for understanding and formalizing the economic, financial and business subjects covered by the degree course as well as the quantitative tools necessary for the development of the related applications. The course covers topics that are usually part of the Mathematics program carried out in scientific high schools or experimental institutes with quantitative guidelines but enriches their contents with demonstrations and theoretical considerations aimed at making the subject less mnemonic and less mechanical and at the same time more easily accessible to those with a different education, too. The course assumes the knowledge of some preliminary topics of Set Theory, Algebra and Analytic Geometry and deals in particular with the following topics: resolution of systems of linear equations; study of the real function of a real variable; integral calculation; introduction to the study of real functions of several real variables. A. Knowledge and understanding Students who pass the exam will know the definitions, concepts and methods of calculation object of the program, but above all the logical-intuitive reasoning, the demonstrations and the geometric interpretations necessary for the understanding of their concrete meaning and for their application. In particular, they will know: the definition of a system of linear equations and the fundamental theorem for its solution; the definition of real function of a real variable and the characteristics of the different types of functions; the concepts of limit, derivative and integral and the relative theorems, properties and methods of calculation; the definition of real function of several real variables and the calculation of partial derivatives. B. Applied knowledge and understanding Students who pass the exam will know how to set up and solve a system of linear equations and will be able to discuss the result when a given parameter changes. They will be able to study the main "characters" of a function (such as, for example, existence, sign, behavior at extremes, continuity, derivability, monotonicity, concavity and convexity, integrability), to graphically represent the behavior and resolve some geometric problems connected. Finally, they will be able to calculate the partial derivatives of a real function of several real variables. C. Making judgment Students will develop the aptitude for mathematical reasoning, the ability to use formal language, the ability to argue the validity of a result through a rigorous demonstration and the ability to interpret and explain a phenomenon through a graphical representation. D. Communication skills The exam consists of a written test and an oral test. Students who pass the exam will then be able to solve the exercises assigned during the written test but also discuss the carrying out of the exercises. In particular, they will be able to motivate the methods of calculation used and justify and interpret the results obtained through an explicit reference to the theoretical topics covered by the program. E. Learning skills The students will have the necessary mathematical bases to support the other quantitative area exams included in the three-year degree course, but also the tools useful for formalizing, understanding, explaining and solving some simple problems of the teachings of other areas.