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87317 - Mathematical Models

Academic Year 2021/2022

                
                        Docente:
                        Lorenzo Torricelli
                    
                        Credits:
                        5
                    
                        SSD:
                        SECS-S/06
                    
                        Language:
                        Italian
                    
                        Teaching Mode:
                        Traditional lectures
                        
                            Campus:
                            Bologna
                        
                            Corso:
                            First cycle degree programme (L) in
                            Economics, Markets and Institutions (cod. 8038)

                            Teaching resources on Virtuale

Learning outcomes

Aim of the course is to provide the mathematical tools needed to study economic and financial models. At the end of the course students are supposed to be familiar with basic notions of linear algebra, matrices and solutions of linear systems.

Course contents

Functions domain and image, composition, injectivity surjectivity, invetibility.

Linear algebra: vectors and matrices, determinant of a matrix, rank of a matrix; linear systems: Cramer theorem, Rouchè-Capelli theorem, linear systems depending on a parameter. Diagonalizable matrices: eigenvalues, eigenvectors, spectral theorem; quadratic forms. Basics notions of linear functions .

Readings/Bibliography

Lecture Notes provided by the teacher and downloadable from the teacher's web site. Additional references are listed below.

Bibliography:

E. Sernesi, Geometria 1, Bollati-Boringhieri.

A. Ambrosetti, I. Musu, Matematica generale e applicazioni all'economia, Liguori.

Peccati, Salsa, Squellati, Matematica per l'Economia e l'Azienda, EGEA, Milano

K. Sydstaer, P. Hammond, A. Strom, A. Carvajal, Metodi matematici per l’economia. Pearson 2021.

Bergamini, Ritelli, Trifone: Fondamenti di Matematica, Zanichelli, Bologna, 2005.

Guerraggio, Matematica, Pearson-prentice-Hall (2a ed.)

Ricci, Matematica Generale, McGraw-Hill

Scaglianti-Torriero, Matematica metodi e applicazioni, CEDAM, Padova

Teaching methods

Classes. For each topic the theoretical results will be presented: for some of them the proof will be provided while for the others only the underlying intuition. Exercises will be solved and examined carefully. Weekly classes taken by the tutor will be devoted to the solution of exercises.

Assessment methods

Written exam. A (mandatory) supplementary interview can be required by the lecturer. The exam consist of a test of 5-6 questions of theoretical or pracitcal nature, which will add up to a total exceeding to 30 points. Grades are attirbuted on a 18-30 scale, and correpspond to the total points allowed in the test, if less or equal 30. Passing the exam requires 18 points or more. A total score in the test of over 30 points will result in the attibiution of a "cum laude" grade.

Teaching tools

Blackboard

Office hours

See the website of Lorenzo Torricelli