Obiettivi formativi
1) To learn some basic methods in Linear Algebra, Linear and Nonlinear Dynamical Systems, Static Optimization. These are essential tools to understand and develop mathematical models in economics and finance.
2)To be able to understand mathematical models and to develop them in simple cases.
Prerequisiti
All Basic mathematics courses of Laurea Triennale in Economics and similar topics.
In particular:
- basic calculus for one and several variable functions;
- serching extremals and zeros for one-variable functions
- basic linear algebra concepts (vector spaces and their bases, linear dependence and independence of vectors, matrices, rank, determinant, linear systems, Rouché-Capelli Theorem)
Risultati di apprendimento attesi
1) Knowledge and understanding:
The course will offer the basic theoretical tools of Linear Algebra, Dynamical Systems, Optimization. These are key tools to understand and develop mathematical models in economics and finance.
2) Applying knowledge and understanding:
The students will be taught how to use the above basic tools
to develop simple mathematical models of real phenomena such as:
- population/infection dynamics and its impact on the society;
- climate change and its economic/social impact;
- web pages ranking;
- economic/financial activities
3) Making judgements:
We expect students to be able to - understand the main features of basic economic/financial models;
- judge the reliability of information on quantitative modeling that they read in the press;
- build simple mathematical models of real phenomena.
4) Communications Skills:
This course will give the students the possibility to acquire and understand major terms and concepts
in order to communicate their ideas, proposals, analysis and critical reasoning in the field of mathematical modelling in the most effective and appropriate way.
5) Learning skills:
This course will contribute to empower learners giving them the tools to evaluate the statements on quantitative mathematical modelling (that they can read in the press or in specialized journals) in an
independent
way.
Contenuti Del Corso
- Review of calculus of Several Variables
- Implicit Functions and Comparative Statics
- Unconstrained Optimizazion
- Constrained Optimization
- Eigenvalues and eigenvectors,
- Spectral decomposition
- Linear/Nonlinear Difference/Differential Equations and Systems
- Use of the above techniques to build mathematica models of real phenomena.
Testi Di Riferimento
1)
MATEMATICS FOR ECONOMISTS
Carl Simon e Lawrence Blume
W.W. NORTON & COMPANY.
2)
Notes given by the teacher.
Metodologie Didattiche
Lessons and Exercises sessions.
Modalità di verifica dell'apprendimento
Lessons and Exercises sessions.
Criteri per l’assegnazione dell’elaborato finale
Interview
Il syllabus affronta temi collegati alla sostenibilità?
Yes. In particular the teachers will develop models on climate change and economics
Settimana 1
Introduction to the course and to mathematical modelling.
Review of several variables calculus.
Settimana 2
Implicit Functions and Comparative Statics.
Basics on Static Optimization.
Settimana 3
Linear operators and matrices.
Change of basis.
Complex numbers.
Settimana 4
Eigenvalues and eigenvectors. Spectral Decomposition of matrices 1.
Settimana 5
Spectral Decomposition of matrices 2.
Introduction to Dynamical Systems.
Settimana 6
Linear Dynamical Systems and their use in mathematical modeling.
Settimana 7
Examples of Linear Dynamical Systems.
Markov matrices, graphs and applications.
Settimana 8
Nonlinear Dynamical Systems and their use in mathematical modeling.
Settimana 9
Unconstrained Optimization. First order necessary conditions.
Second order conditions.
Settimana 10
Constrained optimization.
First order necessary conditions.
Constraint qualifications.
Settimana 11
Concave and quasiconcave functions.
Envelope Theorems.
Application of Constrained Optimization.
Settimana 12
This week does not exist