- Docente: Iliyan Georgiev
- Crediti formativi: 3
- SSD: SECS-S/06
- Lingua di insegnamento: Inglese
- Modalità didattica: Convenzionale - Lezioni in presenza
- Campus: Bologna
- Corso: Laurea Magistrale in Economics (cod. 8408)
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dal 05/09/2022 al 08/11/2022
Conoscenze e abilità da conseguire
At the end of the course the student has reinforced the mathematical reasoning and acquired the necessary skills and ability to work on the mathematical structures of a wide range of economic models. In particular, he/she is able to experience the deep knowledge of a mathematical problem and to comprehend the rigorous logic on which it is based. Furthermore, he/she is able to: - determine and discuss the nature of stationary points of several variables functions, recurrence relations and differential equations, thereby deducing properties of models' steady states; - identify and interpret different kinds of economic dynamics and investigate the related models; - work with Linear Algebra basic tools to construct and solve problems involving eigenvalues and eigenvectors; - formulate Definitions of necessary tools such as equilibrium concepts to be applied in many economic frameworks such as Industrial Organization, Contract Theory, Voting Systems, Game Theory, Macroeconomic Theory; - write correct proofs of Propositions and Theorems.
Contenuti
Linear spaces. Matrices, operations, rank and determinant. Inverse of a nonsingular square matrix. Linear systems, kernel of a matrix, linear maps, eigenvalues, eigenvectors, diagonalization theory. Scalar product, norm, orthogonal subspaces.
Functions of one and several real variables: continuity, convexity, quasi-convexity, (partial) derivatives, differentiability, tangent line/hyperplane, stationary points, Hessian matrix. Constrained and unconstrained optimization. Methods of Lagrange's multipliers and Kuhn-Tucker Theory.
Indefinite and Riemann integrals in one variable. First order ordinary differential equations (separation of variables, linear equations). Some notions of difference equations and dynamical systems.
Testi/Bibliografia
Mathematics for Economists, Carl P. Simon, Lawrence Blume, Norton & Company, New York, London, 1994.
Essential Mathematics for Economic Analysis, Peter Hammond, Knut Sydsaeter, Prentice-Hall, Harlow, 2008.
Further Mathematics for Economic Analysis, Knut Sydsaeter, Peter Hammond, Atle Seierstad, Arne Strom, Prentice-Hall, Harlow, 2008.Metodi didattici
Traditional lectures at the university premises
Modalità di verifica e valutazione dell'apprendimento
- attendance of at least 75% of the classes
- a final pass/fail test
Strumenti a supporto della didattica
A dedicated page on Virtuale
Orario di ricevimento
Consulta il sito web di Iliyan Georgiev
SDGs
L'insegnamento contribuisce al perseguimento degli Obiettivi di Sviluppo Sostenibile dell'Agenda 2030 dell'ONU.