- Docente: Iliyan Georgiev
- Credits: 3
- SSD: SECS-S/06
- Language: English
- Moduli: Iliyan Georgiev (Modulo 1) Iliyan Georgiev (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Economics (cod. 8408)
Learning outcomes
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.
Course contents
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.
Readings/Bibliography
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.
Teaching methods
Traditional lectures
Assessment methods
A pass/fail final test
Teaching tools
A dedicated page on Virtuale
https://virtuale.unibo.it/course/view.php?id=31810
Links to further information
https://virtuale.unibo.it/course/view.php?id=31810
Office hours
See the website of Iliyan Georgiev
SDGs
This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.