00679 - Foundations of Mathematics

Learning outcomes

At the end of the course named Foundations of Mathematics, the students is familiar with those mathematical concepts that are fundamentals in the approach to economics and management

Course contents

Basic Elements
Elementary theory of real numbers. Relations and functions. Intervals, upper and lower bounds. Maximum and minimum of intervals. Algebraic, logarithmic, exponential and radical equations and disequalities. Graphic solution of equations. Analytic geometry: equations of lines, parabolas, hyperboles.

Calculus

Real functions of one real variable: properties, composition, inverse. Increasing and decreasing functions. Polynomial, logarithmic, exponential, rational and radical functions.

Limits in a real point and to infinite. Local and global continuity. Weierstrass theorem and theorem about the existence of roots for a continuous function.

Derivatives: properties and rules. Geometric meaning of the first derivative. The tangent line. Non constrained optimization: existence of maximum and minimum. Concavity and convexity. Qualitative analysis of the graphs of simple functions.

Matrix and vector algebra

Introductory matrix theory and operations with matrixes. Sarrus and Laplace rules for the determinant computation of square matrixes. Properties of the determinant.

Invertible matrix, necessary and sufficient conditions for invertibility. Inverse matrix and rank.

Eigenvalues and eigenvectors of a square matrix.

Systems of linear equations: Cramer and Rouchè-Capelli theorems. Homogeneous systems. Solutions of systems depending on one parameter.
 

Readings/Bibliography

In alternativa:

- A. Guerraggio, Matematica, Bruno Mondadori Editore, Milano.

- K. Sydsaeter, P.Hammond, A. Strom (a cura di D. La Torre) Metodi Matematici per l'Analisi Economica e Finanziaria, Pearson.

- S. Waner and S.R. Costenoble Strumenti quantitativi per la gestione aziendale, Apogeo.

Teaching methods

Traditional lectures together with practice exercises that are highly recomended.

Assessment methods

The written part of foundations of mathematics can be passed through two partial exams, the first one in November and the second one in December. The examination consists in an obligatory written part and in an optional oral part. The final vote is the score obtained in the written part when there is no oral examination.

Teaching tools

Thecrash courseabout basic mathematics is fully recomended. Students can benefit of a bonus at the end of the crash course.

Office hours

See the website of Maria Letizia Guerra