00679 - Mathematics

Learning outcomes

• knows the fundamentals of linear algebra and the theory of limits and sequences. The student is able to solve a system of first-degree linear equations and to calculate the limits of the most important sequences and functions;
• knows the elements of differential and integral calculus and is able to apply them to the solution of simple theoretical and practical problems and to the formulation and interpretation of mathematical models in economics, business, and finance.

Course contents

Linear Algebra:

Linear systems. Matrices. Determinant. Rank. Vector spaces, bases, dimension. Linear dependence. Eigenvalues and eigenvectors.

Mathematical Analysis:

The system of real numbers. The topology of the real line. Functions. Supremum and infimum. Limits and continuity. Differentiability and rules of differentiation. Applications to monotonicity and convexity. The Taylor expansion. The Riemann integral, the fundamental theorem of integral calculus. Antiderivatives. Methods of integration. Functions of several real variables, differentiability, maxima, minima, and saddle points. Constrained maximization: Lagrange multipliers.

Readings/Bibliography

Books

Carl P. Simon , Lawrence E. Blume, Matematica Generale, EGEA, collana I Manuali 2007

or

Knut Sydsaeter, Peter Hammond, Arne Strøm, “Metodi matematici per l'analisi economica e finanziaria” (a cura di D. La Torre e C. Pellizzari), Pearson, 2015. ISBN: 978-8865189535.

For linear algebra 

Silvana Abeasis, ELEMENTI DI ALGEBRA LINEARE E GEOMETRIA, Zanichelli

Teaching methods

Theory, exercises, examples solved by the teacher at the blackboard.

Assessment methods

For students enrolled in the current Academic Year, there are three partial written tests planned for assessment: one at the end of the second sub-cycle of the first semester, one at the end of the first sub-cycle of the second semester, and one at the end of the second sub-cycle of the second semester, according to the schedule set by the School; the final grade is the weighted average of the grades from the partial tests. To be eligible to take subsequent partial tests, a student must achieve a grade of at least 14 in the first partial test and subsequently in the second.

For everyone, there is a comprehensive written test. An oral test is only to supplement the grade.

In the written tests, only the use of non-programmable scientific calculators is allowed.

Teaching tools

PDFs of the lectures will be made available at the end of each lesson, along with a series of exercises related to the various sections of the syllabus covered.

Office hours

See the website of Natascia Angelini

See the website of Silvia Foschi