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. Matrix Diagonalization. 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. Elasticity. 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.

or

Marco Abate

Metodi matematici per l'economia e il management

MC Graw hill

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

EXAM RULES 


1. How to take the written exam
You can choose one of two options:
- three partial exams, only for students enrolled in the current academic year;
- one full written exam covering the whole course, open to all students.


2. Partial exams
The dates are set by the School calendar:
- 1st partial exam: at the end of the second sub-period of the first semester;
- 2nd partial exam: at the end of the first sub-period of the second semester;
- 3rd partial exam: at the end of the second sub-period of the second semester.


You need a grade of at least 14 (out of 30) in each partial exam. If you get less than 14 in any partial exam, you cannot take the next ones and you must take the full written exam.
Your written exam grade is the simple average of the three partial exams.


3. After the written exam
- Grade of 24 or higher: the oral exam is compulsory. If you choose not to take it, a grade of 23 will be recorded.
- Grade of 23 or lower: you can accept your grade or take an optional oral exam.
In both cases, the oral exam contributes to your final grade.


4. Allowed materials
During the written exams, you may only use a non-programmable scientific calculator.

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 Enrico Smargiassi