2020/2021

2020/2021

DM270

SECS-S/06 (MATHEMATICS FOR ECONOMICS, ACTUARIAL STUDIES AND FINANCE)

DEPARTMENT OF ECONOMICS AND MANAGEMENT

BUSINESS ADMINISTRATION, CONTROL AND CORPORATE FINANCE

PERCORSO COMUNE

1°

(28/09/2020 - 22/12/2020)

9

66 lesson hours

Italian

WRITTEN AND ORAL TEST

BOLOGNA SIMONA - 0 ECTS
CAPRARI ELISA - 9 ECTS

Due to a wide difference in high school programs, the incoming students' mathematical background is not so homogeneous. The difficulties to pass exams of quantitative nature are mainly related to drawbacks in the basic preparation of freshmen that are rarely overcome during the lessons.
In particular, a basic knowledge of the following topics is required: graphs and properties of elementary functions (powers, exponentials, logarthms, goniometric functions), equalities and inequalities with one unknown variable, basic analytic geometry (straight lines, parabolas, circles).
The mathematics pre-course, that is held before the start of the course, offers an organic action of strenghtening of the basic mathematical background of incoming students.

The course aim is to give a basic knowledge of mathematics both from a theoretical point of view and in view of perspective economic applications. The course objective is not only to provide theoretical results and calculus tools (Dublin Descriptor 1) but also the ability to apply tools and theory also when the parameters of the models are changing (Dublin descriptor 2). When one considers making judgement, communication lifelong learning skills (Dublin descriptors 3-4-5), the student will be able to express autonomously and with a structured answer the solution to simple problems and exercises, with an acknowledgement of the importance of formalization and of the use of deductive method in reasoning.

Linear algebra. Vectors and vector spaces. Matrices. Determinant. Inverse matrix. Rank. Systems of linear equations.
Elementary topology notions. Limits: definition, theorems, operations with limits. Continuous functions and their properties. Differential calculus. Derivatives of first and higher order. Relationships between differentiability and continuity. Stationary points. Fermat, Rolle and lagrange theorems and their corollaries. De l’Hopital's theorem. maximum and minimum points for differentiable functions. Differential. Taylor's formula. Convexity and inflection points. Graphic of functions.
Antiderivative. definite integral and its geometric interpretation. Mean-value theorem. Torricelli-Barrow's theorem. Generalized integrals.
n-variables functions. Preliminary notions Partial derivatives and gradient vector. Second order partial derivatives and Hessian matrix. Maximizers and minimizers for a 2-variables differentiable function

Given the large number of students, during the coronavirus emergency
the main didactic tool will be lectures with presence of the students in
turns, where students will be involved with questions and exercises. The
lessons will be recorded and it will be possible to follow them at distance.
Problems and questions will be assigned as homework. Tutoring
activities. A weakly homework assigment will be posted on KIRO distance
learning platform. After a while, the homework will also be solved by the
tutors during some special sessions. Only afterwards a written solution
will be published on Kiro, with the intention of stimulating the
autonomous use of direct and cross-over skills acquired. A tutoring
activity is organized for students needing assistance.

Giorgi G., Molho E., Elementi di Matematica, Giappichelli, Torino, 2015, ISBN 978-88-921-0046-6

An intermediate written multiple-choice test will be issued in order to
allow students to check their skills to autonomously solve questions and
problems that involve competences acquired in the course.
The final exam consists in a written test. There is a preliminary part that
is used to test the acquisition of basic competences, both on calculus and
on theoretical notions. The second part of the exam, which one can write
only if the preliminary part is passed, is made of some problems (possibly
with subproblems). An extended, formally correct and motivated answer
to each question is required, based on both theoretical notions and
calculus techniques learnt in the course. Hence not only the learning of
theoretical notions will be tested, but also the ability to use them and
some soft skills such as the use of deductive reasoning and its correct
formalization.
The teacher can ask the student to sit for an additional oral part of the
exam.