Teaching code

4S00181

Teacher

Alberto Peretti

Coordinator

Alberto Peretti

Credits

9

Also offered in courses:

• Mathematics of the course Bachelor's degree in Business Innovation and Economics

Language

Italian

Scientific Disciplinary Sector (SSD)

SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES

Period

Primo semestre (lauree) dal Sep 25, 2023 al Jan 19, 2024.

Courses Single

Authorized

Lessons timetable Moodle Seminars 0

Learning objectives

The course has a dual purpose: first of all, to make students acquire a rigorous scientific language based on deductive logical-mathematical reasoning; in addition, the course aims to provide students with some analytical tools and basic mathematical models to deal quantitatively with the treatment of economic and business problems. In particular, the foundations of differential and integral calculus, optimization and linear algebra will be provided, which constitute effective tools for analyzing economic and business phenomena. At the end of the lessons the student will have to demonstrate that she has developed the aptitude to face mathematical problems with reasoning and the ability to use, in the application contexts, the appropriate methods, tools and mathematical models. The traditional lectures, dedicated to the more general and theoretical aspects of the discipline, but not without applicative references, are accompanied by hours of exercises, aimed exclusively at solving computational problems and applying them. The students also find in the E-learning pages of the course, as the lessons progress, learning verification tests on the various topics covered.

Prerequisites and basic notions

These are the mathematical notions which students should have acquired at the secondary school: algebraic expressions and rules for their transformation, polynomials, powers and logarithms and their properties, simple integer equations and corresponding inequalities, fractional equations and similar inequalities, some elements of analytic geometry, in particular the Cartesian coordinates in the plane, straight lines and their representation with first degree equations. All these topics are however taken up again at the beginning of the course, in terms of a quick review and some in-depth analysis.

Program

Basic notions (algebraic expressions, powers and logarithms, equations and inequalities, analytic geometry)
Functions of one variable
Limits
Differential calculus
Integral calculus
Notes on numerical series
Vector spaces, linear transformations and matrices
Systems of linear equations
Functions of several variables. Differential calculus in several variables. Conditions for maxima and minima
The detailed program and all the teaching material are available on the course web page and by accessing the relative e-learning pages.

Bibliography

Didactic methods

The course gives 6 credits, corresponding to 48 hours of lessons, and 3 credits (36 hours) of exercises.
The traditional lectures, dedicated to the more general and theoretical aspects of the discipline, but not without references to applications, are accompanied by hours of exercises, aimed exclusively at solving exercises for a better understanding of the general aspects. Students will also find in the e-learning pages of the course, as the lessons proceed, learning verification tests on the various topics already covered.
The lecture notes, written by the teacher, are available on the web pages, in which all the topics of the course are developed, togethe with the texts and solutions of the exercises carried out weekly in the classroom, all the previous exam topics with the relative developments.
Furthermore, in the e-learning platform, students can verify their preparation through multiple choice online tests that are made available when the related topics have been dealt with in class. Those who demonstrate regularity and good results in the tests will be awarded 1-2 points in the final grade of the exam.
Throughout the academic year, the individual reception service managed by the teacher is available, at the times indicated on the web pages (without the need to make a specific appointment) and constantly updated.
During the semester of the lessons and near the exam sessions a tutoring service is available carried out by students enrolled in CdLM, suitably chosen through a public selection. This service is initially aimed mainly at students who, due to mathematical deficiencies in the previous school path, have difficulties in the discipline from the first days of class. The tutoring service then continues near the winter and summer exam sessions, now aimed at supporting the final preparation.

Learning assessment procedures

The final exam, the same for attending and non-attending students, consists of a written test, divided into two parts:
- a first part, with open answers, aimed at ascertaining the knowledge of the basic notions and more advanced knowledge, but at a basic level;
- a second part, which consists in solving 3 exercises and 5 theoretical questions, aimed at verifying the student's ability to use analytical tools and fundamental mathematical models, as well as understanding the more rigorous aspects of mathematical theory.
Halfway through the course, there will be an intermediate written test on the topics already covered in the course. This intermediate test has the same characteristics as the general exams described above, and therefore includes a first part of a basic nature and a second more in-depth part, which are assessed in the same way as indicated above for the general tests.
- The intermediate test is optional; the student's participation in the test does not affect his/her right to refuse the grade reported and therefore to take the entire exam at the end of the semester.
- The grade obtained in the intermediate test weighs half of the final grade, which is achieved by passing a similar second final written test. The exam is passed if and only if both partial tests are passed, possibly with the need to take the supplementary oral exam.
- The topics of the mid-term test will be specified in a specific notice on the course web page well in advance of the test date. The topics covered by the mid-term exam are excluded from the written completion test at the end of the semester.
- Useful appeals to complete the exam are the rounds of the exam session immediately following the end of the course, namely the two rounds of the winter session.
The intermediate test is introduced with the aim of attracting the student, from the first day of attendance, to a regular and systematic study of the subject, with the possibility for him to put this commitment to good use in advance, essentially passing a part of the exam. It also ascertains, halfway through, the quality of the study carried out up to that point and the knowledge acquired. In case of failure, it can also provide the student in good time with important information on the criticalities of the preparation.

Evaluation criteria

A minimum score of 6/10 is required in the first part of the written test to be admitted to the second part.
In case of full passing (grade greater than or equal to 18) in the written test, with at least 3 points in the theoretical questions, the exam is passed.
In the case of not serious insufficiency (grade between 16 and 17) or insufficiency in the theoretical questions, admission to a supplementary oral test is obtained, aimed at verifying the overcoming of the gaps that emerged in the written test.

Criteria for the composition of the final grade

The final grade is given by the sum of the points obtained in the first and second part of the written test. As already mentioned, once the exam is passed, the 1-2 points bonus related to e-learning activities is possibly added to the grade.
Students with sufficient results can always ask to take a supplementary oral test: in this case the mark of the written test is only a starting point, but neither the maintenance nor the increase of the mark itself is guaranteed, nor the passing of the exam. The same is true when the oral exam is compulsory.

Exam language

Italiano