Teaching code

4S00181

Academic staff

Athena Picarelli, Corrado De Vecchi

Coordinator

Athena Picarelli

Credits

9

Language

Italian

Scientific Disciplinary Sector (SSD)

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

Period

Primo semestre L dal Sep 23, 2024 al Jan 10, 2025.

Courses Single

Authorized

Lessons timetable Moodle Seminars 0

Learning objectives

The course has a dual purpose: first of all, to provide students with a rigorous scientific language based on a logical-mathematical deductive reasoning; in addition, the course aims to provide students with some analytical tools and basic mathematical models to deal with business-economical problems. The course yields the classical arguments from Mathematical Analysis and Linear Algebra. At the end of the lessons, the student will have to demonstrate that he has acquired the ability to critically review the mathematical concepts encountered in the course and to apply methods, tools and mathematical models.

Prerequisites and basic notions

The prerequisites are the basic mathematical notions acquired in secondary school: algebraic expressions and rules for their transformation (square and cube of a binomial, difference of squares), polynomials, powers and their properties, equations and inequalities of first and second degree, some element of analytic geometry, in particular the Cartesian coordinates in the plane, the lines and their representation with first degree equations.
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

1. Basic mathematical notions
2. One variable functions
3. Limits
4. Differential calculus
5. Integration theory
6. Vector spaces and matrices
7. Systems of linear equations
8. Functions of several variables
The detailed program and further educational material are available in the course web page.

Bibliography

Didactic methods

The course includes 48 hours of lectures (equivalent to 6 credits) and 36 hours of exercise lectures (equivalent to 36 credits).
Beside lectures on theoretical topics, the course includes exercise lectures to complete the knowledge with an adequate calculus ability.

Learning assessment procedures

The exam includes a written test with both multiple choice and open questions.
The use of the calculator is not permitted.
Students who have obtained a grade lower or equal than 16 do not pass the exam.
An additional oral test will be required for students who have obtained score 17 or 18 in written test in order to verify whether or not they have passed the exam and determine the final score and for students with a score greater or equal to 29 in order to determine the final mark and the eventual award of honours. The oral exam covers the entire program of the course: it aims at verifying the overcoming of any gaps that emerged in the written test and to check the student's preparation on the theoretical part of the course. Statements of the main theorems, definitions, proofs of simple propositions may therefore be required. The duration of the oral exam will be approximately 15-20 minutes. Following the oral exam, the grade of the written test can be confirmed, raised or lowered.
In the middle of the course there is an intermediate written assessment test on the topics already covered in the course with the intention of inducing the student to systematically study the topics of the program from the very first lessons and allowing to divide the exam program into two parts , subjected to a separate assessment of learning (intermediate test and final supplementary test).
- The intermediate test is optional; the student's participation in the test does not affect his/her right to refuse the grade reported, so as to take the entire exam at the end of the semester.
- This intermediate test has the same characteristics as the general exams and covers the program up to the time of the test. The subjects of the intermediate exam are excluded from the supplementary written exam at the end of the semester.
- Sessions useful for completing the exam: the outcome of the intermediate test has value on the final passing of the exam exclusively in the exam session immediately following the end of the course.
- The grade achieved weighs half of the final grade, which is obtained by passing a similar second written test (final supplementary test). In order to pass the exam, both partial exams must be passed (that is, they must have obtained a vote of at least 8/15), possibly with the need to take the supplementary oral exam (if the sum of the intermediate test and the final supplementary test is at least 17).

Evaluation criteria

The written tests consists of 30 questions. You get one point for each correct answer and zero points for each blank or incorrect answer.
The partial tests will consist of 15 questions each. The partial test is considered passed with a vote of at least 8/15. The sum of the marks obtained in the partial tests determines the mark of the written test. Students who have obtained a grade lower or equal to 16 in the written test do not pass the exam.

Criteria for the composition of the final grade

In those cases where the oral test is not foreseen, the final grade is determined by the score obtained in the written test. In cases that require the oral test, the final mark is determined by the joint evaluation of both tests.

Exam language

italiano