ID:
500142
Duration (hours):
66
CFU:
9
SSD:
METODI MATEMATICI DELL'ECONOMIA E DELLE SCIENZE ATTUARIALI E FINANZIARIE
Year:
2025
Overview
Date/time interval
Primo Semestre (22/09/2025 - 19/12/2025)
Syllabus
Course Objectives
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.
Course Prerequisites
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 offers an organic action of strenght ening of the basic mathematical background of incoming students.
Teaching Methods
The course includes 66 hours of frontal teaching (lessons with mainly theoretical content) and 24 hours of practice. At the end of the lesson, questions and problems will often be proposed to be solved for the following lesson and an exercise without a solution will be proposed weekly on the KIRO distance learning platform. After giving the students the opportunity to independently try to solve the proposed exercises, the teachers in charge will provide a solution to the exercise. Only later will the written solution also be published on KIRO, to encourage the autonomous application of the direct and transversal skills acquired. A tutoring activity is also planned for students who feel the need for support or strengthening.
Assessment Methods
The learning objectives will be verified through one or more written tests divided into closed-ended questions and open-ended questions in order to verify not only the learning of specific notions but also the ability to apply them and the acquisition of transversal skills such as the use of deductive reasoning and its correct formalization. 1. FULL EXAM: It consists of a written test lasting 90 minutes. The test is divided into two parts. The first part, worth 12 points, consists of eight multiple choice questions, worth 1.5 points each, aimed at testing the acquisition of basic skills both in terms of calculation and theoretical notions. It is considered passed if at least four questions are answered correctly. The second part, which is worth 20 points, will be corrected only if the first part is passed. It consists of three open questions worth 6 or 7 points each, possibly divided into several questions of a theoretical and applied nature. You are required to provide a motivated and formally correct answer based on the theoretical notions and calculation techniques learned. The final grade will be given by the sum of the scores obtained in the two parts (approximately upwards in the case of decimal scores). Alternatively, for newly enrolled students only, there is the possibility of passing the exam through two tests, one of which is ongoing. 2. ONGOING TEST: The ongoing test takes place during the appropriate autumn break, it is worth 12 points and lasts 45 minutes. It consists of eight multiple choice questions worth 1.5 points each on the part of the program covered in class up to the date of the test. The outcome of the first ongoing test will be made known by publishing the scores obtained by the students on the General Mathematics page on the Kiro e-learning portal. The test is considered passed if at least four questions are answered correctly. Passing the first ongoing test gives the Student the right to conclude the exam by taking the integration of the ongoing test in only one of the two winter sessions chosen by the Student. The latter is worth 20 points, lasts 70 minutes and consists of three open questions worth 6 or 7 points each. These questions concern the entire course program and are possibly divided into several questions of a theoretical and applied nature. The student will be asked to provide a motivated and formally correct answer based on the theoretical notions and calculation techniques learned. The final grade will be given by the sum of the scores obtained in the ongoing test and its integration (approximately upwards in case of decimal score). For both exam methods (FULL or with ONGOING TEST) the total points available between the first and second part/test is 32. The exam is considered passed if an overall score of no less than 18/30 is achieved. and a score higher than 30/32 is equivalent to 30 cum laude. During the test, the use of calculators or electronic devices of any kind, books or notes is not permitted. The final result of the exam will be made known to the student on his reserved area (Essetre portal).
Texts
Giorgi G., Molho E., Elementi di Matematica, Giappichelli, Torino, 2015, ISBN 978-88-921-0046-6.
Contents
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
Course Language
Italian
Degrees
Degrees (3)
BUSINESS ADMINISTRATION AND GOVERNANCE
Bachelor’s Degree
3 years
BUSINESS MANAGEMENT
Bachelor’s Degree
3 years
ECONOMICS
Bachelor’s Degree
3 years
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People
People (2)
Teaching staff
No Results Found