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, logarithms, 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 strengthening of the basic mathematical background of incoming students.
In particular, a basic knowledge of the following topics is required: graphs and properties of elementary functions (powers, exponentials, logarithms, 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 strengthening of the basic mathematical background of incoming students.
Teaching Methods
The course consits of 66 hours lessons (with theoretical content) and 24 hours of exercises. 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.
autonomous use of direct and cross-over skills acquired. A tutoring activity is organized for students needing assistance.
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 individual 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: 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.
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 individual 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: 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.
1. FULL EXAM: 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.
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 individual 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: 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.
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
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 (3)
Teaching staff
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