Mathematics
A.Y. 2026/2027
Learning objectives
The teaching aims to present some mathematical concepts and methods, with particular emphasis on developing the aspects of the discipline most useful for a real understanding of the topics covered in the teachings characterizing the whole course of study. Purpose of the teaching is letting the students acquire basic tools and notions of Mathematics, with special focus on the elementary mathematical analysis and an adequate theoretical understanding of the concerned topics, along with a proper ability to perform the involved computational procedures.
As further detailed below, knowledge and understanding are achieved through varied forms of teaching, such as lectures, exercise sessions and tutorials, and are verified through final written and, in some cases, oral tests.
The test evaluations also consider the ability to integrate knowledge acquired with the teachings attended during the first year of the course.
As further detailed below, knowledge and understanding are achieved through varied forms of teaching, such as lectures, exercise sessions and tutorials, and are verified through final written and, in some cases, oral tests.
The test evaluations also consider the ability to integrate knowledge acquired with the teachings attended during the first year of the course.
Expected learning outcomes
At the end of the course, the student will acquire a specific language for communicating what he/she has learned and basic notions introductory to the following professionalizing teachings.
Namely, he/she should be able to use the acquired knowledge, to formulate and solve in a rigorous manner application problems not only in Mathematics, but also in other fundamental teachings such as Physics, Chemistry and Biology and, in general, in a wide variety of contexts relevant to the Viticulture and Oenology graduate's jobs.
He/she should be familiar with basics of mathematical analysis, such as the field of existence, the continuity, the derivability and the study of the maximums and minimums of a function, the integration of a function, in order to solve a plurality of problems.
Finally, he/she will build up critical and judgment skills by analysing and evaluating specific problems with a generalization learning process, so that he/she can later approach on his/her own the study of new cases in various other fields than mathematics.Finally, he/she will build up critical and judgment skills by analysing and evaluating specific problems with a generalization learning process, so that he/she can later approach on his/her own the study of new cases in various other fields than mathematics.
Namely, he/she should be able to use the acquired knowledge, to formulate and solve in a rigorous manner application problems not only in Mathematics, but also in other fundamental teachings such as Physics, Chemistry and Biology and, in general, in a wide variety of contexts relevant to the Viticulture and Oenology graduate's jobs.
He/she should be familiar with basics of mathematical analysis, such as the field of existence, the continuity, the derivability and the study of the maximums and minimums of a function, the integration of a function, in order to solve a plurality of problems.
Finally, he/she will build up critical and judgment skills by analysing and evaluating specific problems with a generalization learning process, so that he/she can later approach on his/her own the study of new cases in various other fields than mathematics.Finally, he/she will build up critical and judgment skills by analysing and evaluating specific problems with a generalization learning process, so that he/she can later approach on his/her own the study of new cases in various other fields than mathematics.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
1. Number sets: the sets N, Z, Q, R. Ordering of the real line and the symbols for "infinity". Absolute value, n-th roots, logarithms and exponentials: definitions and properties. Percentages, averages and proportions, and their use in solving real-world problems (0.5 CFU).
2. Equations and inequalities: first- and second-degree equations and inequalities, and those reducible to them; rational fractional, irrational, exponential and logarithmic equations and inequalities, including those with absolute values; systems of equations and inequalities (0.5 CFU).
3. The orthogonal Cartesian plane: coordinates, equations of lines, orthogonality, parallelism, distance between points, distance from a point to a line, midpoint and perpendicular bisector of a segment. Review of conics: parabolas, circles, hyperbolas. Systems of inequalities in two variables for the description of suitable regions of the plane (1 CFU).
4. Functions of a real variable. The concept of function: domain, codomain, graph. Elementary functions and their graphs: linear functions, powers and roots, exponentials, trigonometric functions, special functions. Elementary operations on graphs: translations, reflections, symmetries, absolute values. Monotone and invertible functions, logarithmic functions and inverse trigonometric functions. Operations with functions (1 CFU).
5. Sequences and limits of sequences. Limits of functions: definition; operations with limits; indeterminate forms and their resolution; standard limits; hierarchy of infinities and infinitesimals; asymptotic estimates for resolving indeterminate forms. Horizontal, vertical and oblique asymptotes. Continuous functions: definition and properties (1 CFU).
6. Derivatives. Derivatives of elementary functions, differentiation rules, derivatives of composite functions. Continuity and differentiability. Geometric meaning of the first derivative and its applications; tangent lines; monotonicity and determination of maximum and minimum points; Lagrange's theorem; de l'Hôpital's theorem. Qualitative study of the graph of a function (1 CFU).
7. Integrals. Indefinite integrals: notion of primitive function, primitives of elementary functions, finding primitives. Methods of integration: immediate integrals, integrals reducible to immediate integrals. Definite integrals: the Fundamental Theorem of Integral Calculus and its applications. Calculation of areas of plane regions (1 CFU).
2. Equations and inequalities: first- and second-degree equations and inequalities, and those reducible to them; rational fractional, irrational, exponential and logarithmic equations and inequalities, including those with absolute values; systems of equations and inequalities (0.5 CFU).
3. The orthogonal Cartesian plane: coordinates, equations of lines, orthogonality, parallelism, distance between points, distance from a point to a line, midpoint and perpendicular bisector of a segment. Review of conics: parabolas, circles, hyperbolas. Systems of inequalities in two variables for the description of suitable regions of the plane (1 CFU).
4. Functions of a real variable. The concept of function: domain, codomain, graph. Elementary functions and their graphs: linear functions, powers and roots, exponentials, trigonometric functions, special functions. Elementary operations on graphs: translations, reflections, symmetries, absolute values. Monotone and invertible functions, logarithmic functions and inverse trigonometric functions. Operations with functions (1 CFU).
5. Sequences and limits of sequences. Limits of functions: definition; operations with limits; indeterminate forms and their resolution; standard limits; hierarchy of infinities and infinitesimals; asymptotic estimates for resolving indeterminate forms. Horizontal, vertical and oblique asymptotes. Continuous functions: definition and properties (1 CFU).
6. Derivatives. Derivatives of elementary functions, differentiation rules, derivatives of composite functions. Continuity and differentiability. Geometric meaning of the first derivative and its applications; tangent lines; monotonicity and determination of maximum and minimum points; Lagrange's theorem; de l'Hôpital's theorem. Qualitative study of the graph of a function (1 CFU).
7. Integrals. Indefinite integrals: notion of primitive function, primitives of elementary functions, finding primitives. Methods of integration: immediate integrals, integrals reducible to immediate integrals. Definite integrals: the Fundamental Theorem of Integral Calculus and its applications. Calculation of areas of plane regions (1 CFU).
Prerequisites for admission
As a first semester course in the first year, there are no specific prerequisites other than those required for entrance to the degree course.
Teaching methods
Lectures, exercises, application of examples to concrete cases, use of an e-learning platform associated with the textbook, use of educational software, group work, use of educational games as a motivational lever for learning the subject and as a tool for verification and self-assessment on curricular topics.
The course uses the e-learning platform MyAriel, where exercise sheets and other educational materials related to the topics covered in the lectures are uploaded on a weekly basis.
Attendance of the course, although not mandatory, is highly recommended.
The course uses the e-learning platform MyAriel, where exercise sheets and other educational materials related to the topics covered in the lectures are uploaded on a weekly basis.
Attendance of the course, although not mandatory, is highly recommended.
Teaching Resources
A.M. Bigatti, L. Robbiano. Matematica di base. CEA. ISBN 978-8808720139.
A.M. Bigatti, G. Tamone. Matematica di base. Esercizi Svolti Testi d'esame Richiami di Teoria. Esculapio. ISBN 978-8874889860.
A.M. Bigatti, G. Tamone. Matematica di base. Esercizi Svolti Testi d'esame Richiami di Teoria. Esculapio. ISBN 978-8874889860.
Assessment methods and Criteria
The examination consists of a compulsory written test, lasting 120 minutes, for which students may obtain a mark of up to 30/30, followed by a compulsory oral examination. Only students who have obtained a mark of at least 16/30 in the written test may sit the oral examination. The oral examination may be taken only in the same examination session as the written test.
In order to sit the examination, students must be duly registered through the online examination registration service, which is also available through Unimia, and must arrive outside the examination room fifteen minutes before the beginning of the written test, bringing with them a photo identity document and protocol sheets. The written test consists of some short-answer exercises and some open-ended exercises, whose steps must be explicitly justified. The purpose of the written test is to assess whether the student possesses the minimum required skills and has acquired the computational tools practised during the course. During the written test, students are not allowed to consult books, notes, computers, tablets, or mobile phones. Communication with other students is also forbidden, under penalty of immediate expulsion from the examination room. The use of a non-programmable scientific calculator is allowed, provided that it has no graphing, symbolic computation, or internet-connection functions. Students are not allowed to leave the examination room during the written test. After the first hour has elapsed, students who so wish may hand in their paper or withdraw. The mark obtained in the written test will be published on the MyAriel website of the course.
The oral examination consists of a brief interview on the topics included in the syllabus, aimed at completing the assessment of the tools and skills acquired. The examination begins with a discussion of the written paper, during which the student may explain the procedures used in solving the exercises and any steps that were unclear. Subsequently, the student's knowledge and understanding of some of the topics covered in class will be assessed, together with their ability to apply such knowledge and understanding to simple exercises and their command of the subject-specific terminology.
The final assessment is expressed as a mark out of thirty and will take both tests into account. The examination is passed if the final mark is at least 18/30.
Students have the opportunity to take an optional mid-term test, consisting of a written test on the minimum required skills and on the topics covered during the first weeks of the course. This mid-term test allows students to obtain a mark of up to 10/10 and is passed with a mark of at least 6/10. Students who pass the mid-term test may use the mark obtained as the mark for one part of the written test. Students may make use of this option only in the first written test they attempt after the mid-term test, and only in the January-February examination session.
Students with specific learning disabilities and students with disabilities are kindly asked to contact the lecturer by email at least 10 days before the scheduled examination date, in order to agree on any individualised arrangements. In the email addressed to the lecturer, the relevant University Services must be copied in: [email protected] for students with specific learning disabilities, and [email protected] for students with disabilities.
In order to sit the examination, students must be duly registered through the online examination registration service, which is also available through Unimia, and must arrive outside the examination room fifteen minutes before the beginning of the written test, bringing with them a photo identity document and protocol sheets. The written test consists of some short-answer exercises and some open-ended exercises, whose steps must be explicitly justified. The purpose of the written test is to assess whether the student possesses the minimum required skills and has acquired the computational tools practised during the course. During the written test, students are not allowed to consult books, notes, computers, tablets, or mobile phones. Communication with other students is also forbidden, under penalty of immediate expulsion from the examination room. The use of a non-programmable scientific calculator is allowed, provided that it has no graphing, symbolic computation, or internet-connection functions. Students are not allowed to leave the examination room during the written test. After the first hour has elapsed, students who so wish may hand in their paper or withdraw. The mark obtained in the written test will be published on the MyAriel website of the course.
The oral examination consists of a brief interview on the topics included in the syllabus, aimed at completing the assessment of the tools and skills acquired. The examination begins with a discussion of the written paper, during which the student may explain the procedures used in solving the exercises and any steps that were unclear. Subsequently, the student's knowledge and understanding of some of the topics covered in class will be assessed, together with their ability to apply such knowledge and understanding to simple exercises and their command of the subject-specific terminology.
The final assessment is expressed as a mark out of thirty and will take both tests into account. The examination is passed if the final mark is at least 18/30.
Students have the opportunity to take an optional mid-term test, consisting of a written test on the minimum required skills and on the topics covered during the first weeks of the course. This mid-term test allows students to obtain a mark of up to 10/10 and is passed with a mark of at least 6/10. Students who pass the mid-term test may use the mark obtained as the mark for one part of the written test. Students may make use of this option only in the first written test they attempt after the mid-term test, and only in the January-February examination session.
Students with specific learning disabilities and students with disabilities are kindly asked to contact the lecturer by email at least 10 days before the scheduled examination date, in order to agree on any individualised arrangements. In the email addressed to the lecturer, the relevant University Services must be copied in: [email protected] for students with specific learning disabilities, and [email protected] for students with disabilities.
MATH-03/A - Mathematical Analysis - University credits: 6
Exercises: 32 hours
Lessons: 32 hours
Lessons: 32 hours
Professor:
Metere Giuseppe
Shifts:
Turno
Professor:
Metere GiuseppeProfessor(s)
Reception:
please write an email
office (building 21030) or remotely, via Teams.