OVERVIEW

The course aims to introduce the language of linear algebra: vector spaces, linear maps, bilinear forms, and matrices. Linear algebra represents one of the most complete and effective languages of modern mathematics, and it is used in all more advanced mathematics courses, both applied and theoretical, found in science and engineering degree programs. Euclidean geometry in the plane and in space will be revisited both to provide some of the most important examples for understanding the general theory and to illustrate certain applications of linear algebra (such as the classification of conic sections and quadric surfaces). The final part of the course is an introduction to projective geometry, also presented as an application of linear algebra.

AIMS AND CONTENT

LEARNING OUTCOMES

The aim of the course is to introduce students to the basic aspects of linear algebra, affine and Euclidean geometry. These topics play a critical role in the study of modern mathematics and physics and will be used in all subsequent courses. In addition, the course will present a theory that is strongly motivated by concrete problems that can be treated in a comprehensive and rigorous manner.

TEACHING METHODS

frontal lessons and tutoring

RECOMMENDED READING/BIBLIOGRAPHY

Main textbook: 

A.Bernardi, A.Gimigliano, Algebra Lineare e Geometria Analitica, Citta'Studi Edizioni. 

Other ones:

.   M.E. Rossi, Algebra lineare, Dispense disponibili nella pagina del corso

.   F. Odetti - M. Raimondo, Elementi di Algebra Lineare e Geometria Analitica, ECIG Universitas.

.  Marco Abate, Algebra Lineare , ed. McGraw-Hill

.  E. Sernesi, Geometria vol 1, ed Bollati-Boringhieri.

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

25th September 2025

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The exam has a written part and an oral part.
The written exam is considered as passed if the student obtains an evaluation at least equal to 18/30. To participare to the written exam the student has to perform the inscription to the exam on the UNIGE website https://servizionline.unige.it/studenti/esami/prenotazione at least two days before the exam. 

During the year there will be two intermediate exams (one at the end of the first semester, the other at the end of the second semester) that, if passed, replace the written exam. The first intermediate exam il considered as passed if the student obtains an evaluation at least equal to 16/30. To take part to the second intermediate exam, the student needs to pass the first intermediate exam. The two intermediate exams are considered as passed if the student obtains an evaluation at least equal to 16/30 in both intermediate exams, and the average of the two evaluations is at least equal to 18/30.

The oral exam takes place during the same exam session of the written exam, and the student that gets to the oral exam after having passed the two intermediate exams may choose to carry out the oral exam either during the exam session of June (the first session) or during the exam session on July (the second session). The final evaluation will be the average of the evaluations of the written and the oral parts of the exam. If the oral exam is considered as not sufficient, the commission may consider to cancel the result of the written exam as well.

Students with DSA certification ("specific learning disabilities"), disability or other special educational needs are advised to contact the teacher at the beginning of the course to agree on teaching and examination methods that, in compliance with the teaching objectives, take account of individual learning arrangements and provide appropriate compensatory tools.

ASSESSMENT METHODS

The written exam consists in the resolution of some exercices about the whole program of the course. The exam lasts three hours. During the exam the student will not have the possibility to use any books, notes, or electronic devices such as calculators, tablet, cell phones or smartwatch, but we suggest the student to prepare an A4 paper handwritten form with the formulas and the results that he/she may consider to be useful for the exam. To take part to the written exam, the student needs to perform the inscription on the UNIGE website not later than two days before the exam. The written exam will be consdiered as passed it the obtained evaluation is at least 18/30. Only for very special cases the commission will take into consideration the possibility to lower this threshold.

There will be moreover two intermediate exams that replace the written exam. The first one will take place at the end of the first semester, and will consist in the resolution of exercices concerning the program of the first semester of the course. The second intermediate exam will take place at the end of the second semester, and it will consist in the resolution of exercices concerning the program of only the second semester of the course. Both intermediate exams last three hours. During the exam the student will not have the possibility to use any books, notes, or electronic devices such as calculators, tablet, cell phones or smartwatch, but we suggest the student to prepare an A4 paper handwritten form with the formulas and the results that he/she may consider to be useful for the exam. To take part to the intermediate exams, the student needs to perform the inscription via specific inscription forms that will be available on the AulaWeb page of the course. The first intermediate exam is considered as passed if the obtained evaluation is at least 16/30, and one may participate to the second intermediate exam only in this case. Both intermediate exams are considered as passed, and in this case they will replace the written exam, if both evaluations are at least 16/30, and the average of the two evaluations is at least 18/30.

The oral exam requires the knowledge and the ability to present the definitions, the statements and the proofs that have been treated alla long the course, the ability to give examples that illustrate the main notions of the course, and the ability to establish if a given statement is true or false by means of proofs or counterexamples. In order to determine if the student is able to use the instrument of Linear Algebra, the teacher will furthermore propose the resolution of some exercices. The oral exam will take place during the same exam session of the written exam, or during the exam sessions of June or July (the first and the second exam sessions) for the student that get to the oral exam after having passed the two intermediate exams  If the oral exam is considered as not sufficient, the commission may consider to cancel the result of the written exam as well.

FURTHER INFORMATION

Students who have valid certification of physical or learning disabilities on file with the University and who wish to discuss possible accommodations or other circumstances regarding lectures, coursework and exams, should speak both with the instructor and with the referent person of Scuola di Scienze MFN, the Department’s disability liaison.