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LINEAR ALGEBRA AND GEOMETRY

Course Details

• Code: 80275
• Academic Year: 2025/2026
• Credits:
  • 12 cfu anno 1 FISICA 11895 (L-30 R) - GENOVA
  • 16 cfu anno 1 MATEMATICA 11897 (L-35 R) - GENOVA
  • 16 cfu anno 1 STATISTICA MATEM. E TRATTAM. INFORMATICO DEI DATI 11900 (L-35 R) - GENOVA
• Language: Italian
• Teaching Location: GENOVA
• Prerequisites: Propedeuticità in uscita. This course is a prerequisite for the following courses:
  • PHYSICS 8758 (coorte 2025/2026)
  • GENERAL PHYSICS 3 57050
  • PHYSICS II 57049
  • PHYSICS 11895 (coorte 2025/2026)
• Modules: This course is composed of:
  • LINEAR ALGEBRA AND GEOMETRY
  • LINEAR ALGEBRA AND GEOMETRY
• Teaching Materials: AULAWEB

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.

PREREQUISITES

There are no specific requirements.

TEACHING METHODS

• Frontal lessons
• Tutoring

RECOMMENDED READING/BIBLIOGRAPHY

• Main textbook: A.Bernardi, A.Gimigliano, Algebra Lineare e Geometria Analitica, Citta'Studi Edizioni.
• Other recommended texts:
  • 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

Teachers

• FABIO TANTURRI
• EMANUELA DE NEGRI
• VICTOR LOZOVANU
• ELEONORA ANNA ROMANO
• LEONE SLAVICH

Exam Board

• President: EMANUELA DE NEGRI
• Members:
  • ELEONORA ANNA ROMANO
  • VICTOR LOZOVANU (President Substitute)
  • LEONE SLAVICH (President Substitute)
  • FABIO TANTURRI (President Substitute)

LESSONS

LESSONS START

• 25th September 2025

Class Schedule

The timetable for this course is available on the 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 participate in the written exam, the student must perform the inscription to the exam on the UNIGE website 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 is considered as passed if the student obtains an evaluation at least equal to 16/30. To take part in the second intermediate exam, the student needs to pass the first intermediate exam. 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 throughout 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 exercises. 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 gets to the oral exam after having passed the two intermediate exams. If the oral exam is considered as not sufficient, the commission may consider canceling the result of the written exam as well.

ASSESSMENT METHODS

• The written exam consists of the resolution of some exercises 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, tablets, cell phones, or smartwatches, but it is suggested that the student prepares an A4 paper handwritten form with the formulas and the results that he/she may consider useful for the exam. To take part in 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 considered as passed if the obtained evaluation is at least 18/30. Only for very special cases will the commission take into consideration the possibility to lower this threshold.

Exam Schedule

• Data appello | Orario | Luogo | Degree type | Note | Subject
  • 07/01/2026 | 14:00 | GENOVA | Scritto | | ALGEBRA LINEARE E GEOMETRIA ANALITICA
  • 12/01/2026 | 09:45 | GENOVA | Orale | | ALGEBRA LINEARE E GEOMETRIA ANALITICA
  • 28/01/2026 | 09:45 | GENOVA | Scritto | | ALGEBRA LINEARE E GEOMETRIA ANALITICA
  • 30/01/2026 | 09:45 | GENOVA | Orale | | ALGEBRA LINEARE E GEOMETRIA ANALITICA
  • 23/06/2026 | 09:45 | GENOVA | Scritto | | ALGEBRA LINEARE E GEOMETRIA ANALITICA
  • 20/07/2026 | 09:45 | GENOVA | Scritto | | ALGEBRA LINEARE E GEOMETRIA ANALITICA
  • 11/09/2026 | 09:45 | GENOVA | Scritto | | ALGEBRA LINEARE E GEOMETRIA ANALITICA

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.

Agenda 2030 - Sustainable Development Goals

• Quality education
• Gender equality