GEOMETRY

CODE	98169
ACADEMIC YEAR	2026/2027
CREDITS	6 cfu anno 1 INGEGNERIA GESTIONALE 11924 (L-9 R) - GENOVA
SCIENTIFIC DISCIPLINARY SECTOR	MATH-02/B
LANGUAGE	Italian
TEACHING LOCATION	GENOVA
SEMESTER	2° Semester
TEACHING MATERIALS	AULAWEB

OVERVIEW

The course provides an introduction to linear algebra and analytic geometry. In particular, it teaches algorithms for solving systems of linear equations, offers an overview of matrix theory and vector spaces, and addresses problems in plane and spatial analytic geometry. It is a first-year course, and the concepts and skills acquired will be useful for subsequent courses.

AIMS AND CONTENT

LEARNING OUTCOMES

The course aims at providing the basic concepts and tools of linear algebra and analytic geometry. At the end of the course the student will be able to: - give correct definitions of the objects and properties studied, using the appropriate mathematical formalism; - recognize in concrete examples the geometrical objects and the algebraic properties studied; - describe the set of solutions of systems of linear equations; - solve exercises of plane and space geometry involving points, lines, planes, angles, distances, scalar products, orthogonal projections, conics, quadrics; - give explicit examples of objects that satisfy the geometrical or algebraic properties studied; - apply the notions and procedures studied in order to solve problems, also of new types and of an abstract nature.

AIMS AND LEARNING OUTCOMES

The first goal of the course is to teach how to solve systems of linear equations over real and complex numbers, making use of the theory of matrices. Inspired by physics, we will study further the geometry of vectors and their basic properties and operations. In particular, vectors will lead us to vector spaces and matrices to linear maps, making an entrance in the realm of linear algebra. In this course special attention will be paid to symmetric and orthogonal matrices, to the interconnection between linear operators and matrices, to diagonalization techniques and their applications to the geometry of vectors, conics and quadrics.

In short the course aims to provide the basic concepts of linear algebra and analytic geometry, to develope a "scientific" approach to studying and solving problems. The student is expected to learn how to understand the text of a problem, carry out solutions in a reasoned and autonomous way, by making use of the methods provided in the course, and finally provide clear and precise conclusions.

PREREQUISITES

Basic knowledge of arithmetics, algebra, trigonometry and set theory.

TEACHING METHODS

The goal of the lectures is to present the theoretical part of the course, as well as providing solutions to problems, whose aim is to help explain better the theory. There will be additional hours (tutorato), devoted to discussions suggested by the professor and providing answers to students questions related to the course. Attendance at lectures and exercises is strongly recommended.

Students with valid certification for Specific Learning Disorders (SLDs), disabilities, or other special educational needs are invited to contact the instructor and the School Disability Coordinator at the beginning of the course in order to agree on any appropriate teaching arrangements which, while respecting the learning objectives of the course, take individual learning needs into account. The contact details of the School Disability Coordinator are available at the following link: University Committee for the Inclusion of Students with Disabilities or Specific Learning Disorders | UniGe | University of Genoa.

SYLLABUS/CONTENT

Basics on sets and functions. Complex numbers and polynomials. Systems of linear equations and Gauss' algorithm. Matrices, determinants and rank.

Cartesian systems of coordinates, points, lines and planes: cartesian and parametric equations, parallelism, angles, distances and orthogonal projections. Free and applied vectors, their geometrical representation, scalar and cross product, their basic geometric properties and their significance.

Vector spaces, subspaces, bases and dimension. Linear maps/operators and associated matrices. Change of basis, with particular attention to orthonormal changes of basis. Translations and rotations and their matrix representation.

Eigenvalues, eigenvectors, diagonalization of matrices and the Spectral theorem, with particular attention to symmetric and orthogonal matrices and their geometric significance.

Quadratic forms and their applications to circles, spheres, conics and basic quadrics.

TEACHERS AND EXAM BOARD

ALESSANDRO ONETO

Ricevimento: By appointment.

FABIO TANTURRI

Ricevimento: Office hours to be decided with the Professor, by writing to his e-mail address: fabio.tanturri@unige.it

LESSONS

LESSONS START

https://corsi.unige.it/en/corsi/11924/studenti-orario

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

Written test that consists in solving some problems similar to those seen during the lectures. There might be a possible oral test. More details will be communicated on Aulaweb.

ASSESSMENT METHODS

The exam aims to verify whether the student has acquired the required skills and knows further how to use and express them in correct terms. In particular, it will asses the student's ability to solve problems related to the main topics of the course, provide adequate explanations on the procedures and express clear conclusions.

FURTHER INFORMATION

Ask the Professor for other information not included in the teaching unit description.