OVERVIEW

The course is designed to provide the basic concepts and tools of linear algebra and analytic geometry. It is a first-semester, first-year course in which concepts that will be used in many subsequent courses are introduced.

AIMS AND CONTENT

LEARNING OUTCOMES

This teaching unit aims to provide the basic concepts and technical tools related to complex numbers, linear algebra, and analytic geometry.

AIMS AND LEARNING OUTCOMES

The main goal of the course is to provide basic concepts of linear algebra and geometry, aiming at the development of a scientific approach to these topics and of the necessary tools to solve problems. Students are expected to gain the skills of understanding the text of a problem, look for solutions by means of the appropriate tools among the ones introduced in the course, solve the problem using appropriate arguments and express the results and conclusion in a clear and precise way.

PREREQUISITES

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

TEACHING METHODS

Lectures will be devoted to developing the theoretic part of the course, as well as to solving problems aimed to a better understanding of the theory. There will be additional hours  devoted to discussion of exercises suggested by the lecturer.

Students with valid certifications for Specific Learning Disorders (SLDs), disabilities or other educational needs are invited to contact the teacher and the School's contact person for disability at the beginning of teaching to agree on possible teaching arrangements that, while respecting the teaching objectives, take into account individual learning patterns. Contacts of the School's disability contact person can be found at the following link Comitato di Ateneo per l’inclusione delle studentesse e degli studenti con disabilità o con DSA | UniGe | Università di Genova

SYLLABUS/CONTENT

Basics on sets and functions. Complex numbers and polynomials. Systems of linear equations and Gauss' algorithm. Matrices, determinant and rank. Cartesian system of coordinates, points, lines and planes: cartesian and parametric equations, angles, distance, orthogonal projections. Free and applied vectors, their geometrical representation, scalar/cross product, their basic geometric properties and their significance. Vector spaces, subspaces, basis and dimension. Linear operators and the associated matrices (translations and rotations along the axis), base change (orthonormal). Eigenvalues, eigenvectors and diagonalization of matrices (symmetric and orthogonal) and their geometric significance. Quadratic forms, circles, spheres and conics.

RECOMMENDED READING/BIBLIOGRAPHY

• A. Bernardi, A. Gimigliano: Algebra Lineare e Geometria Analitica, Città Studi Edizioni
• E. Sernesi: Geometria vol. 1, Bollati-Boringhieri
• D. Gallarati: Appunti di Geometria, Di Stefano Editore-Genova
• M.R. Casali, C. Gagliardi, L. Grasselli: Geometria, Società Editrice Esculapio
• F. Odetti, M. Raimondo: Elementi di Algebra Lineare e Geometria Analitica, ECIG Universitas
• M. Abate: Algebra Lineare, McGraw-Hill
• L. Robbiano: Algebra lineare per tutti, Springer
• F. Bottacin: Esercizi di algebra lineare e geometria, Società Editrice Esculapio
• V. Bertella, A. Damiano: Esercizi su spazi vettoriali e applicazioni lineari, Società Editrice Esculapio
• L. Mauri, E. Schlesinger: Esercizi di algebra lineare e geometria, Zanichelli

Material provided by the lecturer, available on the AulaWeb webpage of the course.

TEACHERS AND EXAM BOARD

Exam Board

MARIA ROSARIA PATI (President)

VICTOR LOZOVANU (President Substitute)

ARVID PEREGO (President Substitute)

ELEONORA ANNA ROMANO (President Substitute)

LEONE SLAVICH (President Substitute)

FRANCESCO VENEZIANO (President Substitute)

LESSONS

LESSONS START

In accordance with the manifesto. All class schedules are posted on the EasyAcademy portal.

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

Written test consisting of some exercises to be solved of the type seen during the course and possible oral test. Details will be communicated on Aulaweb.

ASSESSMENT METHODS

The written exam is intended to verify the student's capacity to solve problems, apply the main algorithms in the course, and show a good understanding of the main theoretical concepts developed during the semester, such as main theorems and definitions. The oral exam aims to verify the student's understanding of the basic concepts, definitions, and properties, seen during the course.

Exam schedule

FURTHER INFORMATION

Ask the professor for other information not included in the teaching schedule.