OVERVIEW

The course provides an introduction to linear algebra and analytic geometry. In particular, it focuses on teaching algorithms to find the solutions of a system of linear equations, giving an overview of basic matrix theory, studying vector spaces and dealing with problems from analitic geometry in the plane and space.

AIMS AND CONTENT

LEARNING OUTCOMES

The course provides an introduction to linear algebra and analytic geometry. In particular, it focuses on describing the solutions of a system of linear equations, basic matrix manipulations, an introduction to vector spaces and dealing with problems from analitic geometry over dimension 2 and 3.

AIMS AND LEARNING OUTCOMES

The first goal of the course is to learn how to solve systems of linear equations, 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 operators, making an entrance in the realm of linear algebra. In this course special attention will be paid to symmetric and orthonormal matrices, to the interconnection between linear operators and matrices, to diagonalization techniques and their applications to the geometry of vectors, conics and quadrics.

At the end of the course, the student will master the main algorithms in order to be able to tackle problems in linear algebra and analytic geometry

PREREQUISITES

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

TEACHING METHODS

The lectures will be taking place either in presence or online (through Microsoft Teams) (or both). This depends on the pandemic situation during the time of the course. The main information will be given at the beginning and throughout the semester.

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

•    Lecture notes (Perelli-Catalisano) (see http://www.diptem.unige.it/catalisano/ )
•    E.Carlini, M.V.Catalisano, F.Odetti, A.Oneto, M.E.Serpico - "Geometria per ingegneria" - Una raccolta di temi d'esame risolti,          ProgettoLeonardo - Editore Esculapio        (Bologna), 2011.
•    S.Greco, P.Valabrega - "Algebra lineare", Levrotto & Bella, 2009.
•    S.Greco, P.Valabrega - "Geometria analitica", Levrotto & Bella, 2009.
•    J. Hefferon - "Linear Algebra" (see https://hefferon.net/linearalgebra/).
•    Lankham, Nachtergaele, Schilling - "Linear Algebra" (see  https://www.math.ucdavis.edu/~anne/linear_algebra/mat67_course_notes.pdf).
•    Cherney, Denton, Thomas, Waldron - "Linear Algebra" (see https://www.math.ucdavis.edu/~linear/linear-guest.pdf).

TEACHERS AND EXAM BOARD

Exam Board

VICTOR LOZOVANU (President)

ARVID PEREGO

FABIO TANTURRI (President Substitute)

LESSONS

LESSONS START

https://corsi.unige.it/8715/p/studenti-orario

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The exam consists of the written and possible oral part. The written exam costists of solving exercises closely related to the main subjects of the course. Admitted to the oral part are those students that got at least 50% of the points at the written exam.  The oral exam consists of answering questions, putting to light student's basic understanding and knowledge of the course. It is optional for those students that got at least 60% of the points at the written exam, and is mandatory for the other adimitted ones.

It is not allowed to use notes, books and electronic devices. During the written exam it will be allowed for consulting a single A4 page (front and back), written strictly by hand by the student.

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