OVERVIEW

The course provides an introduction to linear algebra and analytic geometry. In particular, it teaches algorithms to find the solutions of a system of linear equations, it provides an overview of basic matrix theory, teaches about vector spaces and deals with problems from analitic geometry in the plane and space. It is a first semester course for first year students, whose concepts and expertise will be helpfull for subsequent courses.

AIMS AND CONTENT

LEARNING OUTCOMES

Provide tools for algebraic calculus and knowledge of analytical geometry of the plane and space.

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 reasonable 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.

SYLLABUS/CONTENT

Sets and maps. Complex numbers and polynomials. Linear systems and gaussian elimination. Matrices, determinants, rank. Points, lines and planes: cartesian and parametric equations, parallelism, angles, distances, orthogonal projections. Vector spaces. Vectors in geometry. Subspaces, bases, dimension. Linear maps. Matrices related to a linear map. Eigenvalues, eigenvectors. The diagonal form of a matrix. The Spectral theorem. Quadratic forms.

RECOMMENDED READING/BIBLIOGRAPHY

•    A. Bernardi, A. Gimigliano - "Algebra Lineare e Geometria Analitica", Città Studi Edizioni.
•    E. Carlini, M.V. Catalisano, F. Odetti, A. Oneto, M.E. Serpico - "Geometria per ingegneria", Editore Esculapio (Bologna), 2011.
•    M. V. Catalisano, A. Perelli - "Appunti di Geometria e calcolo numerico" (http://www.diptem.unige.it/catalisano/AppuntiGeometria.pdf )
•    S. Greco, P. Valabrega - "Algebra lineare", Levrotto & Bella, 2009.
•    S. Greco, P. Valabrega - "Geometria analitica", Levrotto & Bella, 2009.
•    F. Odetti, M. Raimondo – "Elementi di algebra lineare e geometria analitica" – ECIG, 2002.
•    J. Hefferon - "Linear Algebra" (https://hefferon.net/linearalgebra/).
•    I. Lankham, B. Nachtergaele, A. Schilling - "Linear Algebra" (https://www.math.ucdavis.edu/~anne/linear_algebra/mat67_course_notes.pdf).
•    D. Cherney, T. Denton, R. Thomas, A. Waldron - "Linear Algebra" (https://www.math.ucdavis.edu/~linear/linear-guest.pdf).
•    V. Bertella e A. Damiano - "Esercizi su spazi vettoriali e applicazioni lineari".

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

https://corsi.unige.it/en/corsi/11881/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 semester. There might be a possible oral test. In such a case the written exam grade will serve as a basis for the final vote, and it will take into account the performance during the oral exam, in a positive or negative way. More details will be communicated on Aulaweb.

Students with a certified learning disability (DSA), a disability, or other special educational needs are invited to contact the instructor at the beginning of the course to discuss teaching and examination arrangements that, while respecting the learning objectives of the course, take individual learning needs into account and provide appropriate accommodations.
Please also note that requests for exam accommodations or exemptions must be submitted using the form available at this link 
https://modulionline.unige.it/richiesta-adattamenti#no-back , to the course professor, the DIME contact person (federico.scarpa@unige.it), and the relevant office (inclusione.studenti@info.unige.it) at least seven working days before the examination, in accordance with the guidelines available at this link 
https://unige.it/disabilita-dsa/richiesta-servizi

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.