# Linear Algebra and Elements of Geometry (2017/2018)

Course code
4S00253
Credits
12
Coordinator
Francesca Mantese
Teaching is organised as follows:
Unit Credits Academic sector Period Academic staff
ALGEBRA LINEARE 6 MAT/02-ALGEBRA I sem. Lidia Angeleri
Francesca Mantese
ELEMENTI DI GEOMETRIA 6 MAT/03-GEOMETRY II sem. Alberto Benvegnu'

#### Learning outcomes

First of all, the students are introduced to the language and formal reasoning required for the study of higher mathematics. Furthermore, the main notions and techniques of linear algebra and matrix theory are presented, focussing both on theoretical and computational aspects. Moreover, the course provides an introduction to planar and spatial analytic geometry, within the projective, affine, and euclidean setting. Finally, the main properties of conics will be discussed. Both analytical (coordinates, matrices) and synthetic tools will be employed.

At the end of the course the student must be able to demonstrate an adequate synthesis and abstraction ability, be able to recognize and produce rigorous demonstrations and be able to formalize and solve problems of moderate difficulty, limited to the syllabus of the teaching.

#### Syllabus

------------------------
MM: ALGEBRA LINEARE
------------------------
Groups, fields. The field of complex numbers. Matrices, matrix operations and their properties. Determinant and rank of a matrix. Inverse matrix. Systems of linear equations. The method of Gaussian elimination. Vector spaces, subspaces, bases, dimension. Linear maps.
------------------------
MM: ELEMENTI DI GEOMETRIA
------------------------
Eigenvalues and eigenvectors. Jordan canonical form. Affine and Euclidean spaces. Lines, planes, hyperplanes. Vector product and mixed product. Affine and isometric transformations. Projective spaces. Geometry of projective plane. Conics.

The course consists of front lessons and classroom exercises. Moreover optional tutoring activities are offered. In particular, weekly home exercises are given. They are individually corrected by a tutor and discussed during the exercise hours.

#### Assessment methods and criteria

The exam consists of:
- a joint written examination on the module Linear Algebra and the module Elements of Geometry,
- a joint oral examination on both modules.

Only students who have passed the written examination will be admitted to the oral examination.
The oral examination can also be supported in a subsequent exam session.
Voting obtained in the written test will remain valid until the February 2019 exam session.

Intermediate Testing: In February 2018, an intermediate test will take place on the contents of the Linear Algebra module. It will be held in conjunction with the last section of the teaching held in the academic year 2016/17 (same time, same classroom).
Students who have passed the intermediate test will have the opportunity (only during the first call of the 2018 summer session) to complete the written test by completing only the part about the topics of the Geometry Elements module.

 Author Title Publisher Year ISBN Note I. N. Herstein Algebra Editori Riuniti 2003 E.Gregorio, L.Salce Algebra Lineare Libreria Progetto Padova 2005 Abate, M. Algebra Lineare Mc Graw Hill 2001 Candilera,Bertapelle Algebra lineare e primi elementi di Geometria Mc Graw Hill 9788838661891 M. Abate, C. de Fabritiis Geometria analitica con elementi di algebra lineare McGraw Hill 2010 9788838665899 Alberto Facchini Algebra e Matematica Discreta (Edizione 1) Edizioni Decibel/Zanichelli 2000 978-8808-09739-2 Giuseppe de Marco Analisi Zero, presentazione rigorosa di alcuni concetti base di matematica per i corsi universitari (Edizione 3) Edizione Decibel/Zanichelli 1997 978-8808-19831-0