Linear Algebra and Elements of Geometry - ALGEBRA LINEARE (2017/2018)

Course code
4S00253
Name of lecturers
Lidia Angeleri, Francesca Mantese
Number of ECTS credits allocated
6
Academic sector
MAT/02 - ALGEBRA
Language of instruction
Italian
Period
I sem. dal Oct 2, 2017 al Jan 31, 2018.

To show the organization of the course that includes this module, follow this link * Course organization

Lesson timetable

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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

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.

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.

Reference books
Author Title Publisher Year ISBN Note
Alberto Facchini Algebra e Matematica Discreta (Edizione 1) Edizioni Decibel/Zanichelli 2000 978-8808-09739-2
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
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
M. Abate, C. de Fabritiis Geometria analitica con elementi di algebra lineare McGraw Hill 2010 9788838665899

Assessment methods and criteria

See the web page of the whole course

STUDENT MODULE EVALUATION - 2017/2018