Linear Algebra and Elements of Geometry - ALGEBRA LINEARE (2013/2014)

Course code
4S00253
Name of lecturer
Lidia Angeleri
Number of ECTS credits allocated
6
Academic sector
MAT/02 - ALGEBRA
Language of instruction
Italian
Period
I semestre dal Oct 1, 2013 al Jan 31, 2014.

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

Lesson timetable

I semestre
Day Time Type Place Note
Tuesday 8:30 AM - 11:30 AM lesson Lecture Hall E from Oct 1, 2013  to Nov 30, 2013
Wednesday 8:30 AM - 11:30 AM lesson Lecture Hall E from Oct 1, 2013  to Nov 30, 2013

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 (second part) 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.

The course aims at strengthening the students' skills in abstract thinking, geometric intuition, and computational abilities, in view of future developments and applications.

Syllabus

Sets. Direct and indirect proofs. The principle of induction. 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. Eigenvalues and eigenspaces.

Reference books
Author Title Publisher Year ISBN Note
E.Gregorio, L.Salce Algebra Lineare Libreria Progetto Padova 2005
Candilera,Bertapelle Algebra lineare e primi elementi di Geometria Mc Graw Hill   9788838661891
M. Abate Geometria Mc Graw Hill   9788838607226
M. Abate, C. de Fabritiis Geometria analitica con elementi di algebra lineare McGraw Hill 2010 9788838665899

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.

Teaching aids

Documents