# Linear Algebra and Elements of Geometry (2014/2015)

Course code
4S00253
Credits
12
Coordinator
Lidia Angeleri
Teaching is organised as follows:
ALGEBRA LINEARE 6 MAT/02-ALGEBRA I sem. Lidia Angeleri
ELEMENTI DI GEOMETRIA 6 MAT/03-GEOMETRY See the unit page See the unit page

#### 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.

#### Syllabus

Module: ALGEBRA LINEARE
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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.

Module: ELEMENTI DI GEOMETRIA
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Affine and Euclidean spaces. Lines, planes, hyperplanes. Vector product and mixed product. Affine and isometric transformations. Projective spaces. Geometry of projective plane. Conics.

#### 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.

 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