Linear Algebra and Elements of Geometry (2014/2015)
The teaching is organized as follows:
See the unit page
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.
Module: ALGEBRA LINEARE
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
Affine and Euclidean spaces. Lines, planes, hyperplanes. Vector product and mixed product. Affine and isometric transformations. Projective spaces. Geometry of projective plane. Conics.
||Libreria Progetto Padova
||Algebra lineare e primi elementi di Geometria
||Mc Graw Hill
||Mc Graw Hill
|M. Abate, C. de Fabritiis
||Geometria analitica con elementi di algebra lineare
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.