Linear Algebra and Elements of Geometry - ELEMENTI DI GEOMETRIA (2011/2012)
Scientific Disciplinary Sector (SSD)
MAT/03 - GEOMETRY
The teaching is organized as follows:
The course provides an introduction to planar and spatial analytic geometry, within the projective, affine, euclidean setting, respectively.
In particular, the respective properties of conics therein
will be extensively covered. Both analytical (coordinates, matrices)
and synthetic tools will be employed. The course aims at strengthening
the students' geometric intuition, abstraction and computational skills,
in view of future developments and applications.
Affine and Euclidean spaces. Affine and isometric transformations.
Ordinary line, plane, space and their geometry. Barycentric coordinates. Ceva's theorem
and applications. Projective spaces. Homogeneous coordinates. Elements at infinity. Homographies. Geometry of projective plane. Conics. Polarity.
Reciprocity theorem. Pencils of conics. Projective, affine, metrical
classification of conics. Centre, diameters, asymptotes, axes.
Circles, isotropic lines, cyclic (or circular) points. Foci. Directrices.
The exam is divided into three parts:
- a written examination on the module Linear Algebra,
- a written examination on the module Elements of Geometry,
- a joint oral examination on both modules.
Only students who have passed both written examinations will be admitted to the oral examination.
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programma ufficiale elegeo -2011/12
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