Linear Algebra and Elements of Geometry - ELEMENTI DI GEOMETRIA (2011/2012)

Course code
Academic sector
Language of instruction
Teaching is organised as follows:
Activity Credits Period Academic staff Timetable
Teoria 3 I semestre Mauro Spera
Esercitazioni 1 I semestre Nicola Sansonetto

Lesson timetable

Learning outcomes

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.

Assessment methods and criteria

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.

Teaching aids
Title Format (Language, Size, Publication date)
elegeo-scritto-18/7/12  pdfpdf (it, 280 KB, 18/07/12)
elegeo-scritto-18/9/12  pdfpdf (it, 171 KB, 18/09/12)
elegeo-scritto-21/2/12  pdfpdf (it, 254 KB, 22/02/12)
elegeo-scritto-4/7/12  pdfpdf (it, 219 KB, 04/07/12)
elegeo-scritto-4/9/12  pdfpdf (it, 196 KB, 04/09/12)
elegeo-scritto-7/2/12  pdfpdf (it, 314 KB, 09/02/12)
foglio 10  pdfpdf (it, 97 KB, 19/12/11)
foglio 11-nuovo  pdfpdf (it, 123 KB, 19/01/12)
programma ufficiale elegeo -2011/12  pdfpdf (it, 35 KB, 11/01/12)