SM/0146 - GEOMETRY AND ALGEBRA COMPLEMENTS
Academic Year 2019/2020
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MARIA PAOLA PIU (Tit.)
- Teaching style
- Lingua Insegnamento
|[60/65] MATHEMATICS||[65/10 - Ord. 2012] Generale||6||48|
KNOWLEDGE AND UNDERSTANDING ABILITIES
The purpose of the course is to enable students to understand the language, techniques and contents of projective geometry and related topics.
The preferred teaching tool for achieving these goals are the frontal lessons, where the various topics of the course will be developed, by introducing fundamental concepts and developing a series of theorems with the respective proofs, alongside significant examples, exercises and applications
CAPACITY OF APPLICATION: the student must be able to apply all the general knowledge necessary for the understanding of projective geometry.
JUDGEMENT: The course aims to stimulate objective teaching evaluation constantly offering students a comparison between the theoretical contents proposed while they were lessons front and obtain them through self-study using the recommended texts and course material provided.
COMMUNICATION SKILLS: ability to express with the appropriate mathematical terminology the basic concepts of projective geometry
The contents of first degree in Mathematics.
Motivation. Projective spaces. Examples. Dependence and subspaces. Reference frames. Projectivities. Perspectivities. Duality. Connection affine-projective space. Improper points. Hyperquadrics. Polarity. Hyperquadrics in the affine and Euclidean spaces. Pencils of conics.
Determination of projective subspaces and of projectivities. Detection of improper points. Computation of pole, polar, vertex, center, principal hyperplanes.
Lecture of traditional type.
Verification of learning
J. Richter-Gebert, Perspectives on projective geometry. A guided tour through real and complex geometry. Springer, Heidelberg, 2011
C. Gagliardi, L. Grasselli, Algebra lineare e geometria, vol. 1-3, coll. Leonardo, ed. Esculapio, 1993
M.R. Casali, C. Gagliardi, L.Grasselli, Geometria, Progetto Leonardo, Bologna, 2002
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