GEOMETRY IN EUCLIDEAN AND METRIC SPACES
cod. 13466

Academic year 2007/08
1° year of course - Second semester
Professor
Academic discipline
Geometria (MAT/03)
Field
Formazione matematica
Type of training activity
Basic
70 hours
of face-to-face activities
7 credits
hub:
course unit
in - - -

Learning objectives

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Lead students to gain mastery of basic analytics of (Projective) Affine and Euclidean Affine spaces starting with a foundational introduction to them.

Prerequisites

Vector spaces. Matrices and determinants. Linear applications: Linear systems. Bilinear and quadratic forms. Euclidean vector spaces. <br />
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Vector spaces. Matrix and determinant. Linear applications. Linear system. Bilinear and quadratic forms. Euclidean vector spaces.

Course unit content

<br />Elements of synthetic and analytical geometry in projective spaces. Synthetic and analytical geometry of affine spaces and Euclidean spaces. Connections between projective spaces and affine spaces. Complexified projective and affine spaces. Fundamental elements of curves and surfaces. Conics in projective, affine and Euclidean spaces. <br />
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Elements ofsynthetic and analytical geometry in projective spaces. Synthetic and analytical geometry of affine spaces. Synthetic and analytical geometry of Euclidean spaces. Connections between projective spaces and affine spaces. Complexified projective and affine spaces. Fundamental elements of curves and surfaces. Conics in projective, affine and Euclidean spaces.  

Full programme

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Bibliography

Vittorio Mangione, Nozioni di algebra lineare, Azzali editore, Parma, 1997. <br />
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Vittorio Mangione, Spazi Curve e Superficie, Azzali editore, Parma, 1998 <br />
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M. Stoka-V. Pipitone, Esercizi di Geometria, Cedam Padova, 1995.

Teaching methods

Written and oral examination. The oral lecture is carried out with or without transparencies or by means of prepared learning routes and provided with projection through a computer.

Assessment methods and criteria

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Other information

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