### Sciences

## Subject: GEOMETRY (A.A. 2020/2021)

### degree course in MATHEMATICS

Course year | 1 |
---|---|

CFU | 6 |

Teaching units |
Unit Geometria
Basic Mathematics (lesson)
- TAF: Basic compulsory subjects SSD: MAT/03 CFU: 6
Simona BONVICINI |

Exam type | oral |

Evaluation | final vote |

Teaching language | Italiano |

### Teachers

### Overview

Knowledge of the fundamentals of affine and Euclidean geometry, with a few hints of projective geometry.

### Admission requirements

Basi Linear Algebra.

### Course contents

Affine space. Proper and improper points. Parallelism. Real vector and affine spaces. Orientations. Norms and scalar products. Euclidean vector spaces. Gram determinant. Orthonormal bases. Gram-Schmidt orthonormalization method. Orthogonal complement of a subspace. Euclidean spaces and subspaces. Cartesians coordinates. Subspace representations. Orthogonality. Orthogonal transformations. Angles. Direction cosines. Unitary operators and isometries. Orthogonal symmetry.

### Teaching methods

The course consists of lectures and exercises. On Dolly, students can find solved exercises, some written tests and exercises for the self-assessment. Because of the covid-19 emergency, lectures and exercises might be delivered online.

### Assessment methods

The exam consists of a written and an oral test. The oral interview aims to evaluate the knowledge of the subject and the ability of presenting the results with the right mathematical formalism and the hypothetical-deductive thinking.

### Learning outcomes

Through lectures and individual study, knowledge of:

Affine space. Proper and improper points. Parallelism. Projective spaces (hints).

Real vector and affine spaces. Orientations. Norms and scalar products. Euclidean vector spaces. Gram determinant. Orthonormal bases. Gram-Schmidt orthonormalization method. Orthogonal complement of a subspace.

Euclidean spaces and subspaces. Cartesians coordinates. Subspace representations. Orthogonality. Orthogonal transformations. Direct and inverse transformations. Rotations and symmetries. Angles. Direction cosines. Simplices. Volumes.

Attitude towards a methodological approach that leads to verify claims and methods through rigorous arguments.

Ability to self-assessment of their skills and abilities.

Ability to deal with a dialectical discourse in a timely and consistent way, arguing with precision.

Lasting acquisition of mathematical knowledge to be used at any time of their cultural journey.

Attitude towards a methodological approach that leads to an improvement in the method of study in order to deepen learning capacity.

### Readings

M.R.CASALI, C. GAGLIARDI, L. GRASSELLI, Geometria, Soc. Ed. Esculapio, Bologna, 2010. ISBN: 978-88-7488-378-3

edizione riveduta e corretta (collana Schaum's), McGraw-Hill Education, Milano, 2003. ISBN: 978-88-3865-076-5

E. SERNESI, Geometria 1 Seconda Edizione, Bollati Boringhieri, Torino, 2000. ISBN: 978-88-339-5447-9