# GEOMETRY 1 - MOD 1 cod. 1010760

1° year of course - First semester
Professor
Michela ZEDDA
Geometria (MAT/03)
Field
Formazione matematica di base
Type of training activity
Basic
56 hours
of face-to-face activities
6 credits
hub: -
course unit
in ITALIAN

Integrated course unit module: GEOMETRY 1

## Learning objectives

The course aims, by means of frontal lessons, to provide knowledge and techniques of linear algebra to solve linear systems, diagonalize matrices and describe the behaviors of geometric bodies in the plane and in 3D space.

Applying knowledge and understanding. The student will be able to:
i) solve systems of linear equations,
ii) simple exercises of analytic geometry in space; operate on vectors and matrices;
iii) diagonalize operators and matrices.

Making judgments: the student must be able to understand the rightness of the results obtained by himself or by others.

Communications skills: through the frontal class and assistance of the teacher, the student acquires scientific vocabulary. At the end of the course, the student is expected to be able to communicate mathematical arguments.

Learning skills: the student who has attended the course will be able to deepen is knowledge of linear algebra and vector spaces.

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## Course unit content

Analytic geometry and linear algebra.

## Full programme

Vectors. Gauss algorithm. Vector spaces and subspaces. Linear combination, linear independence and basis. Sum and intersection of subspaces. Complex, powers and roots. Linear maps, kernel and image. Linear system, parametric and cartesian equations, affine subspaces. Linear applications and matrices, composition, isomorphisms, product of matrices, inverse of a matrix, change of coordinates matrix. Determinant, Binet Theorem, Kronecker Theorem. affine geometry, scalar product, Euclidean geometry. Eigenvalues and eigenvectors. Spectral Theorem. Conics and quadrics.

## Bibliography

The textbook for this course is:
M. Abate , C. De Fabritiis: "Geometria analitica con elementi di algebra lineare", Mc Graw Hill Education.

## Teaching methods

Privileged education mode is the frontal lesson that offered arguments from a formal point of view, accompanied by significant examples, applications and exercise. Exercises are proposed every week. The exercises are uploadoaded on the plattform Elly. The aim is to invites students to check theirselver the knowledge and ability. . Also the pdf files of the lessons are uploades on the platform Elly every week.

## Assessment methods and criteria

This is the first module of an annual course, information about the final examination are given in the syllabus of the second module. There will be at least a written text on the subjects of this first module, which is not mandatory to pass the final exam.

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