cod. 1010761

Academic year 2023/24
1° year of course - Second semester
- Costantino MEDORI
Academic discipline
Geometria (MAT/03)
Formazione matematica di base
Type of training activity
84 hours
of face-to-face activities
9 credits
hub: -
course unit

Integrated course unit module: GEOMETRY 1

Learning objectives

Knowledge and understanding: The course aims to provide the basic knowledge of the spectral theory of the operators on a real or complex Euclidean space, of the theory of bilinear and sesquilinear forms, of the scalar and hermitian products, and of the forms on a Euclidean space. The student should be able to independently read and understand results of Analytical Geometry and Linear Algebra also by consulting scientific monographs.

Skills: The student should be able to solve exercises of Analytical Geometry and Linear Algebra also non-elementary.

Making judgments: The student should be able to construct and develop logical arguments with a clear identification of assumptions and conclusions; it should also be able to recognize correct demonstrations and identify fallacious reasoning.


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Course unit content

Dual space and the transpose of a linear transformation. Inner product spaces. Linear isometries and unitaty operators.
Linear functionals and adjoints. Spectral theory of operators on an inner product space: self-adjoint and normal operators. Bilinear and sesquilinear forms. Scalar and Hermitian products. Forms on inner product spaces. Quadrics. Affine e projective geometry (outline).

Full programme

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Serge Lang. Algebra lineare. (Terza edizione) Bollati Boringhieri, 1970.
Paolo De Bartolomeis. Algebra lineare. La Nuova Italia, 1993.

Other references:
Ciro Ciliberto. Algebra lineare. Bollati Boringhieri, 1994.
Marco Abate. Geometria. McGraw-Hill, 1996.
Mauro Nacinovich. Elementi di geometria analitica. Liguori Editore, 1996.
Edoardo Sernesi: Geometria 1. Bollati Boringhieri, 2000.

Teaching methods

The theoretical topics of the course are presented during class lectures and illustrated with significant examples, applications and several exercises. Homework assignments are proposed during the course, which are then discussed in recitation sessions during class time.

Assessment methods and criteria

The final exam consists of a written part, where students are required to solve some exercises, and of an oral part about the theoretical topics and the applications discussed during the course. Access to the oral part is not recommended if the written part is insufficient.
The final mark turns out to be a weighted average between the evalution of the written and oral parts.

Other information

Part of the educational material may be present on Elly.