58414 - Algebra and Geometry (M-Z)

Learning outcomes

At the end of the course, the student knows the theory of vector spaces (real and complex) of finite dimension and linear applications. He also acquires the fundamental notions of analytic geometry in the plane and in space. In particular, the student is able to: solve linear systems; search for eigenvectors and eigenvalues; diagonalizing real symmetric matrices and Hermitian matrices; solve simple geometry problems.

Course contents

Geometry of the three-dimensional space. Matrices. Linear systems. Vector spaces. Linear applications. Eigenvalues and eigenvectors. Scalar products. Bilinear forms. Conics and quadrics. Dual space, notes on tensors.


The detailed teaching program will be published on Virtuale at the end of the lessons.

Readings/Bibliography

The topics covered in the course are classical topics of linear algebra and geometry, and are found in numerous texts.

The textbook adopted is

Fioresi R. e Morigi M., Introduzione all'algebra lineare. Seconda edizione, Casa Editrice Ambrosiana (2021)

Some parts will be taken from

Lang S., Algebra Lineare, Boringhieri (1970)

As for the exercises, exercise sheets on the topics covered will be published on Virtuale   weekly, and will then be corrected in the classroom. If you want the support of a further text any workbook on geometry and linear algebra can be fine. Here are some titles:

• Barani A., Grasselli L., Landi C., Algebra Lineare e Geometria, Progetto Leonardo, Esculapio 2005.
  
• Abate M., de Fabritiis C., Esercizi di Geometria, McGRaw-Hill 2003.
• Lipschutz S., Lipson M., Algebra lineare, Collana Schaum's, McGraw-Hill 2001.
• Parigi G., Palestini A., Manuale di Geometria - Esercizi, Pitagora 2003.
  

 

Teaching methods

Frontal lesson, dialogue and exercises.

Assessment methods

The exam consists of a written test and an oral test. Both are compulsory and encompass the entire lesson plan.

The written test has a total duration of three hours and aims to assess the student's ability to solve exercises, give examples and counterexamples, enunciate and provide brief arguments on theoretical issues. The written test consists of 6 theoretical exercises or questions and the maximum score is 300. Students are admitted to the oral test if the mark in the written test is at least 180/300. Written and oral must be carried out in the same call. The oral schedule will be published with the results of the written test.


The oral exam consists of an in-depth study of the questions in the written test and has the aim of assessing the student's knowledge and understanding of the topics covered in the teaching and his ability to expose them consistently using a specific language and a correct mathematical formalism. The final outcome of the exam takes into account the results achieved in both tests.


Registrations for the exams are made on AlmaEsami.


Registration for the written exam is mandatory, please note that registrations close 5 days before the date scheduled for the written exam. It is necessary to show up for the tests with a university card or an identity document.

Teaching tools

All teaching materials will be published on  Virtuale.
A visit to the site of Prof. Massimo Ferri is recommended  and particularly to the Chicken's corner.

The  tutor of the course is   Dott. Daniele Galli.

Office hours

See the website of Alessia Cattabriga

See the website of Emanuele Latini