29228 - Geometry and Algebra T

Learning outcomes

Knowledge of the main tools of linear algebra (matrices, vector spaces, linear systems, quadratic forms) and of their applications in a geometric environment, granting both the comprehension of the connections among the different parts and the operational ability.

Course contents

Linear Systems

Matrices

Gaussian elimination

Vector spaces and subspaces

Linear maps

Determinant

Eigenvalues and eigenvectors

Diagonalization of matrices and linear maps

Euclidean scalar product. Othogonal matrices. Diagonalization of symmetric matrices.

Euclidean and affine spaces. Subspaces. Parallelism. Orthogonality.

Classification of conics 

Readings/Bibliography

Textbook:

Fioresi Rita, Morigi Marta, Introduzione all'algebra lineare, Edizioni CEA (2021)

Exercises sheets are available on the course webpage on Virtuale

https://virtuale.unibo.it/

Teaching methods

There are 60 hours in total, devoted both to the theory, with proofs of relevant theorems, and to the complete solution of various exercises of different levels.

Comprehension quizzes administered through Wooclap  will be used during the lessons.

Assessment methods

 

The exam consists of a written test and of an oral part. Both are compulsory and concern the whole program covered in the lectures.

The written test lasts two and a half hours and has the aim of testing the ability of the student in solving exercises, giving examples and counter-examples or short argumentations on theoretical issues. It is not possible to make use of textbooks or personal notes, only one side of a sheet of paper size A4 is allowed, containing whatever formula the student thinks might be useful.

The oral interview lasts 15/20 minutes and aims to assess the student's knowledge and understanding of the topics covered in the course and his ability to present them with coherence using a specific language and a correct mathematical formalism, including proofs of theorems.

Students are admitted to the oral exam after passing the written exam with at least 18/30. If a student passes the written exam, he/she mast take the oral exam either in the same "appello" or in the following one.

If a student does not pass the oral exam, he/she must repeat the written exam.

The final grade is not the result of the arithmetic mean between the written and oral tests but rather the result of an overall assessment of the preparation of the student, based on the written test which has, therefore, a decisive weight.

The student has the right to withdraw from both the written and oral tests and to refuse the final grade proposed once.

Entries to the appeals are made on AlmaEsami.  Enrollment in the written test is mandatory, please note that registrations close 5 days before the date set for the written exam.

It is necessary to come to the tests with the university badge.

Students with disabilities and Specific Learning Disorders (SLD)Students with disabilities or Specific Learning Disorders have the right to special accommodations according to their condition, following an assessment by the Service for Students with Disabilities and SLD. Please do not contact the teacher but get in touch with the Service directly to schedule an appointment. It will be the responsibility of the Service to determine the appropriate adaptations. For more information, visit the page:

https://site.unibo.it/studenti-con-disabilita-e-dsa/en/for-students

Teaching tools

All the corse material will be available on Virtuale.

Office hours

See the website of Marta Morigi