50T001 - GEOMETRIA

The exam consists of a final written test and a possible oral test which can be accessed if at least a predetermined minimum score is achieved in the final written test. Passing any ongoing written tests exempts the Student from the final written test or part of it.

Passing the written test gives the right to take the oral exam only in the session in which the written exam was passed.

The possible topics the written exam will focus on are:

1. Vector spaces and subspaces, the 4 fundamental subspaces

2. Solving linear systems and practical applications

3. Matrix operations, inverse matrix calculation, similar matrices

4. Orthogonality: orthogonality of the four subspaces, projections in the subspaces, least squares approximation, orthogonal matrices and Gram-Schmidt procedure,

5. Linear determinants and applications (properties and applications of determinants)

6. Eigenvalues and eigenvectors (diagonalization, positive definite symmetric matrices, similarity transformations

7. Jordan's canonical form

In the written test, the critical skills achieved by the Student in framing the topics covered by the Course and the methodological rigor of the resolutions proposed in response to the questions formulated are evaluated. This test lasts a maximum of two hours. The oral test consists of an interview on the topics of the written test and

on the theoretical topics that are part of the course program. The student's ability to communicate the knowledge acquired through adequate scientific language and presentation skills is assessed.

The final grade will be attributed according to the following evaluation criterion:

30 - 30 cum laude: excellent knowledge of the topics, excellent language skills, complete and original interpretative ability, strong ability to autonomously apply knowledge to solve the proposed problems;

26 - 29: complete knowledge of the topics, good command of language, complete and effective interpretative ability, able to autonomously apply knowledge to solve the proposed problems;

24 - 25: knowledge of the topics with a good level of learning, fair command of language, correct and confident interpretative ability, ability to correctly apply most of the knowledge to solve the proposed problems;

21 - 23: adequate knowledge of the topics, but lack of mastery of the same, satisfactory language skills, correct interpretative ability, limited ability to autonomously apply knowledge to solve the proposed problems;

18 - 20: basic knowledge of the main topics and technical language, sufficient interpretative ability, ability to apply the knowledge acquired;

Insufficient: does not have acceptable knowledge of the topics covered during the course.