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

Student learning will be assessed through a final exam consisting of two written tests: a first written test focused on exercises, and a second written test containing theoretical questions (definitions, statements of main theorems, and possibly their proofs, if covered during lectures).
Both parts are mandatory and cover the entire content of the course.

The first written test lasts 2.5 hours and aims to evaluate the student’s ability to solve problems or provide brief reasoning on theoretical questions. Books and notes are not allowed, but students may use a personal formula sheet, limited to one side of an A4 sheet.

The theory test lasts 45 minutes and aims to assess the student’s knowledge and understanding of the topics covered in the course, as well as their ability to present them clearly, using appropriate terminology and correct mathematical formalism. Examples, counterexamples, and proofs of theorems will be required.

Students may access the theory test only after having passed the written test with a minimum score of 18/30. The theory test must be taken either in the same sitting or the next one, provided it falls within the same exam session (winter, summer, or autumn). The oral schedule will be published together with the results of the first written test.

The final grade takes into account the results of both tests, but it is not a simple arithmetic average, since the first written test carries greater weight in the final evaluation. If the final grade is insufficient, both tests must be repeated. Students may withdraw from either test and refuse the final proposed grade once.

Exam registration must be completed via AlmaEsami.

Registration for both parts of the exam is mandatory, and closes 5 days before the scheduled date of the written test.

Students must present their university ID card in order to take the exam.

Students with Disabilities and Specific Learning Disorders (SLD)
Students with disabilities or specific learning disorders are entitled to special accommodations based on their condition, subject to assessment by the University Service for Students with Disabilities and SLD. Please do not contact the instructor directly. Students should instead schedule an appointment with the Service, which will determine the appropriate accommodations.
More information is available at:
👉 https://site.unibo.it/studenti-con-disabilita-e-dsa/en/for-students

 

Teaching tools

All course material will be available on Virtuale.

Office hours

See the website of Marta Morigi