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.

Symmetric bilinear forms and quadratic forms. Sylvester's criterion.

The detailed course syllabus will be published on Virtuale at the end of the lectures.

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

Learning assessment consists of an exam divided into two written parts: a first written test, comprising practical exercises, and a second written test, containing theoretical questions (definitions, examples and counterexamples, statements of key theorems, and potentially one proof). Both tests are mandatory, will take place consecutively on the same day, and cover the entire course syllabus. The first test lasts 2 hours, and the second lasts 30 minutes.

A maximum of 24 points can be scored in the first written test, and up to 8 points in the second. The final grade will be the sum of the marks obtained in both parts. To pass the exam, students must achieve a minimum score of 14 points in the first test and 4 points in the second.

The instructor reserves the right to request a short oral examination prior to finalizing and confirming the score of the written tests.

Regardless of the marks obtained in the written tests, students wishing to achieve a final grade higher than 27/30 must undergo a brief oral interview consisting of one theoretical question.

Students have the option to withdraw from either test and may reject the proposed final grade once.

Registration for exam sessions must be completed via AlmaEsami, closing 5 days prior to the date of the written examination.

Students must present their student ID card (tesserino universitario) to take the exam.

No reference materials or electronic devices are permitted, except for a non-programmable scientific calculator. Any use of AI tools during the examination is strictly prohibited and constitutes a violation of academic integrity.

Students with Disabilities and Specific Learning Disabilities (SLD)

Students with disabilities or specific learning disabilities (SLD) are entitled to special accommodation tailored to their needs, subject to prior evaluation by the University Service for Students with Disabilities and SLD. Please do not contact the instructor directly; instead, reach out to the Service to arrange an appointment. The Service will determine the appropriate accommodations. For more information, please visit: 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