Face-to-face teaching will consist of the following components:

• Lectures. The instructor will present the theoretical foundations of the course, including selected proofs. Some of the subjects or applications of the theory will be explained by the students: during one of the lecture sessions, a list of topics will be proposed. Each group will select one topic and work on it independently. The outcome of this work will be submitted as a written report and presented orally to the rest of the class.
• Problem-solving sessions (seminars). Students will be provided with problem sets, which they are expected to prepare before class in order to participate effectively in the discussions held during the sessions.
• Computer laboratory sessions using SageMath. The first three sessions will correspond to the three main topics of the course. The fourth session will include exercises covering all three topics and will be assessed.

Note: Fifteen minutes of one class session, within the timetable established by the School/Degree Programme, will be reserved for students to complete the institutional surveys evaluating the teaching performance of the instructor and the course.

Annotation: within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.

There are four assessed activities: a midterm exam, an oral presentation, an assessed practical session, and a final exam. The final grade for the course will be computed according to the following formula: 0.25 × midterm exam grade + 0.20 × oral presentation grade + 0.20 × assessed practical session grade + 0.35 × final exam grade.

Resit assessment: students may resit the two examinations (60% of the final grade). To be eligible for the resit assessment, students must have participated in at least three of the four assessed activities during the course.

The grade "Not assessed" ("No avaluable") will be awarded to students who have participated in two or fewer assessed activities, provided that none of them is the final exam.

After the final exam, the distinctions with honours ("Matrícula d'Honor") that are deemed clearly justified will be awarded. These distinctions will be final. If the maximum number of honours distinctions permitted has not been reached, the possibility of awarding additional distinctions will be reconsidered after the resit examination, which students may take in order to improve their final course grade.

For the assessment of this course, the use of "Artificial Intelligence" (AI) technologies is permitted exclusively for the preparation of the oral presentation as a support tool for tasks such as literature or information searches, text editing, or translation. Students must clearly identify any content generated using these technologies, specify the AI tools used, and include a critical reflection on how these tools have influenced both the process and the final outcome of the activity. Failure to disclose the use of AI in this assessed activity will be considered a breach of academic integrity and may result in a partial or full reduction of the activity grade, or more severe disciplinary sanctions in serious cases. The use of any external assistance, whether AI-based or otherwise, is not permitted during in-person assessment activities.

Unified evaluation

The assessment of students in the "unified evaluation" modality will take place on the same day as the final exam of the regular modality. There will be an exam on the whole content of the course, followed by a practical assessment and an interview on the subjects presented by peers. The resit assessment will follow the same rules as in the regular modality.