The methodology and training activities are adapted to the training objectives: introducing the mathematical language, learning to use it correctly, seeing proofs (and finding them, and writing them correctly!) and proof methods. To achieve these objectives, it is important that the student understands the theory but also, and even more, it is important that he/she tries to do the exercises.

In the problem classes, the exercises from the lists that the student will have previously worked on on his own will be discussed and solved on the board.

In the seminar sessions, the teacher will provide materials with exercises to practice discovering and writing proofs. Students must ask as many questions as necessary and finally the teacher will explain the resolution of the most representative exercises.

It must be clear that the correct assimilation of the syllabus of this subject requires dedication and continuous and sustained work on the part of the student. It is highly recommended to consult the bibliography as part of this independent work.

Note: 15 minutes of a class will be reserved, within the calendar established by the center/degree, for students to complete the surveys to evaluate the performance of the teaching staff and to evaluate the subject/module.

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.

The course assessment is continuous. The grade is obtained with the following activities:

1) Submission of solved exercises. The weight of these submissions in the final grade is 15%.

2) Activities assessable in seminars. The weight of these activities in the final grade is 25%.

3) Partial exam. 20% of the grade.

4) Final exam of the subject. 40% of the grade.

In order to pass the subject without a retake exam, the final exam grade must be at least 3.5 out of 10.

Those students who have not passed the subject (and only these) may take a retake exam, the grade of which will replace that of sections 3) and 4). This exam requires a minimum grade of 3.5 points out of 10. Activities 1) and 2) are not retaken.

If the final exam or the retake exam does not exceed 3.5 points, the course grade will not exceed 4.5, that is, it will be calculated as the minimum between the weighted average of the grades of the assessment activities and 4.5.

The "non-assessable" grade will be awarded to those who have only participated in assessable activities with a total weight of less than 50%.

Single assessment:

Students who have opted for the single assessment will have a written exam on the entire course content on the same day that the final exam of the subject is taken (60% of the final grade). This exam requires a minimum grade of 3.5 points out of 10. On the same day there will be an oral presentation of some exercises from the course lists, previously set by the teaching staff (15%). Written solutions to the three seminars of the course must be submitted and there will be an oral presentation of one of them (25%). If the course is not passed, either by not achieving the minimum grade in the exam or by not reaching 5 points in weighted average, a retake exam (60%) may be taken. The other activities are not retaken. The final grade is the weighted average of the grades obtained with a maximum of 4.5 if 3.5 points have not been exceeded in the written exam or its retake.

Note: In this subject, the use of Artificial Intelligence (AI) technologies is not allowed in any of its phases