The methodology and training activities are adapted to the learning objectives of the subject: to introduce mathematical language, to learn how to use it correctly, to observe demonstrations and methods of proof. To achieve these objectives, it is important that first-year students not only see and understand the development of the theory, but also—and perhaps more importantly—attempt the exercises themselves, writing them out correctly, imitating what they have seen in the theory classes.

In the problem-solving classes, some of the problems from the lists (which students will have previously worked on independently) will be discussed and solved on the board.

During seminar sessions, the professor will provide material with exercises to practice writing proofs. Students may ask the professor for help as many times as needed (if they do not understand a question, if they are stuck, if they want feedback on their solution, etc.). Finally, the professor will explain the resolution of some key points. In some seminars, exercises will be handed in at the end and graded. See the \"Assessment\" section.

It should be kept in mind that proper understanding of the course material requires dedication, continuous and sustained work from the student. As a guideline, students should devote as many hours of personal study per week as there are class hours for the subject. In case of doubts, it is important to consult with the professors, whether they are teaching theory or problem-solving classes.

Continuous Assessment:

1. Seminar Exercise Submissions: There will be 3 submissions, scheduled in advance. Students must submit part of the work done in class. The first two submissions will not count toward the final grade, but a professor will review and return them with feedback. Some students may be called for a personal interview with the professor to review their submissions. Attending this interview, if summoned, is mandatory. The third submission will be longer and will count toward the final grade. The seminar component accounts for 20% of the final grade.
2. Midterm Exam: 40% of the final grade.
3. Final Exam: 40% of the final grade.
4. Remedial Exam: Students who do not pass the course based on the weighted sum of the grades from points 1), 2), and 3) may take a comprehensive remedial exam. Students who achieve a final average of 5 or higher from 80% of the final exam score and 20% from the seminar grade will receive a final grade of 5 and the status PASSED. If they do not pass this exam, their final grade will be the higher of either the pre-recovery or post-recovery grades. Grade improvement is not allowed.
5. "Not presented No evaluated" A student who does not attend the final exam will receive a final grade of "Not evaluated"

Single Assessment:

Students who opt for single assessment must still submit the seminar exercises as usual (20% of the final grade), and will take a single exam on the day of the final exam, which will count for 80%. The recovery process is the same as above.

AI usage:

In this course, the use of Artificial Intelligence (AI) technologies is not allowed at any stage. Any work that includes AI-generated content will be considered a breach of academic integrity and may result in a partial or total penalty on the grade for the activity, or more serious sanctions in severe cases.