Activities and Methodology

This course includes two weekly hours of lectures, one weekly hour of problem-solving sessions, and three seminar sessions. However, as in all Mathematics courses, achieving a solid understanding primarily depends on the student’s personal work and effort, and the course methodology has been designed with this in mind.

In the lectures, the professor will present and develop the course content. These lectures set the pace for the entire course; the rest of the activities are organized around them.
Understanding the notions introduced in the lectures, the statements of the theorems, and their applications is essential in order to tackle the problems. However, it is also crucial to understand the proofs of the theorems and propositions in order to deepen comprehension of the concepts and to solve problems using similar techniques.

During the lectures or in office hours, students are encouraged to ask any questions they may have.
Special attention will be paid to the use of language and terminology to guide students in using proper mathematical language and to highlight the precision required in formal writing.
Students are encouraged to consult the recommended bibliography to supplement the classroom explanations and to explore alternative approaches. Specific comments and suggestions will be made throughout the course.

There will be a one-hour weekly problem-solving session in which the problems from the lists distributed periodically will be explained.
These problems are based on the lecture content and are intended to help students develop and apply the results and ideas from the lectures—sometimes in an abstract setting, and sometimes through concrete examples.
It is extremely important that students engage thoroughly with the problems beforehand, preparing the exercises prior to class so that they can compare their approaches with those of classmates and the instructor.

The seminars both complete and complement the lecture and problem-solving sessions.
Each seminar session will propose a list of exercises focused on exploring a particular technique or idea from the course in depth, or on allowing students to experiment with a concept that has been or is about to be introduced in the lectures.
Each seminar list will specify the key objectives that students are expected to achieve by working through the problems.
During seminars, students will work in groups on the problem list, asking the professor for help as needed and discussing possible strategies for approaching the problems.
At the end, the professor will explain the solutions to the most representative problems from the list.

Student participation is essential in all course activities, but in the seminars it is especially important, as the sessions are structured around student contributions.
Since solving the exercises requires familiarity with some theoretical content, students are expected to study the relevant material in advance to make the most of the seminar sessions.

In addition to all this, students have access to office hours with the professors in charge of the lectures, problem classes, and seminars, where they can ask questions and seek help with their work.
The course also has a page on the Virtual Campus, where problem and seminar lists, additional materials, and all relevant course information will be posted.

Note: 15 minutes of one class session, within the schedule established by the department/program, will be reserved for students to complete surveys evaluating the teaching performance and the course/module itself.

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.