34733 - Elementary Algebra from an Advanced Standpoint

Learning outcomes

At the end of the module, the student has an advanced knowledge of topics such as numerical sets, polynomials and polynomial equations, algebraic structures, and is able to use various aids to support teaching.

Course contents

Natural, integer, rational, real, complex numbers. Algebraic structures in secondary education: monoids, groups, rings, fields. Study of algebraic structures relevant in the field of geometry. Polynomials and algebraic equations.

Readings/Bibliography

Notes, sheets of exercises distributed during lessons and availabro on Virtuale. Some textbooks for the secondary school will be examinated.

Teaching methods

Lectures, exercise sessions, seminars. Sheets of exercises will be handed out during the lecture.

Assessment methods

Since this is the second module of a course integrated with Elements of Geometry from a higher standpoint, each student must pass the two tests, both written and oral, either in the same session or in different sessions, even in different sessions. The final grade will be the arithmetic mean of the two grades rounded up. Once one of the two modules has been passed, its grade remains valid for the next three exam sessions (summer, autumn, and winter). For example, if the Algebra Elements exam is passed in June or July, the Geometry Elements part must also be passed by the June and July session of the following year.

Regarding the present module:

- the written exam: it will consist of solving some exercises and problems related to the topics covered in the lessons and activities involving the commentary of secondary school textbooks. Its aim is to test the student's ability to apply the course content and to critically connect the concepts seen during the course with their representation in the texts. A calculator is allowed, but notes, books, etc., are not. You are admitted to the oral exam if the grade in the written exam is at least 15/30.

- the oral exam: this exam will consist of a discussion on the course topics and the presentation of an in-depth study chosen from a list of topics proposed by the instructor. Its goal is to verify the knowledge and understanding of the topics and the ability to connect and analyze them from a higher perspective. The oral exam is also considered passed if a grade of at least 15/30 is achieved.

The final grade takes into account both exams (written and oral) in more or less equal parts. It is possible to take the written and oral exams in different calls, but within the same session. The written exam lasts 2 hours, and registration on Almaesami is required.

Teaching tools

The materials provided by the teacher will be published on Virtuale.

Office hours

See the website of Alessia Cattabriga