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Lectures and exercises

Written and oral exam

The contents of a basic algebra course.

The set theory: the Zermelo-Fraenkel axiomatic system.

Introductions of numerical sets (natural, integer, rational and real numbers)

The arithmetics of natural numbers (including divisibility and prime numbers).

The study of numbering systems, Algebraic and transcendent numbers on the rational field.



After mentioning the set theory in its historical evolution and the Zermelo-Fraenkel axiomatic system, different possibilities of introductions of numerical sets (natural, integer, rational, real) are examined and compared. The course also deals with some aspects of arithmetics of natural numbers (including divisibility and prime numbers), the study of numbering systems, polynomials with coefficients in a field and their properties, algebraic and transcendent extensions of the rational field and some elements of elementary number theory.

Some subjects are also examined from a didactical point of view.

Notes of the course