Courses

Introduction to Set Theory. Sets, naive definition, description. Subset relation, power set of a set. Algebra of sets. Infinite unions and intersections, examples (with examples of subsets of the real line). Cartesian product. Binomial relations. Functions, composition of functions, one-to-one functions, exponents, invertible functions. Direct and inverse image of a subset by a function, direct and inverse images of unions and intersections. Equivalence relations, equivalence classes, set-quotient, partitions. Order relations. Countability: countability of NxN, uncountability of the set of real numbers, algebraic and transcendental numbers. Introduction to number theory. The set of natural numbers, induction, strong induction and the principle of well-ordering. Euclidean division, greatest common divisor, least common multiple, prime numbers, fundamental theorem of arithmetic. Equivalence relation modulo n, equivalence classes and their algebra. Introduction to the Field of Complex Numbers. Complex plane, algebra and measure of complex numbers, inequality relations for measure. Trigonometric form of complex numbers. Roots of unity. Polynomials. Division, factorization and roots of polynomials. In order to highlight the special elements of pedagogical and teaching competence contained in the course, emphasis is placed on its historical development, the development of its cognitive object, but also on its applications in technology and/or other sciences.