Master en Enseignement secondaire – Mathématiques

Programme The MSE-M activities account for 120 ECTS, grouped as follows:– Pillar I: Mathematics-Specific Professional Competence (60 ECTS)– Pillar II: Didactic Competence (20 ECTS)– Pillar III: General Professional Competence (20 ECTS).– Internships in schools (six weeks in total), and a Master thesis (20 ECTS).New students are requested to take the Refresher Courses scheduled before the start of the first semester. Admissions Academic Contents Semester 1 Semester 1 Semester 2 Semester 3 Semester 4 Course offer for Mathématiques, Semestre 1 (2026-2027 Winter) Commutative Algebra ECTS credits: 8 Course code: F1_MA_MAT_GM-1 Course title: Commutative Algebra Number of ECTS: 8 Course code: F1_MA_MAT_GM-1 Module(s): Specialisation – Mathematics 1 Language: EN Mandatory: Yes Learn the concepts of commutative algebra in relation to applications in algebraic number theory, algebraic geometry and other fields of mathematics. The successful students possesses deepened and extended knowledge of the topics treated in Commutative Algebra. In number theory one is naturally led to study more general numbers than just the classical integers and, thus, to introduce the concept of integral elements in number fields. The rings of integers in number fields have certain very beautiful properties (such as the unique factorisation of ideals) which characterise them as Dedekind rings. Parallelly, in geometry one studies affine varieties through their coordinate rings. It turns out that the coordinate ring of a curve is a Dedekind ring if and only if the curve is non-singular (e.g. has no self-intersection).With this in mind, we shall work towards the concept and the characterisation of Dedekind rings. Along the way, we shall introduce and demonstrate through examples basic concepts of algebraic geometry and algebraic number theory. Moreover, we shall be naturally led to treat many concepts from commutative algebra.Depending on the previous knowledge of the audience, the lecture will cover