Note from June 29, 2020
Although we do not yet know how long the social distancing related to the Covid-19 pandemic will last, and regardless of the changes that had to be made in the evaluation of the June 2020 session in relation to what is provided for in this learning unit description, new learnig unit evaluation methods may still be adopted by the teachers; details of these methods have been - or will be - communicated to the students by the teachers, as soon as possible.
Although we do not yet know how long the social distancing related to the Covid-19 pandemic will last, and regardless of the changes that had to be made in the evaluation of the June 2020 session in relation to what is provided for in this learning unit description, new learnig unit evaluation methods may still be adopted by the teachers; details of these methods have been - or will be - communicated to the students by the teachers, as soon as possible.
5 credits
30.0 h + 30.0 h
Q1
Teacher(s)
Haine Luc;
Language
French
Prerequisites
The prerequisite(s) for this Teaching Unit (Unité d’enseignement – UE) for the programmes/courses that offer this Teaching Unit are specified at the end of this sheet.
Content
In 2019-2020, the course will address the basic notions of differential geometry:
- submanifolds of euclidean space, abstract varieties.
- vector fields.
- differential forms, Stokes-Cartan formula.
- Cartan's method of moving frame, Poincaré-Hopf theorem, Morse theorem.
One of the aim of the class is to show that a topological invariant of manifolds, the Euler-Poincaré characteristic, manifests itself via the study of the singular points of vector fileds. Elements of Riemannian geometry are also presented via the theory of moving frames, originating from mechanics, as an illustration of the use of differential forms.
- submanifolds of euclidean space, abstract varieties.
- vector fields.
- differential forms, Stokes-Cartan formula.
- Cartan's method of moving frame, Poincaré-Hopf theorem, Morse theorem.
One of the aim of the class is to show that a topological invariant of manifolds, the Euler-Poincaré characteristic, manifests itself via the study of the singular points of vector fileds. Elements of Riemannian geometry are also presented via the theory of moving frames, originating from mechanics, as an illustration of the use of differential forms.
Teaching methods
Learning activities consist of lectures which aim to introduce fundamental concepts, to explain them by showing examples and by determining their results, to show their reciprocal connections and their connections with other courses in the programme for the Bachelor in Mathematics.
For each problem sesssion, some students are assigned exercises that they must prepare beforehand and present on the blackboard. These presentations count for the final note of the examinantion.
For each problem sesssion, some students are assigned exercises that they must prepare beforehand and present on the blackboard. These presentations count for the final note of the examinantion.
Evaluation methods
Assessment is made with a written final exam with theory and exercices on an equal foot. The work done during the problem sessions counts for 5 points over 20 in the final grade.
Online resources
The Moodle site of the course contains the syllabus in French. The syllabus includes the statements of the exercices to be performed during the problem sessions and references.
Bibliography
Teaching materials
- matériel sur moodle
Faculty or entity
MATH
