Geometry 3

lmat1342  2020-2021  Louvain-la-Neuve

Geometry 3
The version you’re consulting is not final. This course description may change. The final version will be published on 1st June.
5 credits
30.0 h + 30.0 h

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.
In 2019-2020, the course will address the basic notions of differential topology:
- submanifolds of euclidean space
- abstract varieties
- vector fields and differential equations
- differential forms and degree theory
- Poincaré-Hopf theorem
One of the goal of the class is to show how a fundamental topological invariant of manifolds, the so-called Euler-Poincaré characteristic reveals itself by studying numerical functions and vector fields. This invariant is at the basis of the classification of compact connected manifolds of dimensions 2.
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.
Evaluation methods
Evaluation 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 course LMAT1342 contains the syllabus of the course in French, the statements of the exercices to be performed during the problem sessions and a detailed plan for the course.
V.I. Arnold, Equations différentielles ordinaires, Editions Mir.Moscou, 1974.
M. Berger et R. Gostiaux, Géométrie différentielle: variétés, courbes et surfaces, P.U.F., Paris 1992.
J. W. Milnor, Topology from the differentiable viewpoint, The University Press of Virginia Charlottesville, Fourth printing 1976.
Faculty or entity

Programmes / formations proposant cette unité d'enseignement (UE)

Title of the programme
Bachelor in Mathematics

Additionnal module in Mathematics

Minor in Mathematics